Leo-III---1.8.0.UNS-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWV621-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 09:00:03 AM UTC 2026

% Result   : Unsatisfiable 26.33s 7.26s
% Output   : Refutation 28.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  895
% Syntax   : Number of formulae    : 1791 ( 287 unt;   0 typ;   0 def)
%            Number of atoms       : 6031 ( 832 equ;   0 cnn)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives : 35966 (3816   ~;4240   |;   0   &;27910   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   88 (  86 usr;   7 con; 0-6 aty)
%            Number of variables   : 4702 (   0   ^;4702   !;   0   ?;4702   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_Finite__Set_Osetsum_decl,type,
    c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).

thf(c_Power_Opower__class_Opower_decl,type,
    c_Power_Opower__class_Opower: $i > $i > $i ).

thf(hAPP_decl,type,
    hAPP: $i > $i > $i ).

thf(c_HOL_Oinverse__class_Odivide_decl,type,
    c_HOL_Oinverse__class_Odivide: $i > $i > $i > $i ).

thf(c_HOL_Oone__class_Oone_decl,type,
    c_HOL_Oone__class_Oone: $i > $i ).

thf(tc_Complex_Ocomplex_decl,type,
    tc_Complex_Ocomplex: $i ).

thf(c_FFT__Mirabelle_Oroot_decl,type,
    c_FFT__Mirabelle_Oroot: $i > $i ).

thf(v_n_decl,type,
    v_n: $i ).

thf(v_k_decl,type,
    v_k: $i ).

thf(c_SetInterval_Oord__class_OatLeastLessThan_decl,type,
    c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).

thf(c_HOL_Ozero__class_Ozero_decl,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

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

thf(c_HOL_Ominus__class_Ominus_decl,type,
    c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).

thf(class_OrderedGroup_Oordered__ab__group__add_decl,type,
    class_OrderedGroup_Oordered__ab__group__add: $i > $o ).

thf(tc_Int_Oint_decl,type,
    tc_Int_Oint: $i ).

thf(class_Ring__and__Field_Ocomm__ring__1_decl,type,
    class_Ring__and__Field_Ocomm__ring__1: $i > $o ).

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

thf(class_Int_Onumber_decl,type,
    class_Int_Onumber: $i > $o ).

thf(class_Orderings_Olinorder_decl,type,
    class_Orderings_Olinorder: $i > $o ).

thf(class_Ring__and__Field_Opordered__ring_decl,type,
    class_Ring__and__Field_Opordered__ring: $i > $o ).

thf(class_Ring__and__Field_Oordered__semiring__strict_decl,type,
    class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).

thf(class_Orderings_Opreorder_decl,type,
    class_Orderings_Opreorder: $i > $o ).

thf(class_Lattices_Oboolean__algebra_decl,type,
    class_Lattices_Oboolean__algebra: $i > $o ).

thf(c_HOL_Ouminus__class_Ouminus_decl,type,
    c_HOL_Ouminus__class_Ouminus: $i > $i > $i ).

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

thf(class_Ring__and__Field_Oordered__semiring_decl,type,
    class_Ring__and__Field_Oordered__semiring: $i > $o ).

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

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

thf(class_Int_Onumber__ring_decl,type,
    class_Int_Onumber__ring: $i > $o ).

thf(class_Ring__and__Field_Oring__no__zero__divisors_decl,type,
    class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).

thf(class_Ring__and__Field_Ono__zero__divisors_decl,type,
    class_Ring__and__Field_Ono__zero__divisors: $i > $o ).

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

thf(class_Ring__and__Field_Omult__mono_decl,type,
    class_Ring__and__Field_Omult__mono: $i > $o ).

thf(class_OrderedGroup_Ogroup__add_decl,type,
    class_OrderedGroup_Ogroup__add: $i > $o ).

thf(class_Ring__and__Field_Ozero__neq__one_decl,type,
    class_Ring__and__Field_Ozero__neq__one: $i > $o ).

thf(class_Ring__and__Field_Omult__zero_decl,type,
    class_Ring__and__Field_Omult__zero: $i > $o ).

thf(class_OrderedGroup_Oab__group__add_decl,type,
    class_OrderedGroup_Oab__group__add: $i > $o ).

thf(class_Power_Opower_decl,type,
    class_Power_Opower: $i > $o ).

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

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

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

thf(class_Ring__and__Field_Osemiring__0_decl,type,
    class_Ring__and__Field_Osemiring__0: $i > $o ).

thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

thf(class_Ring__and__Field_Oidom_decl,type,
    class_Ring__and__Field_Oidom: $i > $o ).

thf(class_HOL_Oord_decl,type,
    class_HOL_Oord: $i > $o ).

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

thf(class_Ring__and__Field_Odvd_decl,type,
    class_Ring__and__Field_Odvd: $i > $o ).

thf(class_OrderedGroup_Olordered__ab__group__add_decl,type,
    class_OrderedGroup_Olordered__ab__group__add: $i > $o ).

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

thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $o ).

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

thf(c_Ring__and__Field_Odvd__class_Odvd_decl,type,
    c_Ring__and__Field_Odvd__class_Odvd: $i > $i > $i > $o ).

thf(c_HOL_Otimes__class_Otimes_decl,type,
    c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).

thf(hBOOL_decl,type,
    hBOOL: $i > $o ).

thf(c_HOL_Oord__class_Oless_decl,type,
    c_HOL_Oord__class_Oless: $i > $i > $i ).

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

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

thf(c_HOL_Oinverse__class_Oinverse_decl,type,
    c_HOL_Oinverse__class_Oinverse: $i > $i > $i ).

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

thf(tc_fun_decl,type,
    tc_fun: $i > $i > $i ).

thf(c_lessequals_decl,type,
    c_lessequals: $i > $i > $i ).

thf(class_Ring__and__Field_Oring__1__no__zero__divisors_decl,type,
    class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).

thf(class_Ring__and__Field_Oring__1_decl,type,
    class_Ring__and__Field_Oring__1: $i > $o ).

thf(class_RealVector_Oreal__normed__algebra_decl,type,
    class_RealVector_Oreal__normed__algebra: $i > $o ).

thf(c_Int_Onumber__class_Onumber__of_decl,type,
    c_Int_Onumber__class_Onumber__of: $i > $i > $i ).

thf(class_Orderings_Obot_decl,type,
    class_Orderings_Obot: $i > $o ).

thf(tc_bool_decl,type,
    tc_bool: $i ).

thf(class_Ring__and__Field_Oordered__comm__semiring__strict_decl,type,
    class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).

thf(class_Ring__and__Field_Omult__mono1_decl,type,
    class_Ring__and__Field_Omult__mono1: $i > $o ).

thf(c_Finite__Set_Ofinite_decl,type,
    c_Finite__Set_Ofinite: $i > $i > $o ).

thf(c_Orderings_Obot__class_Obot_decl,type,
    c_Orderings_Obot__class_Obot: $i > $i ).

thf(class_Ring__and__Field_Odivision__ring_decl,type,
    class_Ring__and__Field_Odivision__ring: $i > $o ).

thf(class_OrderedGroup_Oab__semigroup__idem__mult_decl,type,
    class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).

thf(class_Int_Oring__char__0_decl,type,
    class_Int_Oring__char__0: $i > $o ).

thf(class_SEQ_Obanach_decl,type,
    class_SEQ_Obanach: $i > $o ).

thf(class_RealVector_Oreal__normed__field_decl,type,
    class_RealVector_Oreal__normed__field: $i > $o ).

thf(c_Transcendental_Oexp_decl,type,
    c_Transcendental_Oexp: $i > $i > $i ).

thf(class_Finite__Set_Ofinite_Ofinite_decl,type,
    class_Finite__Set_Ofinite_Ofinite: $i > $o ).

thf(c_SetInterval_Oord__class_OlessThan_decl,type,
    c_SetInterval_Oord__class_OlessThan: $i > $i > $i ).

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

thf(class_RealVector_Oreal__normed__vector_decl,type,
    class_RealVector_Oreal__normed__vector: $i > $o ).

thf(c_Series_Osko__Series__Xseries__zero__1__1_decl,type,
    c_Series_Osko__Series__Xseries__zero__1__1: $i > $i > $i > $i ).

thf(c_Series_Osums_decl,type,
    c_Series_Osums: $i > $i > $i > $o ).

thf(c_COMBK_decl,type,
    c_COMBK: $i > $i > $i > $i ).

thf(c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1_decl,type,
    c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1: $i > $i > $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1_decl,type,
    c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1: $i > $i > $i > $i > $i ).

thf(208,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_2) ).

thf(1322,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(879,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).

thf(2822,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).

thf(556,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).

thf(2094,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(843,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

thf(2744,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).

thf(134,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).

thf(1168,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(546,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).

thf(2072,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(512,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_1) ).

thf(1995,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(753,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_9) ).

thf(2544,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(459,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).

thf(1879,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(214,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).

thf(1337,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(663,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).

thf(2336,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(563,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(2109,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(266,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).

thf(1454,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(528,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__divide_0) ).

thf(2031,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(345,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_3) ).

thf(1633,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(859,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Oone__class_Oone @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_2) ).

thf(2778,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Oone__class_Oone @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).

thf(697,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).

thf(2412,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(166,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_8) ).

thf(1237,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(863,axiom,
    tc_Complex_Ocomplex @ class_Int_Onumber,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).

thf(2787,plain,
    tc_Complex_Ocomplex @ class_Int_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(776,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_6) ).

thf(2595,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(733,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).

thf(2499,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(703,axiom,
    tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

thf(2427,plain,
    tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(725,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_0) ).

thf(2480,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(139,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).

thf(1179,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(661,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( A @ c_Suc )
        = B )
      | ( B @ ( tc_nat @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

thf(2331,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( A @ c_Suc )
        = B )
      | ( B @ ( tc_nat @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(429,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(1818,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(194,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).

thf(1295,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(494,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).

thf(1956,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(307,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less__neg_0) ).

thf(1549,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(636,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).

thf(2280,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(309,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).

thf(1554,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(370,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).

thf(1686,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(623,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).

thf(2250,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(676,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( E
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).

thf(2363,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( E
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(155,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(1211,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(650,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_5) ).

thf(2309,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(561,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).

thf(2104,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(684,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( tc_nat @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).

thf(2381,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( tc_nat @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(424,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
      = ( tc_bool @ ( tc_nat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan0_0) ).

thf(1808,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
      = ( tc_bool @ ( tc_nat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(338,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).

thf(1618,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(622,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).

thf(2248,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(388,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).

thf(1728,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(152,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).

thf(1205,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(559,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(2099,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(199,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

thf(1305,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(398,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).

thf(1750,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(55,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).

thf(977,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(295,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_2) ).

