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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : LCL800-1 : 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 : n012.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 07:52:59 AM UTC 2026

% Result   : Unsatisfiable 17.31s 14.62s
% Output   : Refutation 16.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  289
% Syntax   : Number of formulae    :  579 ( 215 unt;   0 typ;   0 def)
%            Number of atoms       : 1183 ( 428 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives : 6398 ( 562   ~; 604   |;   0   &;5232   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   51 (  49 usr;  10 con; 0-3 aty)
%            Number of variables   : 1356 (   0   ^;1356   !;   0   ?;1356   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_InductTermi_OIT_decl,type,
    c_InductTermi_OIT: $i > $o ).

thf(c_Lambda_OdB_OApp_decl,type,
    c_Lambda_OdB_OApp: $i > $i > $i ).

thf(v_u_____decl,type,
    v_u____: $i ).

thf(c_Lambda_Osubst_decl,type,
    c_Lambda_Osubst: $i > $i > $i > $i ).

thf(v_a_____decl,type,
    v_a____: $i ).

thf(v_i_____decl,type,
    v_i____: $i ).

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

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

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

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

thf(c_HOL_Oplus__class_Oplus_decl,type,
    c_HOL_Oplus__class_Oplus: $i > $i > $i > $i ).

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

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

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

thf(class_OrderedGroup_Omonoid__add_decl,type,
    class_OrderedGroup_Omonoid__add: $i > $o ).

thf(class_Ring__and__Field_Osemiring__1_decl,type,
    class_Ring__and__Field_Osemiring__1: $i > $o ).

thf(c_Nat_Osemiring__1__class_Oof__nat_decl,type,
    c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).

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

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

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

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

thf(class_Ring__and__Field_Osemiring_decl,type,
    class_Ring__and__Field_Osemiring: $i > $o ).

thf(class_OrderedGroup_Ocancel__semigroup__add_decl,type,
    class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).

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

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

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

thf(class_OrderedGroup_Ocancel__ab__semigroup__add_decl,type,
    class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).

thf(class_OrderedGroup_Opordered__comm__monoid__add_decl,type,
    class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).

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

thf(class_Nat_Osemiring__char__0_decl,type,
    class_Nat_Osemiring__char__0: $i > $o ).

thf(class_Ring__and__Field_Ocomm__semiring_decl,type,
    class_Ring__and__Field_Ocomm__semiring: $i > $o ).

thf(class_OrderedGroup_Oab__semigroup__add_decl,type,
    class_OrderedGroup_Oab__semigroup__add: $i > $o ).

thf(c_Lambda_OdB_OVar_decl,type,
    c_Lambda_OdB_OVar: $i > $i ).

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

thf(c_Lambda_Obeta_decl,type,
    c_Lambda_Obeta: $i > $i > $o ).

thf(c_Lambda_OdB_OAbs_decl,type,
    c_Lambda_OdB_OAbs: $i > $i ).

thf(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1_decl,type,
    c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1: $i > $i > $i ).

thf(c_Lambda_Oliftn_decl,type,
    c_Lambda_Oliftn: $i > $i > $i > $i ).

thf(c_Lambda_Osko__Lambda__Xbeta__cases__2__1_decl,type,
    c_Lambda_Osko__Lambda__Xbeta__cases__2__1: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1_decl,type,
    c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1: $i > $i ).

thf(c_Lambda_Olift_decl,type,
    c_Lambda_Olift: $i > $i > $i ).

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

thf(c_Lambda_Osubstn_decl,type,
    c_Lambda_Osubstn: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1_decl,type,
    c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1: $i > $i ).

thf(v_rs_____decl,type,
    v_rs____: $i ).

thf(v_as_____decl,type,
    v_as____: $i ).

thf(tc_Lambda_OdB_decl,type,
    tc_Lambda_OdB: $i ).

thf(v_ua_______decl,type,
    v_ua______: $i ).

thf(v_n_____decl,type,
    v_n____: $i ).

thf(263,axiom,
    v_ua______ @ c_InductTermi_OIT,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).

thf(892,plain,
    v_ua______ @ c_InductTermi_OIT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(147,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).

thf(629,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(36,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).

thf(365,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(21,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).

thf(333,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(264,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).

thf(893,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(29,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).

thf(352,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(205,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(762,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)],[205]) ).

thf(170,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Lambda_OdB_OAbs @ c_Lambda_Obeta ) )
      | ( A
        = ( A @ ( B @ c_Lambda_Osko__Lambda__Xbeta__cases__2__1 ) @ c_Lambda_OdB_OAbs ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I2_J_0) ).

thf(683,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Lambda_OdB_OAbs @ c_Lambda_Obeta ) )
      | ( A
        = ( A @ ( B @ c_Lambda_Osko__Lambda__Xbeta__cases__2__1 ) @ c_Lambda_OdB_OAbs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).

