%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWV840-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:18:51 EDT 2023

% Result   : Unsatisfiable 9.63s 3.23s
% Output   : Refutation 10.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  570
% Syntax   : Number of formulae    : 1040 ( 355 unt; 101 typ;   0 def)
%            Number of atoms       : 1817 ( 606 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives : 13772 ( 918   ~; 878   |;   0   &;11976   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   37 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  219 ( 219   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  103 ( 101 usr;  19 con; 0-10 aty)
%            Number of variables   : 3566 (   0   ^;3566   !;   0   ?;3566   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_Hoare__Mirabelle_Ohoare__derivs_type,type,
    c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).

thf(v_G_type,type,
    v_G: $i ).

thf(c_Set_Oinsert_type,type,
    c_Set_Oinsert: $i > $i > $i > $i ).

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

thf(c_Hoare__Mirabelle_Otriple_Otriple_type,type,
    c_Hoare__Mirabelle_Otriple_Otriple: $i > $i ).

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

thf(v_P_type,type,
    v_P: $i ).

thf(c_Option_Othe_type,type,
    c_Option_Othe: $i > $i ).

thf(tc_Com_Ocom_type,type,
    tc_Com_Ocom: $i ).

thf(c_Com_Obody_type,type,
    c_Com_Obody: $i ).

thf(v_pn_type,type,
    v_pn: $i ).

thf(v_Q_type,type,
    v_Q: $i ).

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

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

thf(tc_Hoare__Mirabelle_Otriple_type,type,
    tc_Hoare__Mirabelle_Otriple: $i > $i ).

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

thf(c_Com_Ocom_OBODY_type,type,
    c_Com_Ocom_OBODY: $i ).

thf(c_Option_Ooption_OSome_type,type,
    c_Option_Ooption_OSome: $i > $i > $i ).

thf(c_Option_Ooption_ONone_type,type,
    c_Option_Ooption_ONone: $i > $i ).

thf(class_Lattices_Oupper__semilattice_type,type,
    class_Lattices_Oupper__semilattice: $i > $o ).

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

thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
    c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).

thf(c_Com_Ocom_OWhile_type,type,
    c_Com_Ocom_OWhile: $i > $i > $i ).

thf(c_Com_Ocom_OCall_type,type,
    c_Com_Ocom_OCall: $i > $i > $i > $i ).

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

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

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

thf(class_Lattices_Olattice_type,type,
    class_Lattices_Olattice: $i > $o ).

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

thf(c_Natural_Oevalc_type,type,
    c_Natural_Oevalc: $i > $i > $i > $o ).

thf(c_Com_Ocom_OSKIP_type,type,
    c_Com_Ocom_OSKIP: $i ).

thf(c_Com_Ocom_OLocal_type,type,
    c_Com_Ocom_OLocal: $i > $i > $i > $i ).

thf(c_Hoare__Mirabelle_Otriple__valid_type,type,
    c_Hoare__Mirabelle_Otriple__valid: $i > $i > $i > $o ).

thf(c_Natural_Oevaln_type,type,
    c_Natural_Oevaln: $i > $i > $i > $i > $o ).

thf(class_Complete__Lattice_Ocomplete__lattice_type,type,
    class_Complete__Lattice_Ocomplete__lattice: $i > $o ).

thf(c_Complete__Lattice_OInf__class_OInf_type,type,
    c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).

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

thf(c_in_type,type,
    c_in: $i > $i > $i > $i ).

thf(c_Com_Ocom_OSemi_type,type,
    c_Com_Ocom_OSemi: $i > $i > $i ).

thf(c_Com_Ocom_OCond_type,type,
    c_Com_Ocom_OCond: $i > $i > $i > $i ).

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

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

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

thf(c_Com_Ocom_Ocom__case_type,type,
    c_Com_Ocom_Ocom__case: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(c_Com_OWT_type,type,
    c_Com_OWT: $i > $o ).

thf(c_Complete__Lattice_OSup__class_OSup_type,type,
    c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).

thf(c_Collect_type,type,
    c_Collect: $i > $i > $i ).

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

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

thf(c_Fun_Ocomp_type,type,
    c_Fun_Ocomp: $i > $i > $i > $i > $i > $i ).

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

thf(c_Set_Oimage_type,type,
    c_Set_Oimage: $i > $i > $i > $i > $i ).

thf(c_COMBB_type,type,
    c_COMBB: $i > $i > $i > $i > $i > $i ).

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

thf(c_COMBI_type,type,
    c_COMBI: $i > $i ).

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

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

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

thf(c_Finite__Set_Ofold1_type,type,
    c_Finite__Set_Ofold1: $i > $i > $i > $i ).

thf(c_The_type,type,
    c_The: $i > $i > $i ).

thf(c_Finite__Set_Ofold1Set_type,type,
    c_Finite__Set_Ofold1Set: $i > $i > $i > $i ).

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

thf(c_Complete__Lattice_Ocomplete__lattice_type,type,
    c_Complete__Lattice_Ocomplete__lattice: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(v_sko__Hoare__Mirabelle__Xconseq12__1_type,type,
    v_sko__Hoare__Mirabelle__Xconseq12__1: $i > $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xconseq12__3_type,type,
    v_sko__Hoare__Mirabelle__Xconseq12__3: $i > $i > $i > $i > $i ).

thf(c_Nitpick_Osko__Nitpick__XEx1__def__1__3_type,type,
    c_Nitpick_Osko__Nitpick__XEx1__def__1__3: $i > $i > $i ).

thf(c_Set_Ocontents_type,type,
    c_Set_Ocontents: $i > $i > $i ).

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

thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_type,type,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3_type,type,
    v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3: $i > $i > $i > $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2_type,type,
    v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2: $i > $i > $i > $i > $i ).

thf(c_COMBS_type,type,
    c_COMBS: $i > $i > $i > $i > $i > $i ).

thf(t_b_type,type,
    t_b: $i ).

thf(t_c_type,type,
    t_c: $i ).

thf(v_R_type,type,
    v_R: $i ).

thf(class_Lattices_Obounded__lattice_type,type,
    class_Lattices_Obounded__lattice: $i > $o ).

thf(c_SetInterval_Oord__class_OatLeastAtMost_type,type,
    c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).

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

thf(v_sko__Hoare__Mirabelle__Xconseq2__1_type,type,
    v_sko__Hoare__Mirabelle__Xconseq2__1: $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xconseq2__2_type,type,
    v_sko__Hoare__Mirabelle__Xconseq2__2: $i > $i > $i ).

thf(tc_Com_Opname_type,type,
    tc_Com_Opname: $i ).

thf(tc_Com_Ostate_type,type,
    tc_Com_Ostate: $i ).

thf(tc_Option_Ooption_type,type,
    tc_Option_Ooption: $i > $i ).

thf(c_COMBC_type,type,
    c_COMBC: $i > $i > $i > $i > $i ).

thf(c_fequal_type,type,
    c_fequal: $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3_type,type,
    v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3: $i > $i > $i > $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2_type,type,
    v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2: $i > $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xconseq1__1_type,type,
    v_sko__Hoare__Mirabelle__Xconseq1__1: $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xconseq1__2_type,type,
    v_sko__Hoare__Mirabelle__Xconseq1__2: $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xconseq12__2_type,type,
    v_sko__Hoare__Mirabelle__Xconseq12__2: $i > $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xescape__1_type,type,
    v_sko__Hoare__Mirabelle__Xescape__1: $i > $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xescape__2_type,type,
    v_sko__Hoare__Mirabelle__Xescape__2: $i > $i > $i > $i > $i ).

thf(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1_type,type,
    c_Natural_Osko__Natural__Xevaln__elim__cases__6__1: $i > $i > $i > $i > $i ).

thf(c_Hoare__Mirabelle_Otriple_Otriple__case_type,type,
    c_Hoare__Mirabelle_Otriple_Otriple__case: $i > $i > $i > $i > $i ).

thf(c_Hoare__Mirabelle_Otriple_Otriple__rec_type,type,
    c_Hoare__Mirabelle_Otriple_Otriple__rec: $i > $i > $i > $i > $i ).

thf(c_Hoare__Mirabelle_Opeek__and_type,type,
    c_Hoare__Mirabelle_Opeek__and: $i > $i > $i > $i ).

thf(c_Not_type,type,
    c_Not: $i ).

thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1_type,type,
    v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1: $i > $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1_type,type,
    v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1: $i > $i > $i > $i > $i ).

thf(c_Finite__Set_Olinorder__class_OMin_type,type,
    c_Finite__Set_Olinorder__class_OMin: $i > $i > $i ).

thf(c_Finite__Set_Olinorder__class_OMax_type,type,
    c_Finite__Set_Olinorder__class_OMax: $i > $i > $i ).

thf(442,axiom,
    ! [B: $i,A: $i] :
      ( ( c_The @ ( hAPP @ ( c_COMBC @ ( c_fequal @ A ) @ A @ A @ tc_bool ) @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the__eq__trivial_0) ).

thf(1501,plain,
    ! [B: $i,A: $i] :
      ( ( c_The @ ( hAPP @ ( c_COMBC @ ( c_fequal @ A ) @ A @ A @ tc_bool ) @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(384,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ A @ B @ C ) @ D @ E @ F )
      | ~ ( c_Natural_Oevaln @ C @ D @ E @ F )
      | ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OIfFalse_0) ).