thf(1522,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(798,axiom,
    v_k @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_k_I1_J_0) ).

thf(2644,plain,
    v_k @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(811,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_0) ).

thf(2671,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(521,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_1) ).

thf(2014,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(566,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).

thf(2114,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(123,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).

thf(1142,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(501,axiom,
    tc_Complex_Ocomplex @ class_Int_Oring__char__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).

thf(1971,plain,
    tc_Complex_Ocomplex @ class_Int_Oring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(892,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).

thf(2854,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).

thf(334,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_6) ).

thf(1608,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(781,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self_0) ).

thf(2607,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(712,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).

thf(2448,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(185,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).

thf(1275,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(789,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_9) ).

thf(2627,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(716,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).

thf(2459,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(770,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(2580,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).

thf(945,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(533,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).

thf(2042,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(768,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_3) ).

thf(2575,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(601,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).

thf(2195,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(378,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ( ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
       != ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).

thf(1705,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ( ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
       != ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(98,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oinverse__class_Oinverse ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).

thf(1078,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oinverse__class_Oinverse ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(415,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_6) ).

thf(1788,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(255,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).

thf(1426,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(454,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_3) ).

thf(1867,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(597,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_division__ring__inverse__diff_0) ).

thf(2184,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(132,axiom,
    tc_bool @ class_HOL_Oord,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(1164,plain,
    tc_bool @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(654,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less_0) ).

thf(2316,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(456,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).

thf(1872,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(829,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_0) ).

thf(2712,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(217,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).

thf(1342,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(14,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__semidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).

thf(913,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(104,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( B
        = ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).

thf(1095,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( B
        = ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(396,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

thf(1746,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(609,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power_1) ).

thf(2216,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(706,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).

thf(2432,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(319,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).

thf(1576,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(261,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( D
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).

thf(1441,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( D
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(85,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).

thf(1046,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(336,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le_0) ).

thf(1613,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(518,axiom,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

thf(2010,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(331,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).

thf(1601,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(592,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_1) ).

thf(2173,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(755,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).

thf(2548,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(412,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).

thf(1782,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(730,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_2) ).

thf(2491,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(169,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).

thf(1243,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(386,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).

thf(1724,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(274,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).

thf(1475,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(544,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).

thf(2067,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(298,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ( ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_geometric__sum_0) ).

thf(1529,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ( ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(499,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).

thf(1967,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(878,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).

thf(2819,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(422,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(1803,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(575,axiom,
    ! [A: $i] : ( A @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).

thf(2136,plain,
    ! [A: $i] : ( A @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(471,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).

thf(1904,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( C @ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__over_0) ).

thf(1265,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( C @ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(377,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_4) ).

thf(1703,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(163,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_4) ).

thf(1228,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(277,axiom,
    tc_nat @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(1482,plain,
    tc_nat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(175,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).

thf(1254,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(248,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).

thf(1409,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(190,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).

thf(1287,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(417,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).

thf(1792,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(848,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono1_0) ).

thf(2755,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(827,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).

thf(2708,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).

thf(203,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).

thf(1313,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(762,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).

thf(2562,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(118,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(1132,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(672,axiom,
    tc_nat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(2356,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(825,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).

thf(2703,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).

thf(876,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ c_Finite__Set_Osetsum ) ) ) )
        = ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( F @ c_Finite__Set_Osetsum ) ) ) ) )
      | ( ( B @ ( A @ ( F @ ( C @ ( E @ ( D @ c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 ) ) ) ) ) @ ( C @ hAPP ) )
       != ( B @ ( A @ ( F @ ( C @ ( E @ ( D @ c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 ) ) ) ) ) @ ( F @ hAPP ) ) )
      | ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__ivl__cong_2) ).

thf(2814,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ c_Finite__Set_Osetsum ) ) ) )
        = ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( F @ c_Finite__Set_Osetsum ) ) ) ) )
      | ( ( B @ ( A @ ( F @ ( C @ ( E @ ( D @ c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 ) ) ) ) ) @ ( C @ hAPP ) )
       != ( B @ ( A @ ( F @ ( C @ ( E @ ( D @ c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 ) ) ) ) ) @ ( F @ hAPP ) ) )
      | ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(508,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).

thf(1985,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(402,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__decreasing_0) ).

thf(1760,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(358,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).

thf(1660,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(472,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_3) ).

thf(1907,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(734,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).

thf(2501,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(710,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__mult_0) ).

thf(2444,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(451,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).

thf(1860,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(179,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__square_0) ).

thf(1264,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(290,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).

thf(1511,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(18,axiom,
    tc_Int_Oint @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).

thf(917,plain,
    tc_Int_Oint @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(33,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring) ).

thf(934,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(144,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

thf(1191,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(421,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_0) ).

thf(1800,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(894,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).

thf(2857,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).

thf(590,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).

thf(2169,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(464,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).

thf(1890,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(317,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_7) ).

thf(1572,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(793,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ogroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).

thf(2635,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ogroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(585,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).

thf(2158,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(283,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_6) ).

thf(1494,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(497,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).

thf(1963,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(410,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).

thf(1778,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(891,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_0) ).

thf(2852,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).

thf(1100,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(443,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).

thf(1847,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(305,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).

thf(1545,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(700,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_9) ).

thf(2420,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(820,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).

thf(2691,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(5,axiom,
    tc_Int_Oint @ class_Int_Onumber,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).

thf(902,plain,
    tc_Int_Oint @ class_Int_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(465,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_7) ).

thf(1892,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(234,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_4) ).

thf(1379,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(171,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_7) ).

thf(1247,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(536,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_5) ).

thf(2049,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(757,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_9) ).

thf(2552,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(525,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).

thf(2024,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(350,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).

thf(1641,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(687,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( D @ ( B @ ( C @ c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1 ) ) ) @ ( B @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__0_H_1) ).

thf(2388,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( D @ ( B @ ( C @ c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1 ) ) ) @ ( B @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(747,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).

thf(2533,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(594,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).

thf(2178,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(25,axiom,
    tc_Int_Oint @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).

thf(924,plain,
    tc_Int_Oint @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(866,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Oone__class_Oone @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_2) ).

thf(2794,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Oone__class_Oone @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(658,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_0) ).

thf(2324,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(232,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( B @ c_Series_Osums ) ) )
      | ( ( A @ ( C @ ( B @ c_Series_Osko__Series__Xseries__zero__1__1 ) ) @ ( B @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_series__zero_1) ).

thf(1373,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( B @ c_Series_Osums ) ) )
      | ( ( A @ ( C @ ( B @ c_Series_Osko__Series__Xseries__zero__1__1 ) ) @ ( B @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(474,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).

thf(1911,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(801,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_8) ).

thf(2650,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(120,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).

thf(1136,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(570,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( D @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult_0) ).

thf(2122,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( D @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(505,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).

thf(1978,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(625,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).

thf(2254,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(496,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_1) ).

thf(1960,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(321,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).

thf(1581,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(188,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_2) ).

thf(1283,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(87,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).

thf(1051,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(8,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) ).

thf(905,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(715,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__def_1) ).

thf(2456,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(517,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).

thf(2007,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(784,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).

thf(2616,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(489,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_positive__imp__inverse__positive_0) ).

thf(1946,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(270,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).

thf(1465,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(82,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__trans_0) ).

thf(1040,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(110,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).

thf(1109,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(252,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_2) ).

thf(1418,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(713,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_4) ).

thf(2451,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(617,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( E
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).

thf(2236,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( E
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(127,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Oboolean__algebra )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).

thf(1151,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Oboolean__algebra )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(36,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__ring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) ).

thf(937,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__ring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(366,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__empty_0) ).

thf(1677,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(751,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).

thf(2540,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(529,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( E @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power__le_0) ).

thf(2034,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( E @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(737,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_Complex_Ocomplex @ ( B @ ( tc_Complex_Ocomplex @ ( A @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Power_Opower__class_Opower ) @ c_Finite__Set_Osetsum ) ) ) )
        = ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__summation_0) ).

thf(2508,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_Complex_Ocomplex @ ( B @ ( tc_Complex_Ocomplex @ ( A @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Power_Opower__class_Opower ) @ c_Finite__Set_Osetsum ) ) ) )
        = ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(481,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_1) ).

thf(1928,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(157,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).

thf(1215,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(462,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_6) ).

thf(1886,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(240,axiom,
    ! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__cube_0) ).

thf(1394,plain,
    ! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(258,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

thf(1433,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(246,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).

thf(1405,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(150,axiom,
    tc_bool @ class_Finite__Set_Ofinite_Ofinite,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).

thf(1201,plain,
    tc_bool @ class_Finite__Set_Ofinite_Ofinite,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(108,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Transcendental_Oexp ) )
        = ( A @ ( A @ ( B @ c_Transcendental_Oexp ) @ c_HOL_Oinverse__class_Oinverse ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field )
      | ~ ( A @ class_SEQ_Obanach ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__minus_0) ).

thf(1104,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Transcendental_Oexp ) )
        = ( A @ ( A @ ( B @ c_Transcendental_Oexp ) @ c_HOL_Oinverse__class_Oinverse ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field )
      | ~ ( A @ class_SEQ_Obanach ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(583,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).

thf(2154,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(374,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_3) ).

thf(1696,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(441,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).

thf(1843,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(540,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_0) ).

thf(2058,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(785,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).

thf(2618,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).

thf(883,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__power_0) ).

thf(2833,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(637,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).

thf(2281,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(467,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_9) ).

thf(1896,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(599,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_1) ).

thf(2190,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(263,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( tc_nat @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).

thf(1447,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( tc_nat @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(45,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).

thf(956,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(419,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).

thf(1796,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(96,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).

thf(1072,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(746,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).

thf(2530,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).

thf(1119,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(340,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_4) ).

thf(1622,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(679,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Omult__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).

thf(2371,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(297,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_0) ).

thf(1526,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(576,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).

thf(2137,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(515,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).

thf(2002,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(64,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(998,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(874,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_3) ).

thf(2809,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).

thf(868,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).

thf(2799,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).

thf(639,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

thf(2286,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(452,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

thf(1863,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(332,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_1) ).

thf(1604,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(519,axiom,
    ! [A: $i] : ( A @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).

thf(2011,plain,
    ! [A: $i] : ( A @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(21,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Ozero__neq__one,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).

thf(920,plain,
    tc_Int_Oint @ class_Ring__and__Field_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(260,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__imp__negative_0) ).

thf(1438,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(26,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) ).

thf(925,plain,
    tc_Int_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(200,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_5) ).

thf(1306,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(149,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

thf(1199,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(128,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

thf(1153,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(568,axiom,
    ! [A: $i] :
      ~ ( A @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).