thf(308,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(196,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

thf(741,plain,
    tc_nat @ class_Ring__and__Field_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(73,axiom,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

thf(449,plain,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(41,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__mult__distrib2_0) ).

thf(379,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(69,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

thf(440,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(98,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_2) ).

thf(511,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__commute_0) ).

thf(384,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(185,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(715,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(275,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubst ) ) @ ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OApp ) @ c_Lambda_Obeta ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).

thf(913,plain,
    ! [B: $i,A: $i] : ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubst ) ) @ ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_OdB_OApp ) @ c_Lambda_Obeta ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(289,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Lambda_OdB_OApp ) )
       != ( D @ ( C @ c_Lambda_OdB_OApp ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).

thf(945,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Lambda_OdB_OApp ) )
       != ( D @ ( C @ c_Lambda_OdB_OApp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(109,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( B = D )
      | ( ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( D @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).

thf(538,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( B = D )
      | ( ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( D @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(165,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono2_0) ).

thf(670,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(52,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).

thf(404,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(267,axiom,
    v_u____ @ c_InductTermi_OIT,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uIT_0) ).

thf(898,plain,
    v_u____ @ c_InductTermi_OIT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(59,axiom,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_4) ).

thf(417,plain,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(261,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Lambda_OdB_OApp ) )
       != ( D @ ( C @ c_Lambda_OdB_OApp ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).

thf(885,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Lambda_OdB_OApp ) )
       != ( D @ ( C @ c_Lambda_OdB_OApp ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(6,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).

thf(301,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).

thf(320,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(120,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).

thf(565,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(122,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

thf(570,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(38,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(372,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)],[38]) ).

thf(284,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_Lambda_Obeta ) )
      | ( C @ ( B @ ( D @ c_Lambda_Osubst ) ) @ ( C @ ( B @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_Obeta ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).

thf(934,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_Lambda_Obeta ) )
      | ( C @ ( B @ ( D @ c_Lambda_Osubst ) ) @ ( C @ ( B @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_Obeta ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(128,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_0) ).

thf(587,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(239,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(838,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)],[239]) ).

thf(277,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
      = ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ c_Lambda_Oliftn ) ) @ ( A @ c_Lambda_Osubst ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).

thf(917,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
      = ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ c_Lambda_Oliftn ) ) @ ( A @ c_Lambda_Osubst ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(178,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_1) ).

thf(702,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(202,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

thf(751,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(229,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).

thf(817,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(61,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(421,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)],[61]) ).

thf(135,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).

thf(606,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(17,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).

thf(325,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(13,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).

thf(316,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(91,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).

thf(492,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(203,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
     != ( B @ c_Lambda_OdB_OAbs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).

thf(756,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
     != ( B @ c_Lambda_OdB_OAbs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(217,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less_0) ).

thf(789,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(40,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).

thf(376,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(144,axiom,
    tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).

thf(623,plain,
    tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(155,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).

thf(646,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(99,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(514,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)],[99]) ).

thf(224,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).

thf(806,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(231,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).

thf(821,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(84,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).

thf(475,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(280,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ c_Lambda_OdB_OApp ) @ ( A @ c_Lambda_Oliftn ) ) )
      = ( D @ ( C @ ( A @ c_Lambda_Oliftn ) ) @ ( D @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ c_Lambda_OdB_OApp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).

thf(924,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ c_Lambda_OdB_OApp ) @ ( A @ c_Lambda_Oliftn ) ) )
      = ( D @ ( C @ ( A @ c_Lambda_Oliftn ) ) @ ( D @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ c_Lambda_OdB_OApp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(88,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_1) ).

thf(485,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(237,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).

thf(834,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(271,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_InductTermi_OIT )
      | ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_OdB_OApp ) @ c_InductTermi_OIT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).

thf(905,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_InductTermi_OIT )
      | ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_OdB_OApp ) @ c_InductTermi_OIT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(86,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

thf(480,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(193,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

thf(734,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(253,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_2) ).

thf(866,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(49,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).

thf(396,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(56,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).

thf(411,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(64,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).

thf(428,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(11,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).

thf(312,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(258,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( A @ c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1 @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__implies__Suc_0) ).

thf(877,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( A @ c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1 @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(173,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).

thf(692,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(2,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).

thf(292,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(74,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).

thf(452,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(169,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( B @ c_Lambda_OdB_OAbs ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).

thf(678,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Lambda_OdB_OAbs )
       != ( B @ c_Lambda_OdB_OAbs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(161,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).

thf(661,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(219,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).

thf(793,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(42,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( E @ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).

thf(381,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( E @ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).

thf(534,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(212,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( tc_nat @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1 ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_1) ).

thf(778,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( tc_nat @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1 ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(131,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(598,plain,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(118,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).