thf(1369,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ A @ B @ C ) @ D @ E @ F )
      | ~ ( c_Natural_Oevaln @ C @ D @ E @ F )
      | ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(110,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OLocal @ A @ B @ C )
     != c_Com_Ocom_OSKIP ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I11_J_0) ).

thf(760,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OLocal @ A @ B @ C )
     != c_Com_Ocom_OSKIP ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(324,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_asm_0) ).

thf(1237,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(61,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(628,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(165,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

thf(893,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(358,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(1315,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(194,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).

thf(962,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(298,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).

thf(1179,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(33,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ A @ B ) )
      | ~ ( c_Com_OWT @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_While_0) ).

thf(555,plain,
    ! [B: $i,A: $i] :
      ( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ A @ B ) )
      | ~ ( c_Com_OWT @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(76,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(666,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(464,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).

thf(1549,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(469,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(1559,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(264,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).

thf(1105,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(466,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).

thf(1554,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(267,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

thf(1110,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(202,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ C @ D @ E )
      | ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ F @ D @ E )
      | ~ ( c_Natural_Oevaln @ B @ C @ D @ F )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OWhileTrue_0) ).

thf(977,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ C @ D @ E )
      | ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ F @ D @ E )
      | ~ ( c_Natural_Oevaln @ B @ C @ D @ F )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(313,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
        = ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__absorb_0) ).

thf(1211,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
        = ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(22,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
       != ( c_Com_Ocom_OLocal @ D @ E @ F ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_0) ).

thf(523,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
       != ( c_Com_Ocom_OLocal @ D @ E @ F ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(217,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ A ) ) @ B @ C )
      | ~ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ A ) @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I6_J_0) ).

thf(1005,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ A ) ) @ B @ C )
      | ~ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ A ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(452,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ C ) @ C @ C @ tc_bool ) @ A ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__def_0) ).

thf(1522,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ C ) @ C @ C @ tc_bool ) @ A ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(462,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Collect @ B @ C ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectI_0) ).

thf(1544,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Collect @ B @ C ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(80,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(677,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(296,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(1173,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(102,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OSemi @ A @ B )
     != ( c_Com_Ocom_OCond @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I44_J_0) ).

thf(741,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OSemi @ A @ B )
     != ( c_Com_Ocom_OCond @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(249,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ A @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__constant_0) ).

thf(1073,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ A @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(156,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_0) ).

thf(873,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(311,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

thf(1205,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(354,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(1305,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(49,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(597,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(408,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

thf(1426,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(279,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

thf(1137,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(356,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != B )
      | ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

thf(1310,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != B )
      | ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(31,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(550,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(13,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(500,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(186,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCond @ A @ B @ C )
     != ( hAPP @ c_Com_Ocom_OBODY @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I54_J_0) ).

thf(945,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCond @ A @ B @ C )
     != ( hAPP @ c_Com_Ocom_OBODY @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(244,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

thf(1063,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(423,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(1458,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(371,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__binary_0) ).

thf(1342,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(104,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Option_Ooption_OSome @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Oinject_0) ).

thf(747,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Option_Ooption_OSome @ A @ B )
       != ( c_Option_Ooption_OSome @ C @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(173,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Obounded__lattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

thf(913,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Obounded__lattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(27,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).

thf(538,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(377,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).

thf(1354,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(318,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( c_Com_Ocom_OSemi @ D @ E ) ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ G ) @ E ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ D ) @ G ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comp_0) ).

thf(1222,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( c_Com_Ocom_OSemi @ D @ E ) ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ G ) @ E ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ D ) @ G ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

thf(930,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(259,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
        = ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).

thf(1095,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
        = ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(415,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Collect @ A @ B )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).

thf(1441,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Collect @ A @ B )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(392,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
        = ( hAPP @ ( hAPP @ E @ B ) @ C ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).

thf(1386,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
        = ( hAPP @ ( hAPP @ E @ B ) @ C ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(37,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(565,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(456,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__singleton_0) ).

thf(1529,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(450,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ A @ ( hAPP @ B @ C ) )
      = ( hAPP @ ( c_Fun_Ocomp @ A @ B @ D @ E @ F ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).

thf(1518,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ A @ ( hAPP @ B @ C ) )
      = ( hAPP @ ( c_Fun_Ocomp @ A @ B @ D @ E @ F ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(327,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ( c_Natural_Oevalc @ C @ B @ D )
      | ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ C @ E ) @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_1) ).

thf(1243,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ( c_Natural_Oevalc @ C @ B @ D )
      | ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ C @ E ) @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(274,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ B @ C ) @ D @ E )
      | ~ ( c_Natural_Oevalc @ C @ D @ E )
      | ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OIfFalse_0) ).

thf(1127,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ B @ C ) @ D @ E )
      | ~ ( c_Natural_Oevalc @ C @ D @ E )
      | ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(434,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Com_Ocom_OBODY @ A )
     != ( c_Com_Ocom_OCond @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I55_J_0) ).

thf(1482,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Com_Ocom_OBODY @ A )
     != ( c_Com_Ocom_OCond @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(332,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).

thf(1254,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(97,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OCall @ A @ B @ C )
       != ( c_Com_Ocom_OCall @ D @ E @ F ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_0) ).

thf(724,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OCall @ A @ B @ C )
       != ( c_Com_Ocom_OCall @ D @ E @ F ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(346,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cut_0) ).

thf(1287,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(410,axiom,
    ! [A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__empty_0) ).

thf(1430,plain,
    ! [A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(351,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( hBOOL @ ( c_in @ D @ A @ C ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(1298,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( hBOOL @ ( c_in @ D @ A @ C ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(719,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(122,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).

thf(785,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(365,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OLocal @ I @ J @ K ) @ L )
      = ( hAPP @ ( hAPP @ ( hAPP @ C @ I ) @ J ) @ K ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I66_J_0) ).

thf(1330,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OLocal @ I @ J @ K ) @ L )
      = ( hAPP @ ( hAPP @ ( hAPP @ C @ I ) @ J ) @ K ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(128,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofold1 @ A @ B @ C )
      = ( c_The @ ( c_Finite__Set_Ofold1Set @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__def_0) ).

thf(802,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofold1 @ A @ B @ C )
      = ( c_The @ ( c_Finite__Set_Ofold1Set @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(357,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

thf(1313,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(421,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

thf(1455,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(304,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ A @ B @ C @ D )
      | ( hBOOL @ ( hAPP @ E @ B ) )
      | ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ E @ F @ A ) @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_0) ).

thf(1191,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ A @ B @ C @ D )
      | ( hBOOL @ ( hAPP @ E @ B ) )
      | ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ E @ F @ A ) @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(46,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OWhile @ A @ B )
       != ( c_Com_Ocom_OWhile @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_0) ).

thf(587,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OWhile @ A @ B )
       != ( c_Com_Ocom_OWhile @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(362,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).

thf(1323,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(142,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ A @ B @ C )
      | ( c_Natural_Oevalc @ D @ B @ C )
      | ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ A ) @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_2) ).

thf(838,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ A @ B @ C )
      | ( c_Natural_Oevalc @ D @ B @ C )
      | ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ A ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(175,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

thf(917,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(105,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(751,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(425,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).

thf(1462,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(242,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ D @ C @ E ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ F @ A @ G @ H @ I @ J @ K @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).

thf(1059,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ D @ C @ E ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ F @ A @ G @ H @ I @ J @ K @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(277,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofold1 @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).

thf(1132,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofold1 @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(169,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
        = C )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ C @ I @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).

thf(902,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
        = C )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ C @ I @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(65,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(638,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(389,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(1379,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(256,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

thf(1087,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(329,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

thf(1247,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(155,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).

thf(870,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(373,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

thf(1347,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(160,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Ominus @ A )
      | ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_HOL_Ominus__class_Ominus @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).

thf(881,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Ominus @ A )
      | ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_HOL_Ominus__class_Ominus @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(269,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Complete__Lattice_Ocomplete__lattice @ A @ B @ ( c_COMBC @ C @ D @ D @ tc_bool ) @ ( c_COMBC @ E @ D @ D @ tc_bool ) @ F @ G @ H @ I @ D )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ A @ C @ E @ G @ F @ I @ H @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).

thf(1115,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Complete__Lattice_Ocomplete__lattice @ A @ B @ ( c_COMBC @ C @ D @ D @ tc_bool ) @ ( c_COMBC @ E @ D @ D @ tc_bool ) @ F @ G @ H @ I @ D )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ A @ C @ E @ G @ F @ I @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(439,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

thf(1494,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(380,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(1362,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(261,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).

thf(1100,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(322,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Collect @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
      = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).

thf(1232,plain,
    ! [B: $i,A: $i] :
      ( ( c_Collect @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
      = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(221,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
        = B )
      | ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

thf(1013,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
        = B )
      | ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(116,axiom,
    class_HOL_Ominus @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).

thf(770,plain,
    class_HOL_Ominus @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(426,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

thf(1465,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(47,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
       != ( c_Com_Ocom_OLocal @ D @ E @ F ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_1) ).

thf(591,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
       != ( c_Com_Ocom_OLocal @ D @ E @ F ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(233,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
        = ( c_Set_Oimage @ A @ C @ D @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).