thf(2118,plain,
    ! [A: $i] :
      ~ ( A @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(215,axiom,
    tc_nat @ class_Power_Opower,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).

thf(1338,plain,
    tc_nat @ class_Power_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(535,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).

thf(2047,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(839,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

thf(2737,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).

thf(389,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_2) ).

thf(1730,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(272,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).

thf(1470,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(476,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_4) ).

thf(1915,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(379,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).

thf(1708,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(202,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_0) ).

thf(1311,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(644,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).

thf(2296,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(649,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).

thf(2307,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(552,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).

thf(2083,plain,
    ! [A: $i] :
      ( ( A @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(732,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).

thf(2496,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(786,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_1) ).

thf(2621,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(806,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).

thf(2660,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).

thf(405,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_7) ).

thf(1768,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(541,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

thf(2061,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(857,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).

thf(2773,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(514,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_1) ).

thf(2000,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(347,axiom,
    tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).

thf(1636,plain,
    tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(629,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_4) ).

thf(2264,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(161,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_1) ).

thf(1223,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(704,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).

thf(2428,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(294,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).

thf(1519,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(580,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).

thf(2147,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(361,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_4) ).

thf(1666,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(280,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).

thf(1487,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(745,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__le_0) ).

thf(2528,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(690,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
        = C )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_0) ).

thf(2396,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
        = C )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(709,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).

thf(2441,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(812,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).

thf(2673,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(237,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A
        = ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucE_0) ).

thf(1387,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A
        = ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(469,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).

thf(1900,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(11,axiom,
    tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).

thf(910,plain,
    tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(761,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_1) ).

thf(2560,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(871,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

thf(2805,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(83,axiom,
    tc_bool @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(1042,plain,
    tc_bool @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(752,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).

thf(2541,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(224,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).

thf(1355,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(635,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).

thf(2277,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(316,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).

thf(1570,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(137,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

thf(1174,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(574,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).

thf(2133,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(431,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).

thf(1824,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(231,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).

thf(1370,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(461,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_2) ).

thf(1883,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(312,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).

thf(1560,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(254,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_3) ).

thf(1423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(17,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Ono__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).

thf(916,plain,
    tc_Int_Oint @ class_Ring__and__Field_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(229,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_0) ).

thf(1365,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(478,axiom,
    ! [A: $i] :
      ( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_0) ).

thf(1920,plain,
    ! [A: $i] :
      ( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(724,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).

thf(2477,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(491,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq__number__of_1) ).

thf(1951,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(463,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_0) ).

thf(1888,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(267,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B = C )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).

thf(1457,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B = C )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(341,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = B )
      | ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).

thf(1624,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = B )
      | ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(603,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( D
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).

thf(2200,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( D
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(130,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).

thf(1159,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(437,axiom,
    tc_nat @ class_Ring__and__Field_Omult__mono,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).

thf(1836,plain,
    tc_nat @ class_Ring__and__Field_Omult__mono,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(356,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_2) ).

thf(1656,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(77,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).

thf(1027,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(667,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less__neg_0) ).

thf(2345,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(841,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).

thf(2741,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).

thf(393,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).

thf(1740,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(53,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Odvd ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvdI_0) ).

thf(974,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Odvd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(803,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(2653,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(485,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( tc_nat @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).

thf(1938,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( tc_nat @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(850,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_2) ).

thf(2758,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).

thf(79,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).

thf(1032,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(438,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_negative__imp__inverse__negative_0) ).

thf(1837,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(147,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).

thf(1195,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(607,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Transcendental_Oexp ) )
        = ( A @ ( A @ ( C @ c_Transcendental_Oexp ) @ ( A @ ( B @ c_Transcendental_Oexp ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field )
      | ~ ( A @ class_SEQ_Obanach ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__diff_0) ).

thf(2211,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Transcendental_Oexp ) )
        = ( A @ ( A @ ( C @ c_Transcendental_Oexp ) @ ( A @ ( B @ c_Transcendental_Oexp ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field )
      | ~ ( A @ class_SEQ_Obanach ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(247,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).

thf(1407,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(239,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_4) ).

thf(1392,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(614,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).

thf(2228,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(565,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).

thf(2112,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(192,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).

thf(1291,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(855,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__by__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).

thf(2769,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__by__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).

thf(71,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

thf(1012,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(244,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).

thf(1402,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(507,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less2_0) ).

thf(1983,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(886,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_0) ).

thf(2841,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(674,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_2) ).

thf(2359,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(448,axiom,
    tc_Complex_Ocomplex @ class_Int_Onumber__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).

thf(1856,plain,
    tc_Complex_Ocomplex @ class_Int_Onumber__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(68,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) ).

thf(1006,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(400,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse_0) ).

thf(1755,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(795,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).

thf(2638,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(631,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).

thf(2268,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(60,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).

thf(989,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(242,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less_0) ).

thf(1397,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(221,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_4) ).

thf(1350,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(484,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__diff_0) ).

thf(1936,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(326,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).

thf(1592,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(646,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_0) ).

thf(2300,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(102,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__idem_0) ).

thf(1089,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(165,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).

thf(1234,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(403,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( B @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).

thf(1762,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( B @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(740,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero_0) ).

thf(2515,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(182,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).

thf(1270,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(445,axiom,
    v_n @ ( tc_nat @ ( v_k @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_k_I2_J_0) ).

thf(1851,plain,
    v_n @ ( tc_nat @ ( v_k @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(407,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_2) ).

thf(1772,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(42,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).

thf(948,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(869,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_2) ).

thf(2801,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(300,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).

thf(1534,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(418,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).

thf(1794,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(492,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).

thf(1953,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(817,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).

thf(2685,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).

thf(769,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).

thf(2577,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(93,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).

thf(1064,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(111,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Int_Oring__char__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__number__of_0) ).

thf(1111,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Int_Oring__char__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(500,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

thf(1970,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(56,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).

thf(980,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(285,axiom,
    ! [A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

thf(1498,plain,
    ! [A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(324,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_0) ).

thf(1587,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(835,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).

thf(2726,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(791,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).

thf(2631,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).

thf(1138,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(834,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).

thf(2724,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(384,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_0) ).

thf(1719,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(749,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_nat @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).

thf(2537,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_nat @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(315,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).

thf(1567,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(717,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).

thf(2460,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(211,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).

thf(1329,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(227,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).

thf(1361,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(487,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).

thf(1942,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(32,axiom,
    tc_Int_Oint @ class_HOL_Oord,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__HOL_Oord) ).

thf(933,plain,
    tc_Int_Oint @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(882,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__diff__distrib__number__of_0) ).

thf(2830,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).

thf(783,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).

thf(2613,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(425,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).

thf(1810,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(669,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__power__dvd_0) ).

thf(2349,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(531,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_0) ).

thf(2038,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(809,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_0) ).

thf(2666,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(351,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).

thf(1644,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(51,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

thf(970,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(395,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).

thf(1744,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(4,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Opordered__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) ).

thf(901,plain,
    tc_Int_Oint @ class_Ring__and__Field_Opordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(97,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

thf(1075,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(250,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

thf(1414,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(538,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).

thf(2053,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(153,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).

thf(1207,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(553,axiom,
    ! [A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).

thf(2085,plain,
    ! [A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(409,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).

thf(1776,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(172,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).

thf(1249,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(195,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Complex_Ocomplex @ ( A @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) @ hAPP ) )
      = ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__unity_0) ).

thf(1297,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Complex_Ocomplex @ ( A @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) @ hAPP ) )
      = ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(265,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_nat @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).

thf(1451,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_nat @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).

thf(1231,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(620,axiom,
    ! [A: $i] :
      ( ( A @ c_FFT__Mirabelle_Oroot )
     != ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__nonzero_0) ).

thf(2243,plain,
    ! [A: $i] :
      ( ( A @ c_FFT__Mirabelle_Oroot )
     != ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(719,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).

thf(2465,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(12,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) ).

thf(911,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(764,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).

thf(2566,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(457,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__diff__distrib__number__of_0) ).

thf(1874,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(256,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).

thf(1429,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(577,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).

thf(2140,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(342,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_8) ).

thf(1627,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(209,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).

thf(1324,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(112,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

thf(1114,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(571,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_8) ).

thf(2125,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(58,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).

thf(985,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(303,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Transcendental_Oexp ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field )
      | ~ ( A @ class_SEQ_Obanach ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__zero_0) ).

thf(1539,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Transcendental_Oexp ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field )
      | ~ ( A @ class_SEQ_Obanach ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(235,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).

thf(1382,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(728,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_7) ).

thf(2487,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(888,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( tc_nat @ ( tc_nat @ ( D @ c_Suc @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__op__ivl__Suc_0) ).

thf(2845,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( tc_nat @ ( tc_nat @ ( D @ c_Suc @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(362,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).

thf(1668,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(503,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( B @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc2_0) ).

thf(1974,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( B @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(66,axiom,
    tc_bool @ class_Orderings_Obot,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(1002,plain,
    tc_bool @ class_Orderings_Obot,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(446,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_6) ).

thf(1852,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(854,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( C @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inverse_0) ).

thf(2766,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( C @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).

thf(726,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ( ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
       != ( C @ c_Suc @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__base_0) ).

thf(2482,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ( ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
       != ( C @ c_Suc @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(330,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).

thf(1599,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(823,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).

thf(2697,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).

thf(606,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_3) ).

thf(2208,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(22,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Omult__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).

thf(921,plain,
    tc_Int_Oint @ class_Ring__and__Field_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(88,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult_0) ).

thf(1054,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(135,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).

thf(1170,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(692,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).

thf(2402,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(292,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).

thf(1515,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(799,axiom,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).

thf(2645,plain,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(664,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).

thf(2338,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(27,axiom,
    tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).

thf(926,plain,
    tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(845,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).

thf(2749,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(449,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).

thf(1857,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(864,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_0) ).

thf(2788,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).

thf(206,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).

thf(1318,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(151,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).

thf(1202,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(604,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

thf(2203,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(427,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).

thf(1814,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(101,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

thf(1086,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(37,axiom,
    tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).

thf(938,plain,
    tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(168,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_2) ).

thf(1241,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(754,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_5) ).

thf(2546,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(852,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_1) ).

thf(2761,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(80,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).

thf(1035,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(678,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).

thf(2368,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(695,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).

thf(2408,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(360,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__divide_0) ).

thf(1663,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(44,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).

thf(953,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(807,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_9) ).

thf(2662,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).

thf(9,axiom,
    tc_Int_Oint @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).

thf(906,plain,
    tc_Int_Oint @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(836,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).

thf(2729,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).

thf(48,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

thf(965,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(173,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).