thf(561,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(62,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).

thf(424,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(54,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).

thf(407,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(191,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).

thf(729,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(251,axiom,
    ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).

thf(862,plain,
    ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(28,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__add_0) ).

thf(349,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(81,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_0) ).

thf(467,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(34,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).

thf(361,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(246,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).

thf(852,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(19,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).

thf(329,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(163,axiom,
    ! [A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).

thf(665,plain,
    ! [A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(114,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(551,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)],[114]) ).

thf(182,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

thf(710,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(102,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__mult_0) ).

thf(522,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(235,axiom,
    tc_nat @ class_Ring__and__Field_Omult__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

thf(830,plain,
    tc_nat @ class_Ring__and__Field_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(76,axiom,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_5) ).

thf(456,plain,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(241,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

thf(842,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(176,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( A @ c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1 @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_0) ).

thf(697,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( A @ c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1 @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(257,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

thf(874,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(157,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( 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(650,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( 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)],[157]) ).

thf(139,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

thf(615,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(189,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).

thf(725,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(45,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).

thf(388,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(31,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(356,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)],[31]) ).

thf(255,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_Oliftn ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn__0_0) ).

thf(869,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_Oliftn ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(137,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).

thf(610,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(214,axiom,
    tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

thf(783,plain,
    tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(101,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_1) ).

thf(519,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(197,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

thf(742,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(125,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(578,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)],[125]) ).

thf(89,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).

thf(488,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(24,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).

thf(339,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(115,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).

thf(554,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(151,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).

thf(637,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(129,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( B @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).

thf(590,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Lambda_OdB_OVar )
       != ( B @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(112,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).

thf(547,plain,
    ! [A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(180,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).

thf(706,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(269,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_InductTermi_OIT )
      | ( B @ ( A @ c_Lambda_Olift ) @ c_InductTermi_OIT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).

thf(901,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_InductTermi_OIT )
      | ( B @ ( A @ c_Lambda_Olift ) @ c_InductTermi_OIT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(171,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).

thf(686,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(47,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).

thf(393,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(274,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( B @ ( A @ c_Lambda_Olift ) @ c_Lambda_Osubst ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).

thf(911,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( B @ ( A @ c_Lambda_Olift ) @ c_Lambda_Osubst ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(96,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(503,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(26,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(343,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)],[26]) ).

thf(286,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Lambda_Obeta ) )
      | ( B @ ( C @ c_Lambda_OdB_OApp ) @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Obeta ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).

thf(938,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Lambda_Obeta ) )
      | ( B @ ( C @ c_Lambda_OdB_OApp ) @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Obeta ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(97,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

thf(508,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(279,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
     != ( C @ ( B @ c_Lambda_OdB_OApp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).

thf(921,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
     != ( C @ ( B @ c_Lambda_OdB_OApp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(110,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_0) ).

thf(541,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(206,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
        = ( B @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).

thf(765,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
        = ( B @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(117,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

thf(558,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(167,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).

thf(674,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(105,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

thf(530,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(186,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).

thf(718,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(281,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
     != ( C @ ( B @ c_Lambda_OdB_OApp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).

thf(926,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OVar )
     != ( C @ ( B @ c_Lambda_OdB_OApp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(149,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).

thf(633,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(33,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

thf(360,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(210,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).

thf(773,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(220,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

thf(794,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).

thf(298,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(57,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).

thf(412,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(201,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

thf(750,plain,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(142,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

thf(618,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(65,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).

thf(430,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(232,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

thf(824,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(199,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

thf(745,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(123,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).

thf(573,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(71,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( C = D )
      | ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( tc_nat @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).

thf(444,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( C = D )
      | ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( tc_nat @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(133,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).

thf(601,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(172,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).

thf(689,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(4,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).

thf(296,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(127,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).

thf(584,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(230,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).

thf(819,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(174,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(694,plain,
    tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(242,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

thf(843,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(233,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).

thf(826,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(153,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( B @ ( A @ c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1 ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_0) ).

thf(641,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( B @ ( A @ c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1 ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(285,axiom,
    v_n____ = v_i____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).

thf(936,plain,
    v_n____ = v_i____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(216,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).

thf(787,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(22,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).

thf(335,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(278,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Osubst ) ) )
      = ( D @ ( C @ ( B @ c_Lambda_Osubst ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OApp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).

thf(919,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Osubst ) ) )
      = ( D @ ( C @ ( B @ c_Lambda_Osubst ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubst ) ) @ c_Lambda_OdB_OApp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(179,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).

thf(704,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(166,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).

thf(672,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(184,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).

thf(713,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(94,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_2) ).

thf(498,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(134,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).

thf(604,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(236,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).

thf(831,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(215,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A = C )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).

thf(784,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A = C )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(60,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).

thf(419,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(121,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_3) ).