thf(1040,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
        = ( c_Set_Oimage @ A @ C @ D @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(367,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

thf(1334,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(196,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ C ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).

thf(966,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ C ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(170,axiom,
    ( ( hAPP @ ( c_COMBS @ v_P @ v_Q @ t_a @ t_b @ t_c ) @ v_R )
    = ( hAPP @ ( hAPP @ v_P @ v_R ) @ ( hAPP @ v_Q @ v_R ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBS__def__raw_0) ).

thf(905,plain,
    ( ( hAPP @ ( c_COMBS @ v_P @ v_Q @ t_a @ t_b @ t_c ) @ v_R )
    = ( hAPP @ ( hAPP @ v_P @ v_R ) @ ( hAPP @ v_Q @ v_R ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(353,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

thf(1302,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(108,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ A @ B ) )
      | ~ ( c_Com_OWT @ B )
      | ~ ( c_Com_OWT @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OSemi_0) ).

thf(756,plain,
    ! [B: $i,A: $i] :
      ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ A @ B ) )
      | ~ ( c_Com_OWT @ B )
      | ~ ( c_Com_OWT @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(405,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Com_Ocom_OBODY @ A )
       != ( hAPP @ c_Com_Ocom_OBODY @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).

thf(1418,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Com_Ocom_OBODY @ A )
       != ( hAPP @ c_Com_Ocom_OBODY @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(59,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ E @ G @ F )
      = ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ B @ E @ G @ D ) @ C @ D @ G @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__assoc_0) ).

thf(623,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ocomp @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ E @ G @ F )
      = ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ B @ E @ G @ D ) @ C @ D @ G @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(7,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).

thf(485,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(140,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
      = ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__compose_0) ).

thf(834,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
      = ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(391,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Com_Ocom_OBODY @ A )
     != ( c_Com_Ocom_OWhile @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I59_J_0) ).

thf(1383,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Com_Ocom_OBODY @ A )
     != ( c_Com_Ocom_OWhile @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(40,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_OWT @ A )
      | ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_1) ).

thf(574,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_OWT @ A )
      | ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(191,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(956,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(153,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(866,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(271,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).

thf(1119,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(454,axiom,
    class_Orderings_Oorder @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(1526,plain,
    class_Orderings_Oorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(213,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ A ) @ A @ A @ tc_bool ) @ B ) @ A )
      = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv_0) ).

thf(998,plain,
    ! [B: $i,A: $i] :
      ( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ A ) @ A @ A @ tc_bool ) @ B ) @ A )
      = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(372,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ A @ B @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).

thf(1345,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ A @ B @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(411,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ B @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ C ) @ D ) @ E ) @ t_b @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Osplit_0) ).

thf(1433,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ B @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ C ) @ D ) @ E ) @ t_b @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(399,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ D @ tc_Com_Opname @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ E @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ D @ tc_Com_Opname @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ E @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ D @ tc_Com_Opname @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ E @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_OBody_0) ).

thf(1405,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ D @ tc_Com_Opname @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ E @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ D @ tc_Com_Opname @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ E @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ D @ tc_Com_Opname @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ E @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(309,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(1201,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(16,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ B @ A ) @ C @ A )
      | ~ ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__lower_0) ).

thf(507,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ B @ A ) @ C @ A )
      | ~ ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(23,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OLocal @ A @ B @ C )
     != ( c_Com_Ocom_OSemi @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I34_J_0) ).

thf(527,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OLocal @ A @ B @ C )
     != ( c_Com_Ocom_OSemi @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(51,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCond @ A @ B @ C )
     != ( c_Com_Ocom_OSemi @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I45_J_0) ).

thf(602,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCond @ A @ B @ C )
     != ( c_Com_Ocom_OSemi @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(204,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) @ C @ C )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OWhileFalse_0) ).

thf(981,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) @ C @ C )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(113,axiom,
    class_Lattices_Olattice @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

thf(766,plain,
    class_Lattices_Olattice @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(294,axiom,
    ( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
    = v_P ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).

thf(1169,plain,
    ( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
    = v_P ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(83,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(687,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(158,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

thf(877,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(85,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ A @ B @ C ) )
      | ~ ( c_Com_OWT @ C )
      | ~ ( c_Com_OWT @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OIf_0) ).

thf(692,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ A @ B @ C ) )
      | ~ ( c_Com_OWT @ C )
      | ~ ( c_Com_OWT @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(176,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ B @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).

thf(920,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ B @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(413,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

thf(1438,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(30,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OCond @ A @ B @ C )
       != ( c_Com_Ocom_OCond @ D @ E @ F ) )
      | ( C = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_2) ).

thf(546,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OCond @ A @ B @ C )
       != ( c_Com_Ocom_OCond @ D @ E @ F ) )
      | ( C = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(178,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
       != ( c_Fun_Ocomp @ F @ G @ H @ D @ E ) )
      | ( ( hAPP @ A @ ( hAPP @ B @ I ) )
        = ( hAPP @ F @ ( hAPP @ G @ I ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).

thf(925,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
       != ( c_Fun_Ocomp @ F @ G @ H @ D @ E ) )
      | ( ( hAPP @ A @ ( hAPP @ B @ I ) )
        = ( hAPP @ F @ ( hAPP @ G @ I ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(308,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ( hBOOL @ ( c_in @ A @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

thf(1199,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ( hBOOL @ ( c_in @ A @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(131,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_OSome @ A @ B )
     != ( c_Option_Ooption_ONone @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__None__eq_1) ).

thf(810,plain,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_OSome @ A @ B )
     != ( c_Option_Ooption_ONone @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(428,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(1470,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

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

thf(534,plain,
    class_Orderings_Oorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(246,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ E @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ B @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ B @ E ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq1_1) ).

thf(1067,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ E @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ B @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ B @ E ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(93,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ A @ B ) @ C @ D )
      | ~ ( c_Natural_Oevalc @ B @ E @ D )
      | ~ ( c_Natural_Oevalc @ A @ C @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSemi_0) ).

thf(714,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ A @ B ) @ C @ D )
      | ~ ( c_Natural_Oevalc @ B @ E @ D )
      | ~ ( c_Natural_Oevalc @ A @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(291,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ B @ E @ D @ F ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ B @ E @ D @ F ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_0) ).

thf(1163,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ B @ E @ D @ F ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ B @ E @ D @ F ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(18,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Com_Ocom_OSemi @ A @ B )
     != c_Com_Ocom_OSKIP ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).

thf(512,plain,
    ! [B: $i,A: $i] :
      ( ( c_Com_Ocom_OSemi @ A @ B )
     != c_Com_Ocom_OSKIP ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(185,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__constant_1) ).

thf(942,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(341,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
        = C )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).

thf(1274,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
        = C )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(172,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ D ) @ B @ E @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__WHILE__case_0) ).

thf(910,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ D ) @ B @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(224,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__eqI_0) ).

thf(1021,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(151,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(862,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(315,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ A ) @ B @ ( c_Suc @ C ) @ D )
      | ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ A ) ) @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OBody_0) ).

thf(1217,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ A ) @ B @ ( c_Suc @ C ) @ D )
      | ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ A ) ) @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(436,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( c_COMBK @ C @ A @ D ) @ D @ A )
        = C )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP__const_0) ).

thf(1487,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( c_COMBK @ C @ A @ D ) @ D @ A )
        = C )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(62,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ A @ B @ C ) )
      | ~ ( c_Com_OWT @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OLocal_0) ).

thf(630,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ A @ B @ C ) )
      | ~ ( c_Com_OWT @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(123,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).

thf(788,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(145,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OWhile @ A @ B )
     != ( c_Com_Ocom_OSemi @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I47_J_0) ).

thf(847,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OWhile @ A @ B )
     != ( c_Com_Ocom_OSemi @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(229,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Com_Ocom_OBODY @ A )
     != ( c_Com_Ocom_OSemi @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I49_J_0) ).

thf(1032,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Com_Ocom_OBODY @ A )
     != ( c_Com_Ocom_OSemi @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(382,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

thf(1365,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(60,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(625,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(159,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Set_Ocontents @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_contents__eq_0) ).

thf(879,plain,
    ! [B: $i,A: $i] :
      ( ( c_Set_Ocontents @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(350,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ C @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ D )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ C @ D )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ D ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).

thf(1296,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ C @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ D )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ C @ D )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ D ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(289,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Un_0) ).

thf(1159,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

thf(493,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(252,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ F @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).

thf(1079,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ F @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(394,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

thf(1392,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(348,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).

thf(1291,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(200,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ c_Com_Ocom_OSKIP ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).

thf(974,plain,
    ! [C: $i,B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ c_Com_Ocom_OSKIP ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(147,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
       != ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

thf(852,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
       != ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(467,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( c_Natural_Oevaln @ D @ E @ F @ C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ B ) @ E ) )
      | ~ ( c_Hoare__Mirabelle_Otriple__valid @ F @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ G ) @ D ) @ A ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple__valid__def2_0) ).

thf(1555,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( c_Natural_Oevaln @ D @ E @ F @ C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ B ) @ E ) )
      | ~ ( c_Hoare__Mirabelle_Otriple__valid @ F @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ G ) @ D ) @ A ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(44,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ A @ B @ C )
      | ~ ( c_Natural_Oevaln @ A @ B @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__eq_1) ).

thf(583,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ A @ B @ C )
      | ~ ( c_Natural_Oevaln @ A @ B @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(138,axiom,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).