thf(1251,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(772,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( A @ ( B @ ( A @ ( F @ ( C @ ( E @ ( D @ c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 ) ) ) ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ c_Finite__Set_Osetsum ) ) ) )
        = ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( F @ c_Finite__Set_Osetsum ) ) ) ) )
      | ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__ivl__cong_1) ).

thf(2585,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( A @ ( B @ ( A @ ( F @ ( C @ ( E @ ( D @ c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 ) ) ) ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ c_Finite__Set_Osetsum ) ) ) )
        = ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( F @ c_Finite__Set_Osetsum ) ) ) ) )
      | ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(831,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).

thf(2717,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(278,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).

thf(1483,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(184,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).

thf(1273,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(779,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_7) ).

thf(2602,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(344,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).

thf(1631,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(627,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).

thf(2260,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(125,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

thf(1146,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(642,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_3) ).

thf(2292,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(688,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_6) ).

thf(2391,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(367,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).

thf(1680,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(375,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( C @ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_COMBK ) ) @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__0_0) ).

thf(1698,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( C @ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_COMBK ) ) @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(759,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).

thf(2556,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(107,axiom,
    tc_Int_Oint @ class_Int_Oring__char__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).

thf(1103,plain,
    tc_Int_Oint @ class_Int_Oring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(634,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).

thf(2275,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(581,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_8) ).

thf(2149,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(527,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Oone__class_Oone )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).

thf(2028,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Oone__class_Oone )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(197,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).

thf(1301,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(328,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( E @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__dvd_0) ).

thf(1595,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( E @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(838,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(2734,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).

thf(743,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).

thf(2524,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(682,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).

thf(2376,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(7,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Opordered__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring) ).

thf(904,plain,
    tc_Int_Oint @ class_Ring__and__Field_Opordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(435,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

thf(1833,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(69,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).

thf(1007,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(613,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( F @ ( C @ ( E @ ( D @ c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 ) ) ) ) ) @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ c_Finite__Set_Osetsum ) ) ) )
        = ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( F @ c_Finite__Set_Osetsum ) ) ) ) )
      | ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__ivl__cong_0) ).

thf(2225,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( F @ ( C @ ( E @ ( D @ c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 ) ) ) ) ) @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ c_Finite__Set_Osetsum ) ) ) )
        = ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( F @ c_Finite__Set_Osetsum ) ) ) ) )
      | ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(337,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).

thf(1615,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(865,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Power_Opower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc_0) ).

thf(2791,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Power_Opower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).

thf(689,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left__number__of_1) ).

thf(2393,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(354,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Oone__class_Oone @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_1) ).

thf(1652,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Oone__class_Oone @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(872,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).

thf(2806,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(376,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_2) ).

thf(1701,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(877,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_1) ).

thf(2817,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(115,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_0) ).

thf(1124,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(881,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).

thf(2827,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).

thf(339,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( B @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).

thf(1620,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( B @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(729,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono_0) ).

thf(2489,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(522,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).

thf(2016,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(739,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).

thf(2514,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(765,axiom,
    tc_nat @ class_Ring__and__Field_Omult__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

thf(2568,plain,
    tc_nat @ class_Ring__and__Field_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(822,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_4) ).

thf(2695,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).

thf(176,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).

thf(1256,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(287,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_2) ).

thf(1503,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(414,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).

thf(1786,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(35,axiom,
    tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).

thf(936,plain,
    tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(611,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Odivide__inverse_0) ).

thf(2220,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(659,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( E @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).

thf(2326,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( E @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(453,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).

thf(1865,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(212,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).

thf(1332,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(826,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).

thf(2706,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).

thf(404,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).

thf(1765,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(20,axiom,
    tc_Int_Oint @ class_OrderedGroup_Ogroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).

thf(919,plain,
    tc_Int_Oint @ class_OrderedGroup_Ogroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(702,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).

thf(2425,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(177,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__1_0) ).

thf(1258,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(723,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( D @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DERIV__inverse__lemma_0) ).

thf(2474,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( D @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(365,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Oone__class_Oone @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_1) ).

thf(1675,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Oone__class_Oone @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(346,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).

thf(1635,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(390,axiom,
    tc_nat @ class_Int_Onumber,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).

thf(1733,plain,
    tc_nat @ class_Int_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(90,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).

thf(1058,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(109,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).

thf(1107,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(167,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_0) ).

thf(1239,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(513,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).

thf(1997,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(539,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).

thf(2055,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(103,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).

thf(1092,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(146,axiom,
    tc_bool @ class_Lattices_Oboolean__algebra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).

thf(1194,plain,
    tc_bool @ class_Lattices_Oboolean__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(742,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( D @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).

thf(2521,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( D @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(154,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).

thf(1209,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(3,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Ocomm__ring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) ).

thf(900,plain,
    tc_Int_Oint @ class_Ring__and__Field_Ocomm__ring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(701,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).

thf(2422,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(318,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono__neg_0) ).

thf(1574,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(296,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

thf(1524,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(86,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).

thf(1048,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(558,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__inverse__le__neg_0) ).

thf(2097,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(304,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).

thf(1542,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(567,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leI_0) ).

thf(2116,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(84,axiom,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

thf(1043,plain,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(893,axiom,
    tc_nat @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

thf(2856,plain,
    tc_nat @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).

thf(1122,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(233,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( C @ ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus_0) ).

thf(1376,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( C @ ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Ouminus__class_Ouminus ) @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(602,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( C @ ( tc_Complex_Ocomplex @ ( B @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__cancel_0) ).

thf(2197,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_Complex_Ocomplex @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( C @ ( tc_Complex_Ocomplex @ ( B @ c_FFT__Mirabelle_Oroot @ c_Power_Opower__class_Opower ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(543,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ c_Suc @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( D @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).

thf(2065,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ c_Suc @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( D @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(550,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_1) ).

thf(2079,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(675,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_2) ).

thf(2361,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(651,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( E
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).

thf(2311,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( E
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(582,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

thf(2151,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(797,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).

thf(2642,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(608,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).

thf(2214,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(685,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = C )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).

thf(2383,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = C )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(787,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_1) ).

thf(2624,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(698,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).

thf(2415,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(466,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).

thf(1894,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(626,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide__number__of_0) ).

thf(2257,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(483,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

thf(1933,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(621,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).

thf(2246,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(282,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).

thf(1492,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(810,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_2) ).

thf(2669,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(124,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).

thf(1144,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(683,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

thf(2378,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(372,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).

thf(1690,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(595,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).

thf(2180,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(880,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__imp__positive_0) ).

thf(2824,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).

thf(596,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_1) ).

thf(2182,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(458,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).

thf(1877,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(875,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power_0) ).

thf(2812,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).

thf(652,axiom,
    tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_1) ).

thf(2314,plain,
    tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(564,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).

thf(2111,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(511,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).

thf(1993,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(860,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Power_Opower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).

thf(2780,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Power_Opower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(430,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oinverse__class_Oinverse ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).

thf(1821,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oinverse__class_Oinverse ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(696,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing_0) ).

thf(2410,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(16,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oring__no__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) ).

thf(915,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oring__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(218,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).

thf(1344,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(193,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).

thf(1293,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(828,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).

thf(2710,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(371,axiom,
    ( ( tc_nat @ ( v_n @ c_HOL_Oord__class_Oless ) )
    = ( tc_nat @ ( v_n @ c_Suc @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le__raw_0) ).

thf(1688,plain,
    ( ( tc_nat @ ( v_n @ c_HOL_Oord__class_Oless ) )
    = ( tc_nat @ ( v_n @ c_Suc @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(216,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(1339,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(782,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).

thf(2610,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(473,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).

thf(1909,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(131,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).

thf(1162,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(711,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_6) ).

thf(2446,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(849,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ono__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).

thf(2757,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(862,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).

thf(2785,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(775,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_1) ).

thf(2593,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

thf(310,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_7) ).

thf(1556,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(268,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).

thf(1460,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(40,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( E @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).

thf(943,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( E @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).

thf(1022,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(624,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_0) ).

thf(2252,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(808,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).

thf(2664,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(660,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_1) ).

thf(2329,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(31,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).

thf(932,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(91,axiom,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).

thf(1061,plain,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(13,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__idom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).

thf(912,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__idom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(440,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).

thf(1841,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(480,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).

thf(1926,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(591,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_0) ).

thf(2171,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).

thf(1066,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(72,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).

thf(1015,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

thf(1176,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(640,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).

thf(2288,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(792,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).

thf(2633,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).

thf(275,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).

thf(1477,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(387,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).

thf(1726,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(584,axiom,
    ! [A: $i] :
      ( ( A @ c_HOL_Oone__class_Oone @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).

thf(2156,plain,
    ! [A: $i] :
      ( ( A @ c_HOL_Oone__class_Oone @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(423,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).

thf(1805,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(856,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).

thf(2770,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(548,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
        = ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_1) ).

thf(2075,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
        = ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(699,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_8) ).

thf(2418,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(156,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).

thf(1213,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(884,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).

thf(2835,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(537,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

thf(2051,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(756,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_1) ).

thf(2550,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(170,axiom,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).

thf(1245,plain,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(65,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).

thf(1000,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(846,axiom,
    ! [A: $i] :
      ~ ( A @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

thf(2752,plain,
    ! [A: $i] :
      ~ ( A @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(748,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).

thf(2535,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(560,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = B )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_3) ).

thf(2101,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = B )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(284,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_Suc @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

thf(1496,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_Suc @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(647,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_5) ).

thf(2303,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(23,axiom,
    tc_Int_Oint @ class_OrderedGroup_Oab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).

thf(922,plain,
    tc_Int_Oint @ class_OrderedGroup_Oab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(821,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).

thf(2693,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).

thf(736,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).

thf(2506,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(313,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).

thf(1562,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(490,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__shift__lb__Suc0__0__upt_0) ).

thf(1948,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(618,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__dvd_0) ).

thf(2239,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(322,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_3) ).

thf(1583,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(401,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).

thf(1758,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(655,axiom,
    ! [A: $i] :
      ~ ( A @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).

thf(2318,plain,
    ! [A: $i] :
      ~ ( A @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(28,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Osemiring__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).

thf(927,plain,
    tc_Int_Oint @ class_Ring__and__Field_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(186,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Oinverse__divide_0) ).

thf(1277,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(119,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).

thf(1134,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(289,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).

thf(1509,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(510,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ ( B @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).

thf(1990,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ ( B @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(38,axiom,
    tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).

thf(939,plain,
    tc_Int_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(273,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).

thf(1472,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(308,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).

thf(1551,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(359,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).

thf(1662,plain,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(557,axiom,
    tc_nat @ class_Ring__and__Field_Ozero__neq__one,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).

thf(2096,plain,
    tc_nat @ class_Ring__and__Field_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(802,axiom,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).