thf(567,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(132,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).

thf(599,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(194,axiom,
    ! [A: $i] :
      ( A
      = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).

thf(737,plain,
    ! [A: $i] :
      ( A
      = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(14,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).

thf(318,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(259,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_InductTermi_OIT )
      | ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).

thf(880,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_InductTermi_OIT )
      | ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(67,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( B = D )
      | ( ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( D @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).

thf(434,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( B = D )
      | ( ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( D @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(140,axiom,
    tc_nat @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(616,plain,
    tc_nat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).

thf(303,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(262,axiom,
    ( v_rs____
    = ( tc_Lambda_OdB @ ( v_as____ @ ( v_a____ @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons_0) ).

thf(890,plain,
    ( v_rs____
    = ( tc_Lambda_OdB @ ( v_as____ @ ( v_a____ @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(85,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
       != ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
      | ~ ( A @ class_Nat_Osemiring__char__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).

thf(477,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
       != ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
      | ~ ( A @ class_Nat_Osemiring__char__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(226,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(811,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)],[226]) ).

thf(92,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc_0) ).

thf(494,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(148,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).

thf(631,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(228,axiom,
    tc_nat @ class_OrderedGroup_Omonoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

thf(816,plain,
    tc_nat @ class_OrderedGroup_Omonoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(16,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).

thf(323,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(221,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(799,plain,
    tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(87,axiom,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_5) ).

thf(483,plain,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(265,axiom,
    ! [A: $i] :
      ( ~ ( A @ c_InductTermi_OIT )
      | ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).

thf(895,plain,
    ! [A: $i] :
      ( ~ ( A @ c_InductTermi_OIT )
      | ( A @ c_Lambda_OdB_OAbs @ c_InductTermi_OIT ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(208,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).

thf(769,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(288,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Osubstn ) ) )
      = ( D @ ( C @ ( B @ c_Lambda_Osubstn ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubstn ) ) @ c_Lambda_OdB_OApp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).

thf(943,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Osubstn ) ) )
      = ( D @ ( C @ ( B @ c_Lambda_Osubstn ) ) @ ( D @ ( C @ ( A @ c_Lambda_Osubstn ) ) @ c_Lambda_OdB_OApp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).

thf(668,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(79,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

thf(462,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(249,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Obeta ) )
      | ( B @ ( A @ c_Lambda_Osko__Lambda__Xbeta__cases__2__1 ) @ ( A @ c_Lambda_Obeta ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I2_J_1) ).

thf(858,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Obeta ) )
      | ( B @ ( A @ c_Lambda_Osko__Lambda__Xbeta__cases__2__1 ) @ ( A @ c_Lambda_Obeta ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(37,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(367,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(244,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_0) ).

thf(848,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(177,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).

thf(700,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(50,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).

thf(399,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(207,axiom,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

thf(768,plain,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(254,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).

thf(868,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(136,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).

thf(608,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(119,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).

thf(563,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(158,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
        = ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).

thf(653,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ c_Lambda_OdB_OVar @ ( A @ c_Lambda_Oliftn ) ) )
        = ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(150,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).

thf(636,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(175,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).

thf(695,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(48,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).

thf(394,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(8,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).

thf(306,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(83,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__0_0) ).

thf(473,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(90,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__mult_0) ).

thf(490,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__mult__distrib_0) ).

thf(426,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(162,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

thf(663,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(39,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).

thf(374,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(156,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_1) ).

thf(648,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(77,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).

thf(458,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(238,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(836,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(141,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

thf(617,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(100,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).

thf(516,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(211,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Obeta ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).

thf(776,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Obeta ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(103,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_3) ).

thf(525,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(183,axiom,
    tc_nat @ class_Nat_Osemiring__char__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

thf(712,plain,
    tc_nat @ class_Nat_Osemiring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(248,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(855,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(58,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(414,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)],[58]) ).

thf(18,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).

thf(327,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(195,axiom,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).

thf(739,plain,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(55,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel_0) ).

thf(409,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).

thf(310,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(218,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).

thf(791,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(20,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).

thf(331,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(240,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).

thf(840,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(82,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).

thf(470,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(225,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).

thf(808,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(111,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).

thf(544,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(272,axiom,
    tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_i____ @ ( v_u____ @ ( v_a____ @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_OdB_OVar @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_u____ @ c_Lambda_Olift ) @ c_Lambda_OdB_OApp ) @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(907,plain,
    tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_i____ @ ( v_u____ @ ( v_a____ @ c_Lambda_Osubst ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Lambda_OdB_OVar @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( v_u____ @ c_Lambda_Olift ) @ c_Lambda_OdB_OApp ) @ c_Lambda_Osubst ) ) @ c_InductTermi_OIT,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(198,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

thf(744,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(159,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).

thf(656,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(252,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).