thf(830,plain,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(306,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ t_a ) @ v_x )
      = ( hAPP @ A @ ( hAPP @ B @ v_x ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__def_0) ).

thf(1195,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ t_a ) @ v_x )
      = ( hAPP @ A @ ( hAPP @ B @ v_x ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(400,axiom,
    class_HOL_Oord @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(1407,plain,
    class_HOL_Oord @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(398,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OWhile @ A @ B )
     != ( hAPP @ c_Com_Ocom_OBODY @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I58_J_0) ).

thf(1402,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OWhile @ A @ B )
     != ( hAPP @ c_Com_Ocom_OBODY @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(42,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCond @ A @ B @ C )
     != ( c_Com_Ocom_OWhile @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I52_J_0) ).

thf(578,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCond @ A @ B @ C )
     != ( c_Com_Ocom_OWhile @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(282,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( A = D )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(1143,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( A = D )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(334,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ A @ B @ D @ C ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) ) @ C ) @ ( c_COMBK @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ A @ B @ D @ C ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_escape_1) ).

thf(1259,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ A @ B @ D @ C ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) ) @ C ) @ ( c_COMBK @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ A @ B @ D @ C ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(458,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ A @ B @ D @ C @ E @ F ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).

thf(1534,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ A @ B @ D @ C @ E @ F ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(364,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ A @ B @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_0) ).

thf(1328,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ A @ B @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(280,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Collect @ A @ C ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectD_0) ).

thf(1138,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Collect @ A @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(54,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ A @ B ) @ C @ D @ E )
      | ~ ( c_Natural_Oevaln @ B @ F @ D @ E )
      | ~ ( c_Natural_Oevaln @ A @ C @ D @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OSemi_0) ).

thf(610,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ A @ B ) @ C @ D @ E )
      | ~ ( c_Natural_Oevaln @ B @ F @ D @ E )
      | ~ ( c_Natural_Oevaln @ A @ C @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(783,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(208,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ C @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__empty2_0) ).

thf(989,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ C @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(379,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).

thf(1360,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(375,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ A ) )
      | ~ ( c_Com_OWT @ ( c_Com_Ocom_OCall @ B @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I8_J_0) ).

thf(1350,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ A ) )
      | ~ ( c_Com_OWT @ ( c_Com_Ocom_OCall @ B @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(87,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OWhile @ A @ B )
     != ( c_Com_Ocom_OCond @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I53_J_0) ).

thf(697,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OWhile @ A @ B )
     != ( c_Com_Ocom_OCond @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(257,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ C @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_0) ).

thf(1089,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ C @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(323,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(1234,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(461,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Com_Ocom_OBODY @ A )
     != ( c_Com_Ocom_OLocal @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I41_J_0) ).

thf(1541,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Com_Ocom_OBODY @ A )
     != ( c_Com_Ocom_OLocal @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(69,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(650,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(187,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

thf(948,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(149,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ B @ E @ D @ F ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ B @ E @ D @ F ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_2) ).

thf(857,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ B @ E @ D @ F ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ B @ E @ D @ F ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(396,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ( hBOOL @ ( c_in @ A @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffI_0) ).

thf(1397,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ( hBOOL @ ( c_in @ A @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(2,negated_conjecture,
    ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ v_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ v_pn ) ) @ v_Q ) @ v_G @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ v_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) ) @ v_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(471,plain,
    ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ v_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ v_pn ) ) @ v_Q ) @ v_G @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ v_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) ) @ v_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(161,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(884,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(227,axiom,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(1028,plain,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(181,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

thf(933,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(106,axiom,
    class_Orderings_Olinorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(753,plain,
    class_Orderings_Olinorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(300,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ( c_Natural_Oevaln @ C @ B @ D @ E )
      | ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ A @ C @ F ) @ B @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_1) ).

thf(1182,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ( c_Natural_Oevaln @ C @ B @ D @ E )
      | ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ A @ C @ F ) @ B @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(77,axiom,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

thf(669,plain,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(407,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).

thf(1424,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).

thf(489,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(314,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Set_Oinsert @ A @ D @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(1214,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Set_Oinsert @ A @ D @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(417,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(1446,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(222,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).

thf(1016,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(250,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B @ t_a ) @ v_x )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_K__record__comp_0) ).

thf(1075,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B @ t_a ) @ v_x )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(4,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(476,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(232,axiom,
    class_Orderings_Obot @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(1039,plain,
    class_Orderings_Obot @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(198,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

thf(970,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(206,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(985,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(422,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__apply_0) ).

thf(1456,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(337,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(1266,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(276,axiom,
    class_Orderings_Opreorder @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(1131,plain,
    class_Orderings_Opreorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(465,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(1552,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(237,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(1050,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(96,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCall @ A @ B @ C )
     != ( c_Com_Ocom_OSemi @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I51_J_0) ).

thf(721,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCall @ A @ B @ C )
     != ( c_Com_Ocom_OSemi @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(215,axiom,
    ( ( hAPP @ ( hAPP @ ( c_COMBC @ v_P @ t_a @ t_b @ t_c ) @ v_Q ) @ v_R )
    = ( hAPP @ ( hAPP @ v_P @ v_R ) @ v_Q ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def__raw_0) ).

thf(1002,plain,
    ( ( hAPP @ ( hAPP @ ( c_COMBC @ v_P @ t_a @ t_b @ t_c ) @ v_Q ) @ v_R )
    = ( hAPP @ ( hAPP @ v_P @ v_R ) @ v_Q ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(68,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OLocal @ A @ B @ C )
     != ( c_Com_Ocom_OCond @ D @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I36_J_0) ).

thf(647,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OLocal @ A @ B @ C )
     != ( c_Com_Ocom_OCond @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(336,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
        = ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( D
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).

thf(1263,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
        = ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( D
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(212,axiom,
    class_Lattices_Obounded__lattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

thf(997,plain,
    class_Lattices_Obounded__lattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(19,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(515,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(285,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).

thf(1150,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(330,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
      | ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

thf(1249,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
      | ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(419,axiom,
    class_Lattices_Oupper__semilattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

thf(1451,plain,
    class_Lattices_Oupper__semilattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(101,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OCond @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I14_J_0) ).

thf(738,plain,
    ! [C: $i,B: $i,A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OCond @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(14,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Otriple__valid @ A @ B @ C )
      | ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ A ) @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple__valid__Suc_0) ).

thf(503,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Otriple__valid @ A @ B @ C )
      | ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ A ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(52,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(605,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(360,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
      = ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).

thf(1318,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
      = ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(326,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ B @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ C ) @ D ) @ E ) @ t_b @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Osplit__asm_0) ).

thf(1241,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ B @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ C ) @ D ) @ E ) @ t_b @ t_a ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(28,axiom,
    ! [A: $i] :
      ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
     != ( c_Suc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).

thf(541,plain,
    ! [A: $i] :
      ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
     != ( c_Suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(230,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D )
      = ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).

thf(1035,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D )
      = ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(248,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(1071,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(449,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_Set_Oimage @ B @ C @ D @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

thf(1515,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_Set_Oimage @ B @ C @ D @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(293,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ( hBOOL @ ( c_in @ D @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(1167,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ( hBOOL @ ( c_in @ D @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(24,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OCall @ A @ B @ C )
       != ( c_Com_Ocom_OCall @ D @ E @ F ) )
      | ( C = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_2) ).

thf(530,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OCall @ A @ B @ C )
       != ( c_Com_Ocom_OCall @ D @ E @ F ) )
      | ( C = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(189,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ A ) @ B @ C )
      | ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ A ) ) @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OBody_0) ).

thf(953,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ A ) @ B @ C )
      | ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ A ) ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(255,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).

thf(1086,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(183,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(938,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(112,axiom,
    ! [B: $i,A: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ A @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OSkip_0) ).

thf(765,plain,
    ! [B: $i,A: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ A @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(239,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(1054,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(118,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OLocal @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I10_J_0) ).

thf(773,plain,
    ! [C: $i,B: $i,A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OLocal @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(125,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(794,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(74,axiom,
    class_Orderings_Obot @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

thf(662,plain,
    class_Orderings_Obot @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(163,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
      | ( ( hAPP @ C @ E )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).

thf(888,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
      | ( ( hAPP @ C @ E )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(447,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ F @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP1__I_0) ).

thf(1510,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ F @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(283,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

thf(1146,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(263,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

thf(1103,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(386,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBI @ A ) @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).

thf(1374,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBI @ A ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(331,axiom,
    ! [A: $i] :
      ( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ A ) )
      | ( ( hAPP @ c_Com_Obody @ A )
        = ( c_Option_Ooption_ONone @ tc_Com_Ocom ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OBody_0) ).

thf(1251,plain,
    ! [A: $i] :
      ( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ A ) )
      | ( ( hAPP @ c_Com_Obody @ A )
        = ( c_Option_Ooption_ONone @ tc_Com_Ocom ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(57,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Com_OWT @ A )
      | ~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I6_J_0) ).

thf(618,plain,
    ! [B: $i,A: $i] :
      ( ( c_Com_OWT @ A )
      | ~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(316,axiom,
    class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).

thf(1219,plain,
    class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(136,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

thf(824,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(287,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).

thf(1154,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(134,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).

thf(819,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(99,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OSemi @ A @ B )
       != ( c_Com_Ocom_OSemi @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).