thf(2652,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(722,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).

thf(2471,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(735,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

thf(2503,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(369,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_0) ).

thf(1684,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(99,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

thf(1081,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(790,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(2629,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(73,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Omult__mono1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono1) ).

thf(1018,plain,
    tc_Int_Oint @ class_Ring__and__Field_Omult__mono1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(763,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_7) ).

thf(2564,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(777,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( C @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).

thf(2597,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( C @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(495,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).

thf(1958,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(50,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).

thf(968,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(140,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

thf(1181,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(442,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).

thf(1845,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(306,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).

thf(1547,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(76,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).

thf(1025,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(129,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).

thf(1156,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(162,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(1225,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(600,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__commutes_0) ).

thf(2192,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(520,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).

thf(2012,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(773,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

thf(2588,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(174,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).

thf(1252,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(593,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Transcendental_Oexp ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field )
      | ~ ( A @ class_SEQ_Obanach ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__not__eq__zero_0) ).

thf(2175,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Transcendental_Oexp ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field )
      | ~ ( A @ class_SEQ_Obanach ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(411,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).

thf(1780,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(105,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).

thf(1098,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(420,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).

thf(1798,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(645,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).

thf(2298,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(67,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).

thf(1003,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(406,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_1) ).

thf(1770,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(814,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).

thf(2678,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(741,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( D @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__divide_0) ).

thf(2518,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( D @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(399,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(1753,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(686,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).

thf(2386,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(890,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_1) ).

thf(2850,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(586,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).

thf(2160,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(62,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(993,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(819,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).

thf(2689,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).

thf(766,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_Suc @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).

thf(2569,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_Suc @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(588,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).

thf(2165,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(348,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__1__mult_0) ).

thf(1637,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(81,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).

thf(1038,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(413,axiom,
    ! [A: $i] : ( A @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).

thf(1785,plain,
    ! [A: $i] : ( A @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(434,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).

thf(1830,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(43,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).

thf(951,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(534,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != B )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).

thf(2044,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != B )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(320,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(1579,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).

thf(907,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(381,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).

thf(1711,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(844,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_4) ).

thf(2747,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).

thf(416,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).

thf(1790,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(509,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oinverse__diff__inverse_0) ).

thf(1987,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(383,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).

thf(1716,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(714,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_1) ).

thf(2454,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(143,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).

thf(1188,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(824,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ c_Suc @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).

thf(2700,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ c_Suc @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(142,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).

thf(1186,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(357,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).

thf(1658,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(657,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1_0) ).

thf(2322,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(189,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_5) ).

thf(1285,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(158,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_6) ).

thf(1218,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(721,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_1) ).

thf(2468,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(159,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).

thf(1220,plain,
    tc_nat @ class_Ring__and__Field_Opordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(160,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__le__div__pos_0) ).

thf(1221,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(397,axiom,
    tc_Complex_Ocomplex @ class_Power_Opower,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).

thf(1749,plain,
    tc_Complex_Ocomplex @ class_Power_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(363,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_0) ).

thf(1670,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(889,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_5) ).

thf(2848,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).

thf(630,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).

thf(2266,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(61,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).

thf(991,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(813,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_1) ).

thf(2675,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(245,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__no__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).

thf(1404,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(226,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).

thf(1358,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(468,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).

thf(1898,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(444,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).

thf(1849,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(885,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).

thf(2838,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).

thf(760,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).

thf(2558,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(301,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).

thf(1536,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(506,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_3) ).

thf(1981,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(223,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).

thf(1353,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(673,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_5) ).

thf(2357,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(493,axiom,
    tc_nat @ class_Ring__and__Field_Omult__mono1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).

thf(1955,plain,
    tc_nat @ class_Ring__and__Field_Omult__mono1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(887,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).

thf(2843,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).

thf(579,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).

thf(2145,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(279,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).

thf(1485,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(502,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).

thf(1972,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(656,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono2_0) ).

thf(2320,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(288,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero_0) ).

thf(1506,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(323,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).

thf(1585,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(122,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

thf(1140,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(738,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__1_0) ).

thf(2511,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(895,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_7) ).

thf(2860,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(833,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_1) ).

thf(2722,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(460,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

thf(1881,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(873,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_0) ).

thf(2807,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(183,axiom,
    tc_Complex_Ocomplex @ class_SEQ_Obanach,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__SEQ_Obanach) ).

thf(1272,plain,
    tc_Complex_Ocomplex @ class_SEQ_Obanach,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(486,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).

thf(1940,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(253,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_9) ).

thf(1421,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(439,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_8) ).

thf(1839,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(554,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(2088,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(498,axiom,
    tc_nat @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(1966,plain,
    tc_nat @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(30,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).

thf(931,plain,
    tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(293,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).

thf(1517,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(116,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).

thf(1126,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(191,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono_0) ).

thf(1289,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(391,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( D @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).

thf(1734,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( D @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(707,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).

thf(2435,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(851,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).

thf(2760,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

thf(788,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).

thf(2626,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(205,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_5) ).

thf(1316,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(353,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).

thf(1649,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(100,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

thf(1084,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(549,axiom,
    ! [A: $i] : ( A @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

thf(2078,plain,
    ! [A: $i] : ( A @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(436,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).

thf(1834,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(475,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).

thf(1913,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(54,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1) ).

thf(976,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(6,axiom,
    tc_Int_Oint @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).

thf(903,plain,
    tc_Int_Oint @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(668,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_Series_Osko__Series__Xseries__zero__1__1 ) ) @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( B @ c_Series_Osums ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_series__zero_0) ).

thf(2347,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_Series_Osko__Series__Xseries__zero__1__1 ) ) @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( B @ c_Series_Osums ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(355,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

thf(1654,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(249,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).

thf(1412,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(842,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

thf(2743,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(598,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
       != ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).

thf(2187,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
       != ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(238,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_0) ).

thf(1390,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(648,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).

thf(2305,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(666,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__inverse_0) ).

thf(2342,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(805,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_1) ).

thf(2658,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(858,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__inverse_0) ).

thf(2775,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(352,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).

thf(1646,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(210,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_0) ).

thf(1326,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(638,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).

thf(2283,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(1,negated_conjecture,
    ( ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( v_n @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_Complex_Ocomplex @ ( v_k @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_n @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Power_Opower__class_Opower ) @ c_Finite__Set_Osetsum ) ) ) )
   != ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ ( v_k @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_n @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ ( v_n @ ( tc_Complex_Ocomplex @ ( v_k @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_n @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(896,plain,
    ( ( tc_Complex_Ocomplex @ ( tc_nat @ ( tc_nat @ ( v_n @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_Complex_Ocomplex @ ( v_k @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_n @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Power_Opower__class_Opower ) @ c_Finite__Set_Osetsum ) ) ) )
   != ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ ( v_k @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_n @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ ( v_n @ ( tc_Complex_Ocomplex @ ( v_k @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_n @ c_FFT__Mirabelle_Oroot @ ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(349,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_5) ).

thf(1639,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(641,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_2) ).

thf(2290,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(694,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_0) ).

thf(2406,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(758,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).

thf(2554,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(92,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).

thf(1062,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(526,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).

thf(2026,plain,
    ! [A: $i] :
      ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(447,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_0) ).

thf(1854,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(853,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).

thf(2764,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

thf(573,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(2130,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(744,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_8) ).

thf(2526,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(774,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).

thf(2591,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(325,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_1) ).

thf(1590,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(46,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(961,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(236,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).

thf(1385,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(385,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).

thf(1721,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(47,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__refl_0) ).

thf(963,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(589,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).

thf(2167,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(633,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).

thf(2273,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(343,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).

thf(1629,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(516,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).

thf(2004,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(63,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).

thf(995,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(311,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( tc_nat @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

thf(1558,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( tc_nat @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(628,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_6) ).

thf(2262,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(78,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

thf(1030,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(551,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).

thf(2081,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(691,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_0) ).

thf(2399,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(800,axiom,
    ! [A: $i] :
      ( ( A @ c_HOL_Oone__class_Oone @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).

thf(2648,plain,
    ! [A: $i] :
      ( ( A @ c_HOL_Oone__class_Oone @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(718,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).

thf(2462,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(201,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).

thf(1308,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(145,axiom,
    tc_bool @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(1193,plain,
    tc_bool @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(587,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_3) ).

thf(2162,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(815,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

thf(2680,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(2,axiom,
    tc_Int_Oint @ class_OrderedGroup_Oordered__ab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) ).

thf(899,plain,
    tc_Int_Oint @ class_OrderedGroup_Oordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(569,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).

thf(2120,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(653,axiom,
    ! [A: $i] : ( A @ c_Suc @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).

thf(2315,plain,
    ! [A: $i] : ( A @ c_Suc @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(523,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_7) ).

thf(2019,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(867,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_3) ).

thf(2796,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).

thf(15,axiom,
    tc_Int_Oint @ class_Int_Onumber__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).

thf(914,plain,
    tc_Int_Oint @ class_Int_Onumber__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(615,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( tc_nat @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( A @ ( tc_nat @ ( tc_nat @ ( E @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff__nat__ivl_0) ).

thf(2230,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( tc_nat @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( A @ ( tc_nat @ ( tc_nat @ ( E @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(643,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).

thf(2294,plain,
    ! [A: $i] :
      ( ( A @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(530,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).

thf(2036,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(840,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).

thf(2739,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).

thf(731,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).

thf(2494,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(262,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_1) ).

thf(1444,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(578,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).

thf(2142,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(610,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_5) ).

thf(2218,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(816,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_1) ).

thf(2683,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(187,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).

thf(1280,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ c_Suc @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(616,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).

thf(2233,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(241,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_0) ).

thf(1395,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(198,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_6) ).

thf(1303,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(276,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_6) ).

thf(1480,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(681,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).

thf(2374,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(220,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).

thf(1348,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(291,axiom,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).

thf(1512,plain,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(408,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_1) ).

thf(1774,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(49,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).

thf(967,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(832,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__lt__two__imp__zero__or__one_0) ).

thf(2719,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).

thf(327,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_4) ).

thf(1593,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(780,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
        = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__unique_0) ).

thf(2604,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
        = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(126,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) )
       != ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__eq__iff_0) ).

thf(1148,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) )
       != ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(364,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).

thf(1673,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(794,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_1) ).

thf(2636,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(19,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Omult__mono,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono) ).

thf(918,plain,
    tc_Int_Oint @ class_Ring__and__Field_Omult__mono,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(428,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).

thf(1816,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(662,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_0) ).

thf(2334,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(136,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
      | ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite_Ofinite ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).

thf(1172,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
      | ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(89,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).

thf(1056,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(677,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_4) ).