thf(864,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(190,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).

thf(727,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(44,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).

thf(386,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(12,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).

thf(314,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(130,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

thf(595,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(138,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(612,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)],[138]) ).

thf(243,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(845,plain,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(146,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Lambda_Obeta ) )
      | ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Obeta ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs_0) ).

thf(627,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Lambda_Obeta ) )
      | ( B @ c_Lambda_OdB_OAbs @ ( A @ c_Lambda_OdB_OAbs @ c_Lambda_Obeta ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(283,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lt_0) ).

thf(931,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(270,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubst ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).

thf(903,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubstn ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Osubst ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(126,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(581,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)],[126]) ).

thf(204,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Oliftn ) ) ) )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).

thf(759,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubstn ) ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_Lambda_Oliftn ) ) ) )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(209,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).

thf(771,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(35,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

thf(363,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(116,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

thf(556,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(227,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
     != ( B @ c_Lambda_OdB_OVar ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).

thf(813,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Lambda_OdB_OAbs )
     != ( B @ c_Lambda_OdB_OVar ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(200,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Suc @ c_Lambda_Oliftn ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ c_Lambda_Olift ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn__lift_0) ).

thf(748,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Suc @ c_Lambda_Oliftn ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_Lambda_Oliftn ) ) @ c_Lambda_Olift ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(46,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

thf(390,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(51,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(401,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)],[51]) ).

thf(192,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Olift ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).

thf(731,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Olift ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(213,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).

thf(781,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Olift ) )
      = ( C @ ( B @ c_Lambda_Olift ) @ ( C @ ( A @ c_Lambda_Olift ) @ c_Lambda_OdB_OApp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).

thf(929,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Olift ) )
      = ( C @ ( B @ c_Lambda_Olift ) @ ( C @ ( A @ c_Lambda_Olift ) @ c_Lambda_OdB_OApp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(268,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Lambda_Obeta ) )
      | ( C @ ( A @ c_Lambda_OdB_OApp ) @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Obeta ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).

thf(899,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Lambda_Obeta ) )
      | ( C @ ( A @ c_Lambda_OdB_OApp ) @ ( B @ ( A @ c_Lambda_OdB_OApp ) @ c_Lambda_Obeta ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(27,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

thf(346,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).

thf(549,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(108,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).

thf(536,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(222,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ c_Suc )
        = B )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

thf(800,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ c_Suc )
        = B )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(1,negated_conjecture,
    ~ ( v_i____ @ ( v_u____ @ ( v_a____ @ c_Lambda_Osubst ) ) @ ( v_u____ @ c_Lambda_OdB_OApp ) @ c_InductTermi_OIT ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(290,plain,
    ~ ( v_i____ @ ( v_u____ @ ( v_a____ @ c_Lambda_Osubst ) ) @ ( v_u____ @ c_Lambda_OdB_OApp ) @ c_InductTermi_OIT ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(276,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Lambda_OdB_OApp ) )
     != ( C @ c_Lambda_OdB_OAbs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).

thf(914,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Lambda_OdB_OApp ) )
     != ( C @ c_Lambda_OdB_OAbs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(143,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(620,plain,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(72,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).

thf(447,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(66,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).

thf(432,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(53,axiom,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_4) ).

thf(405,plain,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(247,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

thf(854,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(3,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).

thf(294,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(25,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).

thf(341,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(32,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).

thf(358,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(68,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

thf(437,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(266,axiom,
    ! [A: $i] : ( A @ c_Lambda_OdB_OVar @ c_InductTermi_OIT ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).

thf(897,plain,
    ! [A: $i] : ( A @ c_Lambda_OdB_OVar @ c_InductTermi_OIT ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(234,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).

thf(828,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).

thf(532,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(187,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(720,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)],[187]) ).

thf(145,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).

thf(624,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(80,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(464,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)],[80]) ).

thf(124,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).

thf(575,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(250,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).

thf(860,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(104,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).

thf(528,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(154,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).

thf(644,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(78,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).

thf(459,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(273,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A = C )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_2) ).

thf(908,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A = C )
      | ( ( C @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
        = ( A @ c_Lambda_OdB_OVar ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(188,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Lambda_Obeta ) )
      | ( B @ ( C @ c_Lambda_Olift ) @ ( B @ ( A @ c_Lambda_Olift ) @ c_Lambda_Obeta ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).

thf(723,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Lambda_Obeta ) )
      | ( B @ ( C @ c_Lambda_Olift ) @ ( B @ ( A @ c_Lambda_Olift ) @ c_Lambda_Obeta ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(245,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).

thf(850,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(70,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).

thf(442,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(256,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

thf(871,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(95,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

thf(501,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(223,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(803,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)],[223]) ).

thf(23,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).

thf(337,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(287,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
        = B )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_1) ).