thf(732,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OSemi @ A @ B )
       != ( c_Com_Ocom_OSemi @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(393,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

thf(1389,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(192,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(958,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(451,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(1520,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(36,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OSemi @ A @ B )
     != ( c_Com_Ocom_OLocal @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I35_J_0) ).

thf(562,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OSemi @ A @ B )
     != ( c_Com_Ocom_OLocal @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(201,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(975,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(218,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

thf(1007,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(86,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
       != ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(694,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
       != ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(144,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OCall @ A @ B @ C )
       != ( c_Com_Ocom_OCall @ D @ E @ F ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_1) ).

thf(843,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OCall @ A @ B @ C )
       != ( c_Com_Ocom_OCall @ D @ E @ F ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(273,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).

thf(1125,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(157,axiom,
    ! [B: $i,A: $i] :
      ( ( c_The @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OThe__psimp_0) ).

thf(875,plain,
    ! [B: $i,A: $i] :
      ( ( c_The @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(92,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

thf(711,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(333,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCall @ A @ B @ C )
     != ( hAPP @ c_Com_Ocom_OBODY @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I63_J_0) ).

thf(1256,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCall @ A @ B @ C )
     != ( hAPP @ c_Com_Ocom_OBODY @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(320,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).

thf(1226,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(443,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

thf(1503,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(325,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__upper_0) ).

thf(1239,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(366,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).

thf(1332,plain,
    ! [B: $i,A: $i] :
      ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(258,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

thf(1092,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(129,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != C )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(804,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != C )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(90,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

thf(704,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(319,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).

thf(1224,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(78,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OCall @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I20_J_0) ).

thf(672,plain,
    ! [C: $i,B: $i,A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OCall @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(66,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OWhile @ A @ B )
     != ( c_Com_Ocom_OCall @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I60_J_0) ).

thf(641,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OWhile @ A @ B )
     != ( c_Com_Ocom_OCall @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(409,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Otriple__valid @ A @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) ) @ E ) @ B )
      | ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( hAPP @ c_Com_Ocom_OBODY @ D ) ) @ E ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Body__triple__valid__Suc_1) ).

thf(1428,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Otriple__valid @ A @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) ) @ E ) @ B )
      | ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( hAPP @ c_Com_Ocom_OBODY @ D ) ) @ E ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(339,axiom,
    class_HOL_Ominus @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).

thf(1271,plain,
    class_HOL_Ominus @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(385,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
        = B )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).

thf(1371,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
        = B )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(241,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).

thf(1058,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(265,axiom,
    class_Lattices_Olattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(1107,plain,
    class_Lattices_Olattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(203,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ D @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ D @ E ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq2_1) ).

thf(979,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ D @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ D @ E ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(401,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ A @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ D ) @ E ) @ B @ F )
      = ( hAPP @ ( hAPP @ ( hAPP @ A @ C ) @ D ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Ocases_0) ).

thf(1408,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ A @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ D ) @ E ) @ B @ F )
      = ( hAPP @ ( hAPP @ ( hAPP @ A @ C ) @ D ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(344,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(1282,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(270,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ C @ F ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ F @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__I_0) ).

thf(1117,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ C @ F ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ F @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(220,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).

thf(1011,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(453,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( hAPP @ c_Com_Ocom_OBODY @ D ) ) @ E ) @ B )
      | ~ ( c_Hoare__Mirabelle_Otriple__valid @ A @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) ) @ E ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Body__triple__valid__Suc_0) ).

thf(1524,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( hAPP @ c_Com_Ocom_OBODY @ D ) ) @ E ) @ B )
      | ~ ( c_Hoare__Mirabelle_Otriple__valid @ A @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) ) @ E ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(374,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(1349,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(438,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).

thf(1492,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(355,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Set_Oinsert @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

thf(1307,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Set_Oinsert @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(236,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(1048,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(100,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ A @ B @ ( c_Suc @ C ) @ D )
      | ~ ( c_Natural_Oevaln @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__Suc_0) ).

thf(736,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ A @ B @ ( c_Suc @ C ) @ D )
      | ~ ( c_Natural_Oevaln @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(17,axiom,
    ! [B: $i,A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OWhile @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I16_J_0) ).

thf(509,plain,
    ! [B: $i,A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OWhile @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(234,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
      | ~ ( c_lessequals @ D @ A @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_thin_0) ).

thf(1043,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
      | ~ ( c_lessequals @ D @ A @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(56,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(616,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(272,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
        = ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ~ ( hBOOL @ ( c_in @ E @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant_0) ).

thf(1122,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
        = ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ~ ( hBOOL @ ( c_in @ E @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(50,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OLocal @ A @ B @ C )
     != ( c_Com_Ocom_OWhile @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I38_J_0) ).

thf(599,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OLocal @ A @ B @ C )
     != ( c_Com_Ocom_OWhile @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(387,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).

thf(1376,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(414,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(1439,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(429,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ B @ A @ C @ D ) ) )
      | ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ B ) @ C @ A @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_0) ).

thf(1471,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ B @ A @ C @ D ) ) )
      | ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ B ) @ C @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(468,axiom,
    ( ( hAPP @ ( c_COMBB @ v_P @ v_Q @ t_a @ t_b @ t_c ) @ v_R )
    = ( hAPP @ v_P @ ( hAPP @ v_Q @ v_R ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def__raw_0) ).

thf(1557,plain,
    ( ( hAPP @ ( c_COMBB @ v_P @ v_Q @ t_a @ t_b @ t_c ) @ v_R )
    = ( hAPP @ v_P @ ( hAPP @ v_Q @ v_R ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(26,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).

thf(535,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(133,axiom,
    ! [A: $i] :
      ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
     != ( c_Suc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).

thf(816,plain,
    ! [A: $i] :
      ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
     != ( c_Suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(127,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_ONone @ A )
     != ( c_Option_Ooption_OSome @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).

thf(799,plain,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_ONone @ A )
     != ( c_Option_Ooption_OSome @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(166,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_OWT @ ( c_Com_Ocom_OCall @ A @ B @ C ) )
      | ~ ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OCall_0) ).

thf(895,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_OWT @ ( c_Com_Ocom_OCall @ A @ B @ C ) )
      | ~ ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(195,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

thf(964,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(174,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ B @ E @ A ) @ A )
      | ~ ( hBOOL @ ( c_in @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SUPI_0) ).

thf(915,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ B @ E @ A ) @ A )
      | ~ ( hBOOL @ ( c_in @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(424,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(1460,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(349,axiom,
    ! [A: $i] :
      ( ( hAPP @ c_Com_Ocom_OBODY @ A )
     != c_Com_Ocom_OSKIP ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I19_J_0) ).

thf(1293,plain,
    ! [A: $i] :
      ( ( hAPP @ c_Com_Ocom_OBODY @ A )
     != c_Com_Ocom_OSKIP ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(390,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(1381,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(243,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ A @ B @ C ) @ D @ E @ F )
      | ~ ( c_Natural_Oevaln @ B @ D @ E @ F )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OIfTrue_0) ).

thf(1061,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ A @ B @ C ) @ D @ E @ F )
      | ~ ( c_Natural_Oevaln @ B @ D @ E @ F )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(109,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(758,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(369,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ D @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).

thf(1339,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(88,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OSemi @ A @ B )
     != ( c_Com_Ocom_OCall @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I50_J_0) ).

thf(700,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OSemi @ A @ B )
     != ( c_Com_Ocom_OCall @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(21,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCond @ A @ B @ C )
     != ( c_Com_Ocom_OLocal @ D @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I37_J_0) ).

thf(520,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCond @ A @ B @ C )
     != ( c_Com_Ocom_OLocal @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(295,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ A ) ) @ B @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ A @ C @ B @ D ) @ D )
      | ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ A ) @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_1) ).

thf(1171,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ A ) ) @ B @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ A @ C @ B @ D ) @ D )
      | ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ A ) @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(205,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ B @ C ) @ D @ E )
      | ~ ( c_Natural_Oevalc @ B @ D @ E )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OIfTrue_0) ).

thf(983,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ B @ C ) @ D @ E )
      | ~ ( c_Natural_Oevalc @ B @ D @ E )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(430,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(1474,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(328,axiom,
    ! [A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).

thf(1245,plain,
    ! [A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(154,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(868,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(120,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ E @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(780,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ E @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(268,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(1113,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(432,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

thf(1477,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(381,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

thf(1364,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(440,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
        = C )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__diff_0) ).

thf(1496,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
        = C )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(262,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

thf(1102,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(15,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ A @ B @ C )
      | ~ ( c_Natural_Oevaln @ A @ B @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__evalc_0) ).

thf(505,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ A @ B @ C )
      | ~ ( c_Natural_Oevaln @ A @ B @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(71,axiom,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).

thf(653,plain,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(177,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Com_Ocom_OBODY @ A )
     != ( c_Com_Ocom_OCall @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I62_J_0) ).

thf(922,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Com_Ocom_OBODY @ A )
     != ( c_Com_Ocom_OCall @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(115,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(768,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(137,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(827,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(297,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ B ) @ C ) @ D )
       != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ E ) @ F ) @ G ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).

thf(1176,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ B ) @ C ) @ D )
       != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ E ) @ F ) @ G ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(53,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(608,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(214,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

thf(1000,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(412,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__singleton_0) ).