thf(2366,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(830,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).

thf(2714,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

thf(612,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__le_0) ).

thf(2223,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(532,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_0) ).

thf(2040,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(861,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_8) ).

thf(2783,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(259,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_9) ).

thf(1436,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(450,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).

thf(1859,plain,
    tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(228,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).

thf(1363,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(204,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).

thf(1314,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(213,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_3) ).

thf(1335,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(373,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).

thf(1693,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(545,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).

thf(2070,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(767,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).

thf(2572,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( C @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(380,axiom,
    ! [A: $i] : ( A @ c_Suc @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).

thf(1710,plain,
    ! [A: $i] : ( A @ c_Suc @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(148,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).

thf(1197,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(555,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left__number__of_0) ).

thf(2091,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ( ( tc_nat @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(693,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).

thf(2404,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(665,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).

thf(2340,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(133,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

thf(1165,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(524,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).

thf(2021,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(219,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono2_0) ).

thf(1346,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(542,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_2) ).

thf(2063,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(335,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__infinite_0) ).

thf(1610,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(394,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).

thf(1742,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(29,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).

thf(928,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(74,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

thf(1019,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(720,axiom,
    ! [A: $i] : ( A @ c_Suc @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).

thf(2467,plain,
    ! [A: $i] : ( A @ c_Suc @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(196,axiom,
    ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).

thf(1299,plain,
    ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(470,axiom,
    ! [A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).

thf(1902,plain,
    ! [A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(680,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less_0) ).

thf(2372,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(482,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).

thf(1930,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(671,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_3) ).

thf(2353,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(619,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).

thf(2241,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(59,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

thf(987,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(572,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).

thf(2127,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(222,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ozero__neq__one,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).

thf(1352,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(837,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).

thf(2731,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).

thf(433,axiom,
    tc_nat @ class_Ring__and__Field_Odvd,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).

thf(1829,plain,
    tc_nat @ class_Ring__and__Field_Odvd,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(504,axiom,
    tc_nat @ class_Orderings_Obot,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

thf(1977,plain,
    tc_nat @ class_Orderings_Obot,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(117,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

thf(1129,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(432,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_5) ).

thf(1827,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(178,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
        = ( tc_bool @ ( tc_nat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThanSuc_1) ).

thf(1261,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
        = ( tc_bool @ ( tc_nat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(705,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).

thf(2430,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(181,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
      = ( tc_nat @ ( A @ c_SetInterval_Oord__class_OlessThan ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast0LessThan_0) ).

thf(1268,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
      = ( tc_nat @ ( A @ c_SetInterval_Oord__class_OlessThan ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(870,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).

thf(2803,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(299,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

thf(1532,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(778,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).

thf(2600,plain,
    ! [A: $i] :
      ~ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

thf(727,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_1) ).

thf(2485,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(302,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_4) ).

thf(1537,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(225,axiom,
    ! [A: $i] : ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).

thf(1357,plain,
    ! [A: $i] : ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(771,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).

thf(2583,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(286,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).

thf(1500,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(479,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_1) ).

thf(1923,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(750,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).

thf(2539,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(382,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_0) ).

thf(1713,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(329,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_0) ).

thf(1597,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(818,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).

thf(2687,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_Suc @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(57,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).

thf(982,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(257,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).

thf(1431,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(243,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).

thf(1399,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ c_Suc @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(632,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).

thf(2270,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(333,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le__neg_0) ).

thf(1606,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(847,axiom,
    tc_nat @ class_HOL_Oord,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

thf(2754,plain,
    tc_nat @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).

thf(796,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).

thf(2640,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(207,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).

thf(1320,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(477,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( D @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).

thf(1917,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) @ hAPP ) )
        = ( A @ ( D @ ( A @ ( C @ c_Power_Opower__class_Opower ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Power_Opower__class_Opower ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(670,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).

thf(2351,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(562,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).

thf(2106,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(271,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_0) ).

thf(1468,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(95,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).

thf(1069,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(804,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).

thf(2655,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).

thf(488,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).

thf(1944,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(230,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).

thf(1367,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(39,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).

thf(940,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(34,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Odvd,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Odvd) ).

thf(935,plain,
    tc_Int_Oint @ class_Ring__and__Field_Odvd,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(70,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

thf(1009,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(24,axiom,
    tc_Int_Oint @ class_Power_Opower,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).

thf(923,plain,
    tc_Int_Oint @ class_Power_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(605,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_0) ).

thf(2206,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(392,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).

thf(1737,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(368,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_4) ).

thf(1681,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(141,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).

thf(1184,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(547,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).

thf(2074,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(269,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).

thf(1463,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(314,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).

thf(1565,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(708,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).

thf(2438,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(281,axiom,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OlessThan ) )
    = ( tc_bool @ ( tc_nat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__0_0) ).

thf(1490,plain,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OlessThan ) )
    = ( tc_bool @ ( tc_nat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(264,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_8) ).

thf(1449,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(426,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

thf(1812,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( tc_nat @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( B @ ( tc_nat @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(251,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Odvd,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).

thf(1417,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Odvd,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(455,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__inverse__le_0) ).

thf(1870,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(52,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).