thf(940,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Lambda_OdB_OVar @ c_Lambda_Osubst ) ) )
        = B )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(30,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).

thf(354,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(160,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(659,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)],[160]) ).

thf(152,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(639,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)],[152]) ).

thf(168,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_0) ).

thf(676,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(181,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).

thf(708,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(260,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Lambda_OdB_OApp ) )
     != ( C @ c_Lambda_OdB_OVar ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).

thf(882,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Lambda_OdB_OApp ) )
     != ( C @ c_Lambda_OdB_OVar ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(93,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).

thf(496,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(75,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).

thf(454,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(1475,plain,
    $false,
    inference(e,[status(thm)],[892,629,365,333,893,352,762,683,308,741,449,379,440,511,384,715,913,945,538,670,404,898,417,885,301,320,565,570,372,934,587,838,917,702,751,817,421,606,325,316,492,756,789,376,623,646,514,806,821,475,924,485,834,905,480,734,866,396,411,428,312,877,692,292,452,678,661,793,381,534,778,598,561,424,407,729,862,349,467,361,852,329,665,551,710,522,830,456,842,697,874,650,615,725,388,356,869,610,783,519,742,578,488,339,554,637,590,547,706,901,686,393,911,503,343,938,508,921,541,765,558,674,530,718,926,633,360,773,794,298,412,750,618,430,824,745,573,444,601,689,296,584,819,694,843,826,641,936,787,335,919,704,672,713,498,604,831,784,419,567,599,737,318,880,434,616,303,890,477,811,494,631,816,323,799,483,895,769,943,668,462,858,367,848,700,399,768,868,608,563,653,636,695,394,306,473,490,426,663,374,648,458,836,617,516,776,525,712,855,414,327,739,409,310,791,331,840,470,808,544,907,744,656,864,727,386,314,595,612,845,627,931,903,581,759,771,363,556,813,748,390,401,731,781,929,899,346,549,536,800,290,914,620,447,432,405,854,294,341,358,437,897,828,532,720,624,464,575,860,528,644,459,908,723,850,442,871,501,803,337,940,354,659,639,676,708,882,496,454]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01  % Problem  : LCL800-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04  % 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
% 0.08/10.34  % Computer : n012.cluster.edu
% 0.08/10.34  % Model    : x86_64 x86_64
% 0.08/10.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.34  % Memory   : 8046.5625MB
% 0.08/10.34  % OS       : Linux 6.8.0-71-generic
% 0.08/10.34  % CPULimit : 300
% 0.08/10.34  % WCLimit  : 300
% 0.08/10.35  % DateTime : Fri Sep 25 23:35:20 UTC 2026
% 0.08/10.35  % CPUTime  : 
% 0.08/10.35  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
% 0.09/10.81  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.36/11.09  % [INFO] 	 Parsing done (279ms). 
% 1.36/11.10  % [INFO] 	 Running in sequential loop mode. 
% 2.57/11.43  % [INFO] 	 eprover registered as external prover. 
% 2.57/11.43  % [INFO] 	 Scanning for conjecture ... 
% 2.79/11.56  % [INFO] 	 Found a conjecture (or negated_conjecture) and 389 axioms. Running axiom selection ... 
% 3.51/11.71  % [INFO] 	 Axiom selection finished. Selected 288 axioms (removed 101 axioms). 
% 3.89/11.86  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 3.89/11.88  % [INFO] 	 Type checking passed. 
% 3.89/11.88  % [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 ... 
% 17.31/14.61  % External prover 'e' found a proof!