thf(1435,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(79,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).

thf(675,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(81,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OSemi @ A @ B )
       != ( c_Com_Ocom_OSemi @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).

thf(680,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OSemi @ A @ B )
       != ( c_Com_Ocom_OSemi @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCond @ A @ B @ C )
     != c_Com_Ocom_OSKIP ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I15_J_0) ).

thf(663,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCond @ A @ B @ C )
     != c_Com_Ocom_OSKIP ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(342,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(1277,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(253,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OLocal @ A @ B @ C )
     != ( hAPP @ c_Com_Ocom_OBODY @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I40_J_0) ).

thf(1081,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OLocal @ A @ B @ C )
     != ( hAPP @ c_Com_Ocom_OBODY @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(223,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ B ) @ C ) @ D )
       != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ E ) @ F ) @ G ) )
      | ( D = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).

thf(1018,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ B ) @ C ) @ D )
       != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ E ) @ F ) @ G ) )
      | ( D = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_OWT @ A )
      | ~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I3_J_0) ).

thf(754,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_OWT @ A )
      | ~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(32,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_OWT @ A )
      | ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ B @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_0) ).

thf(553,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_OWT @ A )
      | ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ B @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(141,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Com_OWT @ A )
      | ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_0) ).

thf(836,plain,
    ! [B: $i,A: $i] :
      ( ( c_Com_OWT @ A )
      | ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(403,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).

thf(1413,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_OSome @ A @ B )
     != ( c_Option_Ooption_ONone @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).

thf(473,plain,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_OSome @ A @ B )
     != ( c_Option_Ooption_ONone @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(310,axiom,
    ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
    = ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).

thf(1203,plain,
    ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
    = ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(312,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ B ) @ C ) @ D )
       != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ E ) @ F ) @ G ) )
      | ( C = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).

thf(1208,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ B ) @ C ) @ D )
       != ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ E ) @ F ) @ G ) )
      | ( C = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(278,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
      | ( ( hAPP @ B @ E )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).

thf(1134,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
      | ( ( hAPP @ B @ E )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(487,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(197,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OSemi @ I @ J ) @ K )
      = ( hAPP @ ( hAPP @ D @ I ) @ J ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I67_J_0) ).

thf(968,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OSemi @ I @ J ) @ K )
      = ( hAPP @ ( hAPP @ D @ I ) @ J ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(299,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_Hoare__Mirabelle_Otriple__valid @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ B ) @ ( hAPP @ c_Com_Ocom_OBODY @ C ) ) @ D ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Body__triple__valid__0_0) ).

thf(1181,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_Hoare__Mirabelle_Otriple__valid @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ B ) @ ( hAPP @ c_Com_Ocom_OBODY @ C ) ) @ D ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(119,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OCond @ A @ B @ C )
       != ( c_Com_Ocom_OCond @ D @ E @ F ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_1) ).

thf(776,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OCond @ A @ B @ C )
       != ( c_Com_Ocom_OCond @ D @ E @ F ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(34,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OSemi @ A @ B )
     != ( c_Com_Ocom_OWhile @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I46_J_0) ).

thf(557,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OSemi @ A @ B )
     != ( c_Com_Ocom_OWhile @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(148,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ C @ A @ G @ H @ I @ J @ K @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).

thf(855,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ C @ A @ G @ H @ I @ J @ K @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(84,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
      = ( c_Set_Oimage @ ( c_COMBB @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__image_0) ).

thf(690,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
      = ( c_Set_Oimage @ ( c_COMBB @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(226,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

thf(1025,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(91,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

thf(707,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(383,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).

thf(1368,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(260,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_0) ).

thf(1098,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(210,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

thf(993,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(441,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(1499,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(124,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).

thf(791,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(302,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

thf(1186,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(45,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Collect @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).

thf(585,plain,
    ! [B: $i,A: $i] :
      ( ( c_Collect @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(143,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCall @ A @ B @ C )
     != c_Com_Ocom_OSKIP ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I21_J_0) ).

thf(840,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCall @ A @ B @ C )
     != c_Com_Ocom_OSKIP ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(368,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__partition_0) ).

thf(1336,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(317,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(1220,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(352,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(1300,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(420,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).

thf(1452,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(1,negated_conjecture,
    c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ v_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) ) @ v_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(470,plain,
    c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ v_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) ) @ v_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(41,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( c_lessequals @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A )
      | ~ ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__upper_0) ).

thf(576,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( c_lessequals @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A )
      | ~ ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(460,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OSemi @ A @ B )
     != ( hAPP @ c_Com_Ocom_OBODY @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).

thf(1538,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OSemi @ A @ B )
     != ( hAPP @ c_Com_Ocom_OBODY @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(188,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).

thf(951,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(29,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ c_Com_Ocom_OSKIP @ I )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I64_J_0) ).

thf(544,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ c_Com_Ocom_OSKIP @ I )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(171,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
        = B )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).

thf(907,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
        = B )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(103,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCond @ A @ B @ C )
     != ( c_Com_Ocom_OCall @ D @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I56_J_0) ).

thf(744,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCond @ A @ B @ C )
     != ( c_Com_Ocom_OCall @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(89,axiom,
    class_Lattices_Oupper__semilattice @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

thf(703,plain,
    class_Lattices_Oupper__semilattice @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(459,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

thf(1536,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(345,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
       != ( hAPP @ D @ ( hAPP @ E @ F ) ) )
      | ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ G @ H @ I ) @ C )
        = ( hAPP @ ( c_Fun_Ocomp @ D @ E @ J @ H @ K ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__cong_0) ).

thf(1284,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
       != ( hAPP @ D @ ( hAPP @ E @ F ) ) )
      | ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ G @ H @ I ) @ C )
        = ( hAPP @ ( c_Fun_Ocomp @ D @ E @ J @ H @ K ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(152,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(864,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(444,axiom,
    ! [B: $i,A: $i] :
      ( ( c_The @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the__sym__eq__trivial_0) ).

thf(1504,plain,
    ! [B: $i,A: $i] :
      ( ( c_The @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(281,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__insert_0) ).

thf(1140,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(39,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(571,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(48,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(595,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(12,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCall @ A @ B @ C )
     != ( c_Com_Ocom_OLocal @ D @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I43_J_0) ).

thf(497,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCall @ A @ B @ C )
     != ( c_Com_Ocom_OLocal @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(150,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
        = ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).

thf(859,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
        = ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(209,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__Un_0) ).

thf(991,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(72,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OWhile @ A @ B )
     != ( c_Com_Ocom_OLocal @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I39_J_0) ).

thf(656,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OWhile @ A @ B )
     != ( c_Com_Ocom_OLocal @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(225,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).

thf(1023,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(435,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(1485,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(238,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OWhile @ I @ J ) @ K )
      = ( hAPP @ ( hAPP @ F @ I ) @ J ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I69_J_0) ).

thf(1052,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OWhile @ I @ J ) @ K )
      = ( hAPP @ ( hAPP @ F @ I ) @ J ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(445,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).

thf(1506,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(340,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ A @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ D ) @ E ) @ B @ F )
      = ( hAPP @ ( hAPP @ ( hAPP @ A @ C ) @ D ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Orecs_0) ).

thf(1272,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ A @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ D ) @ E ) @ B @ F )
      = ( hAPP @ ( hAPP @ ( hAPP @ A @ C ) @ D ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(55,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
       != ( c_Com_Ocom_OLocal @ D @ E @ F ) )
      | ( C = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_2) ).

thf(612,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
       != ( c_Com_Ocom_OLocal @ D @ E @ F ) )
      | ( C = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(406,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ B @ A )
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).

thf(1421,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ B @ A )
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(6,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCall @ A @ B @ C )
     != ( c_Com_Ocom_OWhile @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I61_J_0) ).

thf(482,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCall @ A @ B @ C )
     != ( c_Com_Ocom_OWhile @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(288,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__mono_0) ).

thf(1157,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(43,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Com_OWT @ A )
      | ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_1) ).

thf(581,plain,
    ! [B: $i,A: $i] :
      ( ( c_Com_OWT @ A )
      | ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(164,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ A @ B @ D @ C @ G @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ A @ B @ D @ C ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ G ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).

thf(891,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ A @ B @ D @ C @ G @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ A @ B @ D @ C ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ G ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(347,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( c_Com_Ocom_OWhile @ D @ E ) ) @ ( c_Hoare__Mirabelle_Opeek__and @ C @ ( c_Fun_Ocomp @ c_Not @ D @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ ( c_Hoare__Mirabelle_Opeek__and @ C @ D @ B ) ) @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Loop_0) ).

thf(1289,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( c_Com_Ocom_OWhile @ D @ E ) ) @ ( c_Hoare__Mirabelle_Opeek__and @ C @ ( c_Fun_Ocomp @ c_Not @ D @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ ( c_Hoare__Mirabelle_Opeek__and @ C @ D @ B ) ) @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(117,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(771,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(266,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).

thf(1108,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(359,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( hAPP @ c_Com_Ocom_OBODY @ I ) @ J )
      = ( hAPP @ G @ I ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I70_J_0) ).

thf(1316,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( hAPP @ c_Com_Ocom_OBODY @ I ) @ J )
      = ( hAPP @ G @ I ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(254,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(1084,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(418,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
        = ( hAPP @ ( hAPP @ E @ B ) @ C ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).