thf(972,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(2914,plain,
    $false,
    inference(e,[status(thm)],[1322,2822,2094,2744,1168,2072,1995,2544,1879,1337,2336,2109,1454,2031,1633,2778,2412,1237,2787,2595,2499,2427,2480,1179,2331,1818,1295,1956,1549,2280,1554,1686,2250,2363,1211,2309,2104,2381,1808,1618,2248,1728,1205,2099,1305,1750,977,1522,2644,2671,2014,2114,1142,1971,2854,1608,2607,2448,1275,2627,2459,2580,945,2042,2575,2195,1705,1078,1788,1426,1867,2184,1164,2316,1872,2712,1342,913,1095,1746,2216,2432,1576,1441,1046,1613,2010,1601,2173,2548,1782,2491,1243,1724,1475,2067,1529,1967,2819,1803,2136,1904,1265,1703,1228,1482,1254,1409,1287,1792,2755,2708,1313,2562,1132,2356,2703,2814,1985,1760,1660,1907,2501,2444,1860,1264,1511,917,934,1191,1800,2857,2169,1890,1572,2635,2158,1494,1963,1778,2852,1100,1847,1545,2420,2691,902,1892,1379,1247,2049,2552,2024,1641,2388,2533,2178,924,2794,2324,1373,1911,2650,1136,2122,1978,2254,1960,1581,1283,1051,905,2456,2007,2616,1946,1465,1040,1109,1418,2451,2236,1151,937,1677,2540,2034,2508,1928,1215,1886,1394,1433,1405,1201,1104,2154,1696,1843,2058,2618,2833,2281,1896,2190,1447,956,1796,1072,2530,1119,1622,2371,1526,2137,2002,998,2809,2799,2286,1863,1604,2011,920,1438,925,1306,1199,1153,2118,1338,2047,2737,1730,1470,1915,1708,1311,2296,2307,2083,2496,2621,2660,1768,2061,2773,2000,1636,2264,1223,2428,1519,2147,1666,1487,2528,2396,2441,2673,1387,1900,910,2560,2805,1042,2541,1355,2277,1570,1174,2133,1824,1370,1883,1560,1423,916,1365,1920,2477,1951,1888,1457,1624,2200,1159,1836,1656,1027,2345,2741,1740,974,2653,1938,2758,1032,1837,1195,2211,1407,1392,2228,2112,1291,2769,1012,1402,1983,2841,2359,1856,1006,1755,2638,2268,989,1397,1350,1936,1592,2300,1089,1234,1762,2515,1270,1851,1772,948,2801,1534,1794,1953,2685,2577,1064,1111,1970,980,1498,1587,2726,2631,1138,2724,1719,2537,1567,2460,1329,1361,1942,933,2830,2613,1810,2349,2038,2666,1644,970,1744,901,1075,1414,2053,1207,2085,1776,1249,1297,1451,1231,2243,2465,911,2566,1874,1429,2140,1627,1324,1114,2125,985,1539,1382,2487,2845,1668,1974,1002,1852,2766,2482,1599,2697,2208,921,1054,1170,2402,1515,2645,2338,926,2749,1857,2788,1318,1202,2203,1814,1086,938,1241,2546,2761,1035,2368,2408,1663,953,2662,906,2729,965,1251,2585,2717,1483,1273,2602,1631,2260,1146,2292,2391,1680,1698,2556,1103,2275,2149,2028,1301,1595,2734,2524,2376,904,1833,1007,2225,1615,2791,2393,1652,2806,1701,2817,1124,2827,1620,2489,2016,2514,2568,2695,1256,1503,1786,936,2220,2326,1865,1332,2706,1765,919,2425,1258,2474,1675,1635,1733,1058,1107,1239,1997,2055,1092,1194,2521,1209,900,2422,1574,1524,1048,2097,1542,2116,1043,2856,1122,1376,2197,2065,2079,2361,2311,2151,2642,2214,2383,2624,2415,1894,2257,1933,2246,1492,2669,1144,2378,1690,2180,2824,2182,1877,2812,2314,2111,1993,2780,1821,2410,915,1344,1293,2710,1688,1339,2610,1909,1162,2446,2757,2785,2593,1556,1460,943,1022,2252,2664,2329,932,1061,912,1841,1926,2171,1066,1015,1176,2288,2633,1477,1726,2156,1805,2770,2075,2418,1213,2835,2051,2550,1245,1000,2752,2535,2101,1496,2303,922,2693,2506,1562,1948,2239,1583,1758,2318,927,1277,1134,1509,1990,939,1472,1551,1662,2096,2652,2471,2503,1684,1081,2629,1018,2564,2597,1958,968,1181,1845,1547,1025,1156,1225,2192,2012,2588,1252,2175,1780,1098,1798,2298,1003,1770,2678,2518,1753,2386,2850,2160,993,2689,2569,2165,1637,1038,1785,1830,951,2044,1579,907,1711,2747,1790,1987,1716,2454,1188,2700,1186,1658,2322,1285,1218,2468,1220,1221,1749,1670,2848,2266,991,2675,1404,1358,1898,1849,2838,2558,1536,1981,1353,2357,1955,2843,2145,1485,1972,2320,1506,1585,1140,2511,2860,2722,1881,2807,1272,1940,1421,1839,2088,1966,931,1517,1126,1289,1734,2435,2760,2626,1316,1649,1084,2078,1834,1913,976,903,2347,1654,1412,2743,2187,1390,2305,2342,2658,2775,1646,1326,2283,896,1639,2290,2406,2554,1062,2026,1854,2764,2130,2526,2591,1590,961,1385,1721,963,2167,2273,1629,2004,995,1558,2262,1030,2081,2399,2648,2462,1308,1193,2162,2680,899,2120,2315,2019,2796,914,2230,2294,2036,2739,2494,1444,2142,2218,2683,1280,2233,1395,1303,1480,2374,1348,1512,1774,967,2719,1593,2604,1148,1673,2636,918,1816,2334,1172,1056,2366,2714,2223,2040,2783,1436,1859,1363,1314,1335,1693,2070,2572,1710,1197,2091,2404,2340,1165,2021,1346,2063,1610,1742,928,1019,2467,1299,1902,2372,1930,2353,2241,987,2127,1352,2731,1829,1977,1129,1827,1261,2430,1268,2803,1532,2600,2485,1537,1357,2583,1500,1923,2539,1713,1597,2687,982,1431,1399,2270,1606,2754,2640,1320,1917,2351,2106,1468,1069,2655,1944,1367,940,935,1009,923,2206,1737,1681,1184,2074,1463,1565,2438,1490,1449,1812,1417,1870,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWV621-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40  % Computer : n020.cluster.edu
% 0.13/0.40  % Model    : x86_64 x86_64
% 0.13/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40  % Memory   : 8046.5625MB
% 0.13/0.40  % OS       : Linux 6.8.0-71-generic
% 0.13/0.40  % CPULimit : 300
% 0.13/0.40  % WCLimit  : 300
% 0.13/0.40  % DateTime : Sat Sep 26 14:39:05 UTC 2026
% 0.13/0.40  % CPUTime  : 
% 0.13/0.40  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.84/0.98  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.33/1.43  % [INFO] 	 Parsing done (440ms). 
% 2.33/1.45  % [INFO] 	 Running in sequential loop mode. 
% 3.27/1.82  % [INFO] 	 eprover registered as external prover. 
% 3.27/1.83  % [INFO] 	 Scanning for conjecture ... 
% 3.92/2.08  % [INFO] 	 Found a conjecture (or negated_conjecture) and 896 axioms. Running axiom selection ... 
% 5.14/2.39  % [INFO] 	 Axiom selection finished. Selected 894 axioms (removed 2 axioms). 
% 7.00/2.81  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 7.00/2.86  % [INFO] 	 Type checking passed. 
% 7.00/2.87  % [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 ... 
% 26.33/7.24  % External prover 'e' found a proof!
% 26.33/7.24  % [INFO] 	 Killing All external provers ... 
% 26.33/7.25  % Time passed: 6698ms (effective reasoning time: 5792ms)
% 26.33/7.26  % Axioms used in derivation (894): cls_mult__eq__1__iff_1, cls_divide__le__eq__number__of_9, cls_less__iff__diff__less__0_0, cls_xt1_I9_J_0, cls_le__divide__eq_8, cls_minus__le__iff_0, cls_power__0_0, cls_le__0__eq_1, cls_divide__eq__eq_3, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1, cls_neg__0__le__iff__le_1, cls_less__divide__eq_3, clsarity_nat__HOL_Oord, cls_divide__le__eq__number__of1_9, cls_not__one__less__zero_0, cls_mult__less__cancel__left__disj_5, cls_k_I2_J_0, cls_root__cancel_0, cls_linorder__antisym__conv2_1, cls_one__le__mult__iff_1, cls_atLeast0LessThan_0, cls_le__divide__eq_3, cls_order__le__less__trans_0, cls_mult__cancel2_0, cls_mult__zero__right_0, cls_zero__less__one_0, cls_divide__le__eq_2, cls_mult__nonneg__nonneg_0, cls_eq__divide__eq__number__of1_4, cls_Suc__inject_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_divide__less__0__iff_0, cls_setsum__ivl__cong_1, cls_Suc__mono_0, cls_nat__0__less__mult__iff_1, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, cls_zero__less__divide__iff_5, cls_divide__eq__eq__number__of_4, cls_less__divide__eq__number__of1_6, cls_le__minus__self__iff_0, cls_mult__imp__le__div__pos_0, cls_divide__pos__pos_0, clsarity_Int__Oint__Int_Onumber, cls_mult__right__mono_0, cls_mult__right_Ozero_0, cls_dvd__mult__right_0, cls_dvd__mult2_0, cls_eq__imp__le_0, cls_mult_Odiff__left_0, cls_mult__less__cancel__right__disj_0, cls_divide__self_0, cls_mult__nonneg__nonpos2_0, cls_negative__imp__inverse__negative_0, cls_Suc__n__not__n_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, cls_divide__le__eq__number__of_4, cls_square__eq__iff_1, cls_le__divide__eq__number__of1_0, cls_minus__zero_0, cls_mult__is__0_2, cls_Lim_Ominus__diff__minus_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult, cls_setsum__0_0, cls_inverse__zero__imp__zero_0, cls_xt1_I12_J_0, clsarity_Complex__Ocomplex__Int_Onumber, cls_divide__nonpos__neg_0, cls_exp__not__eq__zero_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_mult__less__cancel__left__disj_1, cls_zero__le__one_0, cls_power__eq__0__iff_1, cls_termination__basic__simps_I5_J_0, cls_nat__lt__two__imp__zero__or__one_0, cls_inverse__eq__iff__eq_0, cls_less__antisym_0, cls_divide__less__eq__number__of1_5, cls_le__divide__eq__number__of_6, clsarity_fun__Orderings_Oorder, cls_COMBK__def_0, cls_zero__le__divide__iff_2, cls_power__le__zero__eq_3, cls_power__inject__exp_0, cls_zero__le__mult__iff_3, cls_linorder__neqE_0, cls_divide__1_0, clsarity_Int__Oint__Orderings_Oorder, cls_power__increasing_0, cls_one__le__mult__iff_0, cls_inverse__le__1__iff_2, clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add, cls_divide__le__eq__number__of1_4, clsarity_Int__Oint__Ring__and__Field_Opordered__ring, cls_less__divide__eq__number__of_8, cls_nonzero__inverse__eq__divide_0, cls_divide__less__eq_4, cls_divide__le__eq_8, cls_less__divide__eq__number__of_3, cls_divide__less__eq__number__of1_0, cls_divide__less__eq__number__of_1, cls_less__imp__inverse__less__neg_0, cls_class__semiring_Osemiring__rules_I10_J_0, cls_divide__le__0__1__iff_1, cls_less__Suc__eq_2, cls_divide__le__eq_7, cls_not__less__eq_1, cls_minus__diff__eq_0, cls_frac__le_0, cls_compl__eq__compl__iff_0, cls_inverse__less__1__iff_2, cls_one__le__inverse__iff_2, cls_zero__less__divide__iff_0, cls_dvd__diff_0, cls_le__divide__eq__number__of1_5, cls_Suc__lessI_0, cls_mult__nonpos__nonneg_0, cls_power__less__zero__eq_1, cls_inverse__1_0, cls_minus__le__self__iff_0, cls_minus__divide__right_0, cls_inverse__negative__iff__negative_1, clsarity_nat__Orderings_Olinorder, cls_eq__divide__eq__number__of_4, cls_mult__nonpos__nonpos_0, cls_power__le__imp__le__exp_0, cls_minus__minus_0, cls_power__one_0, cls_mult__less__imp__less__right_0, cls_Suc__mult__cancel1_0, cls_left__inverse_0, cls_order__less__trans_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_divide__less__eq_5, cls_neg__less__iff__less_1, cls_power__0__left__number__of_0, cls_eq__divide__eq__number__of_1, cls_left__diff__distrib__number__of_0, cls_divide__less__eq__number__of1_6, clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict, cls_mult__le__cancel__left__pos_0, cls_minus__dvd__iff_1, cls_divide__eq__eq_0, cls_power__gt1_0, clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add, cls_less__minus__iff_0, cls_power__less__imp__less__exp_0, cls_mult__less__cancel1_0, cls_split__mult__neg__le_0, cls_inverse__nonnegative__iff__nonnegative_0, cls_mult__less__cancel__left__disj_4, cls_mult__less__imp__less__left_0, cls_le__divide__eq__number__of1_9, cls_divide__le__eq__number__of_5, cls_gr0I_0, cls_less__divide__eq_4, cls_mult__less__cancel2_1, cls_mult__less__cancel__right__disj_3, cls_inverse__divide_0, clsarity_bool__Finite__Set_Ofinite_Ofinite, clsarity_Int__Oint__Ring__and__Field_Oring__1, cls_power__less__zero__eq__number__of_1, cls_divide__strict__left__mono_0, cls_le__0__eq_0, cls_divide__le__0__iff_3, cls_mult__eq__