% 17.31/14.61  % [INFO] 	 Killing All external provers ... 
% 17.31/14.61  % Time passed: 4145ms (effective reasoning time: 3501ms)
% 17.31/14.61  % Axioms used in derivation (288): cls_mult__eq__1__iff_1, cls_Suc__pred_0, cls_mult__less__cancel__left__disj_5, cls_add__0__left_0, cls_subst__lt_0, cls_natgb_Oadd__r0__iff_1, cls_dB_Osimps_I6_J_0, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_mult__cancel2_0, cls_add__Suc__shift_0, cls_xt1_I9_J_0, cls_add__is__1_1, cls_mult__zero__right_0, cls_of__nat__add_0, cls_lift_Osimps_I2_J_0, cls_Suc__inject_0, cls_subst__App_0, cls_comm__semiring__class_Odistrib_0, cls_Suc__mono_0, cls_nat__0__less__mult__iff_1, cls_of__nat__0_0, cls_subst__eq_0, cls_mult__less__cancel__right__disj_0, cls_beta__cases_I2_J_1, cls_one__is__add_4, cls_Suc__n__not__n_0, cls_mult__less__cancel__left__disj_1, cls_mult__is__0_2, cls_nat__add__left__cancel__less_1, cls_liftn_Osimps_I1_J_1, cls_left__add__mult__distrib_0, cls_dB_Osimps_I8_J_0, cls_sum__squares__eq__zero__iff_0, cls_list_Oinject_0, cls_add__is__1_2, cls_add__strict__right__mono_0, cls_less__antisym_0, cls_liftn_Osimps_I2_J_0, cls_CHAINED_0, cls_less__add__Suc2_0, cls_of__nat__less__iff_0, cls_not__sum__squares__lt__zero_0, cls_pos__add__strict_0, cls_uIT_0, cls_add__is__0_0, cls_not__Cons__self2_0, cls_less__Suc__eq_2, cls_not__less__eq_1, cls_nat__add__left__cancel__less_0, cls_one__is__add_1, cls_appR_0, cls_termination__basic__simps_I1_J_0, cls_substn__subst__0_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_Suc__lessI_0, cls_diff__cancel_0, cls_add__imp__eq_0, cls_app__Var__IT_0, cls_Suc__mult__cancel1_0, cls_substn_Osimps_I1_J_2, cls_of__nat__0__less__iff_0, clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict, cls_add__left__cancel_0, cls_natgb_Oadd__mul__solve_0, cls_mult__less__cancel1_0, cls_beta_0, cls_mult__less__cancel__left__disj_4, cls_gr0I_0, cls_dB_Osimps_I7_J_0, cls_mult__less__cancel2_1, cls_subst__preserves__beta_0, cls_mult__Suc__right_0, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_add__gr__0_0, cls_mult__less__cancel__right__disj_3, cls_add__is__0_1, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_gr__implies__not0_0, cls_add__less__mono_0, cls_nat__mult__eq__cancel1_0, cls_diff__diff__left_0, cls_less__add__iff2_0, clsarity_nat__Ring__and__Field_Ocomm__semiring, cls_gr0__implies__Suc_0, cls_n__less__n__mult__m_0, cls_nat__0__less__mult__iff_0, cls_mult__eq__1__iff_0, cls_substn__subst__n_0, cls_Suc__mult__less__cancel1_0, cls_liftn__0_0, cls_dB_Osimps_I3_J_0, cls_add__Suc_0, cls_subst__Var_2, cls_linorder__neqE__nat_0, cls_not__add__less2_0, cls_Cons_0, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_diff__add__inverse2_0, cls_diff__mult__distrib2_0, cls_xt1_I10_J_0, cls_mult__is__0_1, cls_mult__less__cancel2_2, cls_nat__add__left__commute_0, cls_no__zero__divisors_0, cls_one__is__add_5, cls_diff__Suc__Suc_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_beta__cases_I2_J_0, cls_add__strict__left__mono_0, cls_add__less__mono1_0, cls_less__add__iff1_0, cls_combine__common__factor_0, cls_dB_Osimps_I4_J_0, cls_add__is__1_0, cls_mult__less__cancel__left__disj_0, cls_one__is__add_0, cls_Var_I3_J_0, cls_Suc__neq__Zero_0, cls_diff__add__0_0, cls_less__add__Suc1_0, cls_Var__IT_0, cls_add__right__cancel_0, cls_less__add__iff2_1, clsarity_nat__Nat_Osemiring__char__0, cls_of__nat__eq__iff_0, cls_mult__less__cancel1_1, cls_nat__add__assoc_0, cls_True_0, cls_of__nat__0__less__iff_1, cls_add__strict__mono_0, cls_natgb_Onoteq__reduce_1, cls_sum__squares__eq__zero__iff_1, cls_lessI_0, cls_less__iff__Suc__add_1, cls_not__add__less1_0, cls_mult__less__cancel__right__disj_2, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, cls_less__Suc__eq__0__disj_3, cls_less__add__eq__less_0, cls_sum__squares__gt__zero__iff_2, cls_not__Cons__self_0, cls_natgb_Oadd__scale__eq__noteq_0, cls_dB_Osimps_I1_J_0, cls_of__nat__mult_0, cls_no__zero__divirors__neq0_0, cls_subst__Var_1, cls_mult__Suc_0