thf(1448,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
        = ( hAPP @ ( hAPP @ E @ B ) @ C ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(303,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( hAPP @ c_Com_Ocom_OBODY @ D ) ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( hAPP @ c_Com_Ocom_OBODY @ D ) ) @ E ) @ A @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_BodyN_0) ).

thf(1189,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( hAPP @ c_Com_Ocom_OBODY @ D ) ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( hAPP @ c_Com_Ocom_OBODY @ D ) ) @ E ) @ A @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(363,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(1326,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(132,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OLocal @ A @ B @ C )
     != ( c_Com_Ocom_OCall @ D @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I42_J_0) ).

thf(813,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OLocal @ A @ B @ C )
     != ( c_Com_Ocom_OCall @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(20,axiom,
    ! [B: $i,A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OSemi @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).

thf(517,plain,
    ! [B: $i,A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OSemi @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(431,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(1476,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(370,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(1341,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(446,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ A @ B @ D @ C @ E @ F ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_2) ).

thf(1508,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ A @ B @ D @ C @ E @ F ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(70,axiom,
    class_Orderings_Opreorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(652,plain,
    class_Orderings_Opreorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(63,axiom,
    ! [A: $i] :
      ( A
     != ( c_Suc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

thf(632,plain,
    ! [A: $i] :
      ( A
     != ( c_Suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(211,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__fold1SetE_0) ).

thf(995,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(228,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__iff_2) ).

thf(1030,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(38,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).

thf(568,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(305,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

thf(1193,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(111,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_COMBI @ A ) @ B @ A @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__ident_0) ).

thf(763,plain,
    ! [B: $i,A: $i] :
      ( ( c_Set_Oimage @ ( c_COMBI @ A ) @ B @ A @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(168,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ D )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

thf(899,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ D )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(82,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCall @ A @ B @ C )
     != ( c_Com_Ocom_OCond @ D @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I57_J_0) ).

thf(684,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OCall @ A @ B @ C )
     != ( c_Com_Ocom_OCond @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(416,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBS @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ ( hAPP @ B @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBS__def_0) ).

thf(1444,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBS @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ ( hAPP @ B @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(235,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ D ) @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__WHILE__case_0) ).

thf(1045,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ D ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(251,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ C @ F ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ F @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__iff_2) ).

thf(1077,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ C @ F ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ F @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(5,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OWhile @ A @ B )
       != ( c_Com_Ocom_OWhile @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_1) ).

thf(478,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OWhile @ A @ B )
       != ( c_Com_Ocom_OWhile @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(94,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_Natural_Oevalc @ C @ D @ A )
      | ~ ( c_Natural_Oevalc @ C @ D @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com__det_0) ).

thf(716,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_Natural_Oevalc @ C @ D @ A )
      | ~ ( c_Natural_Oevalc @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(290,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ B @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ B @ E ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq1_0) ).

thf(1161,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ B @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ B @ E ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(58,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(620,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(448,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_Collect @ B @ A ) )
      | ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).

thf(1512,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_Collect @ B @ A ) )
      | ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(343,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(1280,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

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

thf(833,plain,
    class_HOL_Oord @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(321,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).

thf(1229,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(463,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

thf(1546,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(395,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( hAPP @ A @ B ) @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
      | ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ A @ F @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).

thf(1395,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( hAPP @ A @ B ) @ C @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
      | ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ A @ F @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(433,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ D ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

thf(1480,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ D ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(455,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ B @ G @ D @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ B @ G @ D @ E ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ G ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_1) ).

thf(1527,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ B @ G @ D @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ B @ G @ D @ E ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ G ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(284,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ C @ D @ C )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OWhileFalse_0) ).

thf(1148,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ A @ B ) @ C @ D @ C )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(130,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(807,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(240,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ E @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ D @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ D @ E ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq2_0) ).

thf(1056,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ E @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ D @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ D @ E ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(307,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(1197,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(245,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ A @ B @ D @ C @ G @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ A @ B @ D @ C ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ G ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_1) ).

thf(1065,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ A @ B @ D @ C @ G @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ A @ B @ D @ C ) ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ G ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(292,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ A @ B @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_escape_0) ).

thf(1165,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
      | ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ A @ B @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(190,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

thf(955,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(126,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Com_Ocom_OWhile @ A @ B )
     != c_Com_Ocom_OSKIP ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I17_J_0) ).

thf(796,plain,
    ! [B: $i,A: $i] :
      ( ( c_Com_Ocom_OWhile @ A @ B )
     != c_Com_Ocom_OSKIP ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(167,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ A @ B @ C )
      | ( hBOOL @ ( hAPP @ D @ B ) )
      | ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ D @ E @ A ) @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_0) ).

thf(897,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ A @ B @ C )
      | ( hBOOL @ ( hAPP @ D @ B ) )
      | ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ D @ E @ A ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(402,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).

thf(1410,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(114,axiom,
    c_Com_OWT @ c_Com_Ocom_OSKIP,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OSkip_0) ).

thf(767,plain,
    c_Com_OWT @ c_Com_Ocom_OSKIP,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(193,axiom,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Ominus @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).

thf(960,plain,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Ominus @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(64,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(635,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(162,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(886,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(179,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__empty_0) ).

thf(928,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(98,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OCond @ A @ B @ C )
       != ( c_Com_Ocom_OCond @ D @ E @ F ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_0) ).

thf(728,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OCond @ A @ B @ C )
       != ( c_Com_Ocom_OCond @ D @ E @ F ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(207,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ c_Com_Ocom_OBODY @ D ) ) @ ( hAPP @ E @ D ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
      | ~ ( hBOOL @ ( c_in @ D @ F @ tc_Com_Opname ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ E @ tc_Com_Opname @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ F @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ E @ tc_Com_Opname @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ F @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Body1_0) ).

thf(987,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ c_Com_Ocom_OBODY @ D ) ) @ ( hAPP @ E @ D ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
      | ~ ( hBOOL @ ( c_in @ D @ F @ tc_Com_Opname ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ E @ tc_Com_Opname @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ F @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) ) @ E @ tc_Com_Opname @ ( tc_fun @ B @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ F @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(376,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ D ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).

thf(1352,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ D ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(275,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

thf(1129,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(335,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) @ C @ D )
      | ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) @ E @ D )
      | ~ ( c_Natural_Oevalc @ B @ C @ E )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OWhileTrue_0) ).

thf(1261,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) @ C @ D )
      | ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) @ E @ D )
      | ~ ( c_Natural_Oevalc @ B @ C @ E )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(338,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

thf(1268,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(286,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

thf(1152,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(457,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( c_Com_Ocom_OCond @ D @ E @ F ) ) @ G ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ ( c_Hoare__Mirabelle_Opeek__and @ C @ ( c_Fun_Ocomp @ c_Not @ D @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ B ) ) @ F ) @ G ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ ( c_Hoare__Mirabelle_Opeek__and @ C @ D @ B ) ) @ E ) @ G ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_OIf_0) ).

thf(1532,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( c_Com_Ocom_OCond @ D @ E @ F ) ) @ G ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ ( c_Hoare__Mirabelle_Opeek__and @ C @ ( c_Fun_Ocomp @ c_Not @ D @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ B ) ) @ F ) @ G ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ ( c_Hoare__Mirabelle_Opeek__and @ C @ D @ B ) ) @ E ) @ G ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(388,axiom,
    ! [B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty_0) ).

thf(1378,plain,
    ! [B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(67,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(644,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(378,axiom,
    ! [A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( hAPP @ c_Com_Ocom_OBODY @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).

thf(1357,plain,
    ! [A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( hAPP @ c_Com_Ocom_OBODY @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(135,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(822,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(146,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(850,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(216,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(1004,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(397,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

thf(1399,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(361,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

thf(1320,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(184,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(940,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(301,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

thf(1184,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(73,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_ONone @ A )
     != ( c_Option_Ooption_OSome @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).

thf(659,plain,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_ONone @ A )
     != ( c_Option_Ooption_OSome @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(404,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ D @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__insert_0) ).

thf(1416,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ D @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(427,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).

thf(1468,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(199,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_weaken_0) ).

thf(972,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(182,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
        = B )
      | ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(935,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
        = B )
      | ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(219,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OCond @ I @ J @ K ) @ L )
      = ( hAPP @ ( hAPP @ ( hAPP @ E @ I ) @ J ) @ K ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I68_J_0) ).

thf(1009,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OCond @ I @ J @ K ) @ L )
      = ( hAPP @ ( hAPP @ ( hAPP @ E @ I ) @ J ) @ K ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(437,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OCall @ I @ J @ K ) @ L )
      = ( hAPP @ ( hAPP @ ( hAPP @ H @ I ) @ J ) @ K ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I71_J_0) ).

thf(1490,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_Ocom__case @ A @ B @ C @ D @ E @ F @ G @ H @ ( c_Com_Ocom_OCall @ I @ J @ K ) @ L )
      = ( hAPP @ ( hAPP @ ( hAPP @ H @ I ) @ J ) @ K ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(231,axiom,
    ( ( hAPP @ ( c_COMBK @ v_P @ t_a @ t_b ) @ v_Q )
    = v_P ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def__raw_0) ).