0__iff_0, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_exp__diff_0, clsarity_bool__HOL_Oord, clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors, clsarity_nat__Ring__and__Field_Osemiring__0, clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1, cls_nat__mult__eq__cancel1_0, clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult, cls_divide__less__eq__number__of_6, clsarity_nat__OrderedGroup_Omonoid__mult, cls_gr__implies__not0_0, cls_mult__left__mono__neg_0, clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict, cls_le__antisym_0, cls_less__divide__eq__number__of1_2, cls_less__eq__Suc__le__raw_0, cls_mult_Ozero__left_0, cls_setsum__shift__lb__Suc0__0__upt_0, cls_divide__neg__neg_0, cls_n__less__n__mult__m_0, cls_less__iff__diff__less__0_1, cls_nat__less__cases_0, cls_eq__divide__eq_4, cls_mult__mono_0, cls_class__semiring_Omul__0_0, cls_right__inverse__eq_0, cls_field__power__not__zero_0, clsarity_nat__Ring__and__Field_Oordered__semiring, cls_neg__equal__iff__equal_0, cls_frac__eq__eq_0, cls_setsum__op__ivl__Suc_0, cls_one__le__power_0, cls_divide__eq__eq_4, cls_Suc__le__mono_0, cls_order__less__asym_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_linorder__not__less_0, cls_atLeastLessThan__empty__iff2_0, cls_inverse__le__1__iff_1, cls_power__eq__0__iff__number__of_2, cls_less__divide__eq__number__of1_0, cls_power__0__left_0, cls_order__less__asym_H_0, cls_eq__number__of_0, cls_mult_Ozero__right_0, cls_divide__le__eq__number__of_8, cls_divide__less__eq__number__of1_8, cls_class__semiring_Omul__c_0, cls_Suc__mult__less__cancel1_0, clsarity_Int__Oint__Ring__and__Field_Odvd, cls_mult__pos__neg_0, cls_nat__0__less__mult__iff_0, cls_order__eq__refl_0, cls_zero__le__mult__iff_0, cls_le__divide__eq__number__of_7, cls_divide__eq__eq__number__of1_0, cls_inverse__eq__1__iff_1, cls_mult__strict__mono_0, clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero, 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cls_divide__left__mono__neg_0, cls_setsum__diff__nat__ivl_0, cls_inverse__nonzero__iff__nonzero_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_divide__right__mono_0, cls_divide__right__mono__neg_0, cls_less__le__not__le_2, cls_divide__neg__pos_0, cls_xt1_I10_J_0, cls_le__divide__eq_2, cls_not__less__iff__gr__or__eq_0, cls_le__divide__eq__number__of_3, cls_divide__le__eq__number__of1_6, cls_no__zero__divisors_0, cls_mult__frac__num_0, cls_neg__less__eq__nonneg_1, cls_le__imp__power__dvd_0, cls_divide__le__eq__number__of1_5, clsarity_Int__Oint__Int_Oring__char__0, cls_le__minus__iff_0, cls_mult__is__0_1, cls_less__divide__eq__number__of_7, cls_mult__less__cancel2_2, cls_neg__less__eq__nonneg_0, cls_divide__le__eq_3, cls_series__zero_1, clsarity_Complex__Ocomplex__SEQ_Obanach, cls_zero__le__mult__iff_4, cls_power__gt1__lemma_0, cls_mult__le__mono_0, cls_divide__less__eq_0, cls_mult__frac__frac_0, clsarity_Int__Oint__Ring__and__Field_Oordered__semidom, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_finite_0, cls_mult__1__right_0, cls_divide__eq__eq__number__of_3, clsarity_fun__HOL_Oord, cls_less__divide__eq_2, cls_not__less__eq__eq_1, cls_mult__neg__pos_0, clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult, cls_mult__left_Odiff_0, cls_zero__less__divide__iff_1, cls_lessThan__eq__iff_0, cls_divide__less__eq__number__of1_2, clsarity_nat__OrderedGroup_Ocomm__monoid__mult, cls_power__0__Suc_0, cls_divide__less__eq__number__of_0, cls_inverse__le__imp__le__neg_0, cls_mult__le__0__iff_0, cls_power__strict__increasing_0, cls_le__divide__eq__number__of1_6, cls_le__iff__diff__le__0_0, cls_mult__right__le__imp__le_0, cls_mult__pos__neg2_0, cls_divide__eq__eq__number__of1_3, cls_Suc__neq__Zero_0, clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors, cls_le__imp__inverse__le_0, cls_divide__le__eq__number__of_0, cls_power__mult_0, cls_neg__le__0__iff__le_0, cls_less__Suc__eq__le_1, clsarity_fun__Finite__Set_Ofinite_Ofinite, 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cls_inverse__less__1__iff_1, cls_mult__zero__left_0, cls_dvd__mult__cancel__right_0, cls_nat__less__le_2, cls_divide__le__0__iff_4, cls_less__eq__neg__nonpos_0, clsarity_Int__Oint__Ring__and__Field_Oidom, cls_le__divide__eq_9, clsarity_bool__Lattices_Oboolean__algebra, clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult, cls_divide__less__eq__number__of_9, clsarity_nat__Ring__and__Field_Opordered__semiring, cls_le__divide__eq_4, cls_less__divide__eq_6, cls_nonzero__power__divide_0, cls_neg__0__equal__iff__equal_0, cls_mult__left__le__imp__le_0, cls_neg__le__iff__le_0, cls_class__fieldgb_Odivide__inverse_0, cls_atLeastLessThan__empty_0, cls_less__minus__self__iff_1, cls_divide__less__0__iff_1, cls_order__less__irrefl_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field, clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1, cls_class__semiring_Osemiring__rules_I27_J_0, cls_frac__less2_0, cls_divide__le__eq__number__of1_3, cls_one__less__inverse__iff_1, cls_diff__frac__eq_0, cls_power__eq__0__iff_0, cls_eq__eqI_1, cls_Suc__n__not__le__n_0, cls_dvd__0__right_0, cls_one__less__power_0, cls_divide__le__eq__number__of1_8, clsarity_Int__Oint__OrderedGroup_Oab__group__add, cls_power__Suc__less__one_0, cls_dvd__power__le_0, cls_mult__pos__pos_0, cls_less__eqI_0, clsarity_Int__Oint__Ring__and__Field_Omult__mono1, cls_mult__strict__right__mono__neg_0, clsarity_nat__Ring__and__Field_Ono__zero__divisors, cls_divide__less__eq__number__of1_4, cls_zero__less__divide__iff_4, cls_power__less__imp__less__base_0, cls_divide__le__0__iff_0, cls_n__not__Suc__n_0, cls_mult__right__less__imp__less_0, cls_dvd__power_0, cls_divide__less__eq_9, cls_inverse__zero_0, cls_Suc__leD_0, cls_le__divide__eq__number__of1_1, cls_inverse__less__imp__less__neg_0, clsarity_fun__Orderings_Opreorder, cls_root__unity_0, cls_k_I1_J_0, cls_inverse__eq__divide_0, cls_less__minus__self__iff_0, cls_DERIV__inverse__lemma_0, cls_power__inject__base_0, cls_less__divide__eq__number__of_2, cls_inverse__le__imp__le_0, cls_equation__minus__iff_1, cls_less__SucI_0, cls_nat__mult__le__cancel1_0, clsarity_Complex__Ocomplex__Power_Opower, cls_eq__divide__eq__number__of1_0, cls_nat__0__less__mult__iff_2, cls_not__less0_0, cls_mult__divide__mult__cancel__right_0, cls_nat__mult__assoc_0, cls_dvdI_0, cls_frac__less_0, clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add, cls_class__semiring_Opwr__mul_0, cls_divide__le__eq_9, cls_eq__iff__diff__eq__0_1, cls_class__ringb_Osubr0__iff_1, cls_divide__strict__right__mono_0, cls_nonzero__minus__divide__divide_0, cls_mult__less__cancel__left__disj_2, cls_finite_OemptyI_0, cls_power__eq__0__iff__number__of_0, cls_divide__inverse_0, cls_field__inverse_0, cls_nat__mult__commute_0, cls_mult__less__cancel__right__disj_1, cls_minus__dvd__iff_0, cls_atLeastLessThan__empty__iff_0, cls_divide__less__eq_6, cls_less__divide__eq__number__of1_9, cls_divide__eq__eq__number__of_2, cls_inverse__mult__distrib_0, cls_Suc__less__eq_0, cls_divide__nonpos__pos_0, cls_zero__le__power_0, cls_lessThan__0_0, cls_less__divide__eq_0, cls_inverse__less__imp__less_0, cls_divide__less__eq__number__of_2, cls_mult__cancel1_0, cls_inverse__positive__imp__positive_0, cls_eq__divide__eq__number__of_0, cls_le__eqI_1, cls_power__minus_0, cls_class__semiring_Opwr__0_0, cls_mult__eq__0__iff_1, cls_le__iff__diff__le__0_1, cls_power__increasing__iff_0, cls_divide__less__eq_3, cls_nonzero__inverse__mult__distrib_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, cls_nonzero__power__inverse_0, cls_order__less__imp__le_0, cls_le__divide__eq__number__of1_4, cls_minus__equation__iff_1, cls_atLeastLessThanSuc_1, cls_mult__idem_0, cls_less__divide__eq__number__of_5, cls_division__ring__inverse__diff_0, cls_le__divide__eq__number__of_4, cls_series__zero_0, cls_le__less__Suc__eq_1, cls_divide__less__eq__number__of1_1, cls_class__ringb_Osubr0__iff_0, cls_le__eq__less__or__eq_0, cls_dvd__mult_0, cls_le__imp__inverse__le__neg_0, cls_zero__le__divide__iff_1, cls_power__strict__increasing__iff_0, cls_less__Suc0_1, cls_divide__eq__eq_1, cls_le__divide__eq_5, cls_divide__le__eq__number__of1_0, cls_minus__mult__minus_0, clsarity_nat__Ring__and__Field_Omult__zero, clsarity_nat__OrderedGroup_Ocomm__monoid__add, clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add, cls_zero__less__power__eq__number__of_2, clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors, cls_eq__iff__diff__eq__0_0, cls_setsum__infinite_0, cls_xt1_I7_J_0, cls_divide_Ominus_0, cls_less__divide__eq__number__of1_5, cls_mult__divide__mult__cancel__left_0, cls_mult__le__less__imp__less_0, cls_mult__left_Ozero_0, cls_divide__less__0__1__iff_1, clsarity_nat__Ring__and__Field_Oordered__semiring__strict, clsarity_Int__Oint__Ring__and__Field_Oordered__semiring, cls_le__divide__eq__number__of1_8, cls_power__Suc__less_0, cls_divide__less__eq__number__of_5, cls_less__eqI_1, cls_square__eq__iff_0, cls_zero__less__divide__1__iff_0, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_mult__le__0__iff_3, cls_inverse__nonpositive__iff__nonpositive_1, cls_nat__mult__less__cancel1_0, cls_nat__mult__eq__cancel__disj_0, cls_mult__neg__neg_0, cls_linorder__not__less_1, cls_zero__less__Suc_0, cls_mult__less__cancel__left__neg_0, clsarity_Complex__Ocomplex__Int_Onumber__ring, cls_le__neq__implies__less_0, cls_not__one__le__zero_0, cls_nat__less__le_1, cls_mult__less__le__imp__less_0, cls_power__decreasing_0, clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult, cls_zero__le__divide__1__iff_0, cls_less__divide__eq_9, cls_le__divide__eq__number__of_9, cls_less__divide__eq__number__of_9, cls_mult__right_Odiff_0, cls_le__divide__eq__number__of_0, cls_mult__less__cancel__left__pos_0, cls_divide__less__0__iff_4, cls_split__mult__neg__le_1, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0, cls_power__mono_0, cls_divide__le__eq_1, cls_le__refl_0, cls_neg__less__iff__less_0, cls_dvd__mult__cancel__left_0, cls_dvd__power__same_0, cls_le__SucI_0, cls_divide__le__eq__number__of_3, cls_not__less__eq__eq_0, clsarity_Int__Oint__Ring__and__Field_Oordered__idom, cls_power__le__zero__eq__number__of_3, cls_power__0__left_1, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__cancel2_1, cls_mult__strict__left__mono__neg_0, cls_mult__eq__1__iff_2, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors, cls_le__number__of__eq__not__less_0, cls_right__inverse__eq_1, cls_divide__le__eq__number__of_6, cls_less__divide__eq__number__of1_1, cls_exp__zero_0, cls_zero__le__mult__iff_2, cls_dvd__0__left_0, cls_root__summation_0, cls_divide__le__0__1__iff_0
% 26.33/7.26  % No. of inferences in proof: 1791
% 26.33/7.26  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6698 ms resp. 5792 ms w/o parsing
% 28.12/7.82  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 28.12/7.84  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------