, cls_less__imp__diff__less_0, cls_natgb_Oadd__cancel_0, cls_less__Suc__eq__0__disj_0, cls_diff__less_0, cls_neq0__conv_1, cls_Suc__mult__less__cancel1_1, cls_one__is__add_2, cls_mult__less__cancel__right__disj_5, cls_mult__is__0_0, cls_not__less__less__Suc__eq_0, cls_lift__preserves__beta_0, cls_add__Suc__right_0, cls_nat__add__right__cancel_0, cls_diff__less__Suc_0, cls_less__not__refl_0, cls_not__square__less__zero_0, cls_add__mult__distrib_0, cls_gr0__conv__Suc_1, clsarity_nat__OrderedGroup_Oab__semigroup__mult, cls_less__add__iff1_1, cls_mult__cancel1_1, cls_linorder__neqE__ordered__idom_0, cls_Suc__diff__diff_0, cls_diff__cancel2_0, cls_dB_Osimps_I2_J_1, cls_sum__squares__gt__zero__iff_1, cls_natgb_Onoteq__reduce_0, cls_mult__less__mono1_0, clsarity_nat__Ring__and__Field_Osemiring, cls_less__diff__conv_1, cls_mult__strict__left__mono__comm_0, cls_less__diff__conv_0, cls_mult__less__cancel__left__neg_1, cls_nat_Oinject_0, cls_add__lessD1_0, cls_even__less__0__iff_1, cls_less__SucE_0, cls_diff__mult__distrib_0, cls_mult__less__mono2_0, cls_Nat_Oadd__0__right_0, cls_liftn__lift_0, cls_Suc__lessD_0, cls_substn_Osimps_I2_J_0, cls_not__less__less__Suc__eq_1, cls_nat_Osimps_I2_J_0, cls_Zero__neq__Suc_0, cls_nat__neq__iff_0, cls_mult__less__cancel__left__pos_1, cls_natgb_Oadd__r0__iff_0, cls_add__is__1_4, cls_add__is__1_5, cls_nat__mult__less__cancel1_1, cls_diff__self__eq__0_0, cls_add__neg__neg_0, cls_trans__less__add2_0, cls_zero__less__diff_0, cls_mult__less__cancel1_2, cls_mult__less__cancel2_0, cls_less__Suc0_0, cls_sum__squares__eq__zero__iff_2, cls_n__less__m__mult__n_0, cls_lift__IT_0, cls_add__mult__distrib2_0, cls_abs_0, cls_diff__Suc__less_0, cls_mult__less__cancel__left__disj_3, cls_gr0__conv__Suc_0, cls_mult__less__cancel__right__disj_4, cls_diff__less__mono2_0, cls_nat_Osimps_I3_J_0, cls_less__trans__Suc_0, cls_liftn_Osimps_I1_J_0, cls_one__less__mult_0, cls_not__less__eq_0, cls_trans__less__add1_0, cls_mult__zero__left_0, cls_plus__nat_Oadd__0_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_diff__0__eq__0_0, cls_add__is__0_2, cls_nat__add__left__cancel_0, cls_minus__nat_Odiff__0_0, cls_add__is__1_3, cls_list_Oinject_1, cls_zero__less__diff_1, cls_mult__strict__right__mono__neg_0, clsarity_nat__Ring__and__Field_Ono__zero__divisors, cls_substn_Osimps_I1_J_1, cls_add__eq__self__zero_0, cls_add__pos__pos_0, cls_n__not__Suc__n_0, cls_sum__squares__gt__zero__iff_0, cls_less__SucI_0, cls_beta__cases_I1_J_0, cls_nat__0__less__mult__iff_2, cls_not__less0_0, cls_nat__mult__assoc_0, cls_diffs0__imp__equal_0, cls_subst__Var__IT_0, cls_one__is__add_3, cls_dB_Osimps_I2_J_0, cls_mult__less__cancel__left__disj_2, cls_less__Suc__eq__0__disj_1, cls_dB_Osimps_I5_J_0, cls_diff__add__inverse_0, cls_nat__mult__commute_0, cls_mult__less__cancel__right__disj_1, cls_Lambda_0, cls_Suc__less__eq_0, cls_add__gr__0_2, cls_lift_Osimps_I1_J_0, clsarity_nat__Ring__and__Field_Osemiring__1, cls_mult__cancel1_0, cls_add__gr__0_1, cls_diff__commute_0, cls_less__Suc0_1, cls_subst__lift_0, cls_termination__basic__simps_I2_J_0, clsarity_nat__Ring__and__Field_Omult__zero, cls_monoid__add__class_Oadd__0__right_0, cls_of__nat__less__iff_1, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_nat__mult__less__cancel1_0, cls_appL_0, cls_nat__less__le_1, cls_natgb_Oadd__mul__solve_1, cls_dB_Osimps_I9_J_0, cls_nat__mult__eq__cancel__disj_0, cls_mult__neg__neg_0, cls_zero__less__Suc_0, cls_mult__less__cancel__left__neg_0, cls_even__less__0__iff_0, cls_mult__eq__1__iff_2, cls_mult__less__cancel__left__pos_0, cls_nat__add__commute_0, cls_add__diff__inverse_0, cls_of__nat__less__0__iff_0, cls_mult__cancel2_1, cls_mult__strict__left__mono__neg_0
% 17.31/14.61  % No. of inferences in proof: 579
% 17.31/14.62  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4145 ms resp. 3501 ms w/o parsing
% 16.89/14.78  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.89/14.79  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------