thf(1037,plain,
    ( ( hAPP @ ( c_COMBK @ v_P @ t_a @ t_b ) @ v_Q )
    = v_P ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(35,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ A @ B @ C @ D )
      | ( c_Natural_Oevaln @ E @ B @ C @ D )
      | ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ A ) @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_2) ).

thf(560,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Natural_Oevaln @ A @ B @ C @ D )
      | ( c_Natural_Oevaln @ E @ B @ C @ D )
      | ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ A ) @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(11,axiom,
    ! [A: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).

thf(496,plain,
    ! [A: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(247,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Option_Othe @ A ) @ ( c_Option_Ooption_OSome @ B @ A ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the_Osimps_0) ).

thf(1069,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Option_Othe @ A ) @ ( c_Option_Ooption_OSome @ B @ A ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(1693,plain,
    $false,
    inference(cvc4,[status(thm)],[1501,1369,760,1237,628,893,1315,962,1179,555,666,1549,1559,1105,1554,1110,977,1211,523,1005,1522,1544,677,1173,741,1073,873,1205,1305,597,1426,1137,1310,550,500,945,1063,1458,1342,747,913,538,1354,1222,930,1095,1441,1386,565,1529,1518,1243,1127,1482,1254,724,1287,1430,1298,719,785,1330,802,1313,1455,1191,587,1323,838,917,751,1462,1059,1132,902,638,1379,1087,1247,870,1347,881,1115,1494,1362,1100,1232,1013,770,1465,591,1040,1334,966,905,1302,756,1418,623,485,834,1383,574,956,866,1119,1526,998,1345,1433,1405,1201,507,527,602,981,766,1169,687,877,692,920,1438,546,925,1199,810,1470,534,1067,714,1163,512,942,1274,910,1021,862,1217,1487,630,788,847,1032,1365,625,879,1296,1159,493,1079,1392,1291,974,852,1555,583,830,1195,1407,1402,578,1143,1259,1534,1328,1138,610,783,989,1360,1350,697,1089,1234,1541,650,948,857,1397,471,884,1028,933,753,1182,669,1424,489,1214,1446,1016,1075,476,1039,970,985,1456,1266,1131,1552,1050,721,1002,647,1263,997,515,1150,1249,1451,738,503,605,1318,1241,541,1035,1071,1515,1167,530,953,1086,938,765,1054,773,794,662,888,1510,1146,1103,1374,1251,618,1219,824,1154,819,732,1389,958,1520,562,975,1007,694,843,1125,875,711,1256,1226,1503,1239,1332,1092,804,704,1224,672,641,1428,1271,1371,1058,1107,979,1408,1282,1117,1011,1524,1349,1492,1307,1048,736,509,1043,616,1122,599,1376,1439,1471,1557,535,816,799,895,964,915,1460,1293,1381,1061,758,1339,700,520,1171,983,1474,1245,868,780,1113,1477,1364,1496,1102,505,653,922,768,827,1176,608,1000,1435,675,680,663,1277,1081,1018,754,553,836,1413,473,1203,1208,1134,487,968,1181,776,557,855,690,1025,707,1368,1098,993,1499,791,1186,585,840,1336,1220,1300,1452,470,576,1538,951,544,907,744,703,1536,1284,864,1504,1140,571,595,497,859,991,656,1023,1485,1052,1506,1272,612,1421,482,1157,581,891,1289,771,1108,1316,1084,1448,1189,1326,813,517,1476,1341,1508,652,632,995,1030,568,1193,763,899,684,1444,1045,1077,478,716,1161,620,1512,1280,833,1229,1546,1395,1480,1527,1148,807,1056,1197,1065,1165,955,796,897,1410,767,960,635,886,928,728,987,1352,1129,1261,1268,1152,1532,1378,644,1357,822,850,1004,1399,1320,940,1184,659,1416,1468,972,935,1009,1490,1037,560,496,1069]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWV840-1 : TPTP v8.1.2. Released v4.1.0.
% 0.15/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n027.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Fri May 19 02:43:22 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.93/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.62/1.05  % [INFO] 	 Parsing done (207ms). 
% 1.62/1.06  % [INFO] 	 Running in sequential loop mode. 
% 2.19/1.25  % [INFO] 	 eprover registered as external prover. 
% 2.26/1.25  % [INFO] 	 cvc4 registered as external prover. 
% 2.26/1.26  % [INFO] 	 Scanning for conjecture ... 
% 2.46/1.36  % [INFO] 	 Found a conjecture and 467 axioms. Running axiom selection ... 
% 3.04/1.47  % [INFO] 	 Axiom selection finished. Selected 467 axioms (removed 0 axioms). 
% 3.40/1.60  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 3.40/1.61  % [INFO] 	 Type checking passed. 
% 3.40/1.61  % [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 ... 
% 9.63/3.23  % External prover 'cvc4' found a proof!
% 9.63/3.23  % [INFO] 	 Killing All external provers ... 
% 9.63/3.23  % Time passed: 2705ms (effective reasoning time: 2166ms)
% 9.63/3.23  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 9.63/3.23  % Axioms used in derivation (467): clsarity_nat__HOL_Oord, cls_com_Osimps_I55_J_0, cls_option_Oinject_0, cls_atLeastatMost__subset__iff_2, cls_the__sym__eq__trivial_0, cls_com_Osimps_I18_J_0, cls_Diff__iff_2, cls_bot__fun__eq_0, cls_WTs__elim__cases_I6_J_0, cls_Diff__cancel_0, cls_INT__extend__simps_I4_J_0, cls_asm_0, cls_subset__insert_1, cls_evaln_OWhileFalse_0, cls_sup__ge1_0, cls_image__constant_0, cls_insertE_0, cls_Un__Diff_0, cls_com_Osimps_I3_J_0, cls_equalityI_0, cls_Un__subset__iff_0, cls_Suc__inject_0, cls_order__eq__iff_0, cls_com_Osimps_I5_J_0, cls_COMBC__def_0, cls_subset__empty_1, cls_subset__image__iff_2, cls_Suc__n__not__n_0, cls_empty__is__image_1, cls_com_Osimps_I44_J_0, cls_com_Osimps_I14_J_0, cls_image__mono_0, cls_Un__empty__left_0, cls_le__funD_0, cls_sup__bot__right_0, cls_insert__code_1, cls_WT_OSemi_0, cls_le__SUPI_0, cls_WTs__elim__cases_I4_J_1, cls_inf__sup__aci_I6_J_0, cls_Un__upper1_0, cls_fold1Set__sing_1, cls_Un__commute_0, clsarity_fun__Orderings_Oorder, cls_COMBK__def_0, cls_UnCI_1, cls_complete__lattice_OSup__singleton_0, cls_conseq_0, cls_evaln__WHILE__case_0, cls_triple_Oinject_1, cls_evalc_OSemi_0, cls_empty__iff_0, cls_hoare__derivs_OBody_0, clsarity_bool__HOL_Ominus, cls_Diff__subset__conv_0, cls_option_Osimps_I2_J_0, cls_mem__def_1, clsarity_nat__Orderings_Olinorder, cls_com_Osimps_I56_J_0, cls_WT_OSkip_0, cls_Inf__lower_0, cls_insert__absorb_0, cls_com_Osimps_I7_J_1, cls_com_Osimps_I5_J_1, cls_evalc__WHILE__case_0, cls_conseq12_1, cls_K__record__comp_0, clsarity_fun__Lattices_Oupper__semilattice, cls_com_Osimps_I4_J_2, cls_le__sup__iff_0, cls_com_Osimps_I66_J_0, cls_com_Osimps_I43_J_0, cls_insert__iff_1, cls_COMBI__def__raw_0, cls_insert__subset_0, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_COMBB__def_0, cls_evaln_OSkip_0, cls_CollectI_0, cls_com_Osimps_I47_J_0, cls_subset__insert__iff_2, cls_WTs__elim__cases_I5_J_0, cls_Un__left__commute_0, cls_com_Osimps_I54_J_0, cls_evalc__elim__cases_I1_J_0, cls_hoare__derivs_OSkip_0, cls_contents__eq_0, cls_Min__singleton_0, cls_Comp_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_COMBS__def_0, cls_BodyN_0, cls_fold1__def_0, cls_com_Osimps_I45_J_0, cls_Collect__empty__eq_0, cls_Inf__singleton_0, cls_COMBC__def__raw_0, cls_UN__extend__simps_I1_J_0, cls_CollectD_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_evalc__elim__cases_I6_J_0, cls_le__supI_0, cls_triple_Ocases_0, cls_Un__subset__iff_1, cls_evaln__elim__cases_I5_J_1, cls_empty__is__image_0, cls_SUP__const_0, cls_rev__image__eqI_0, cls_right__minus__eq_0, cls_SUP1__I_0, cls_triple_Oinject_2, cls_le__supE_1, cls_UN__iff_2, cls_UN__extend__simps_I3_J_0, cls_order__eq__refl_0, cls_UN__absorb_0, clsarity_fun__Orderings_Obot, cls_le__iff__sup_0, cls_WTs__elim__cases_I4_J_0, cls_image__constant__conv_1, cls_triple__valid__Suc_0, cls_conseq1_1, cls_Un__absorb2_0, cls_atLeastatMost__subset__iff_3, cls_inf__sup__aci_I8_J_0, cls_Un__empty__right_0, cls_insert__ident_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_com_Osimps_I61_J_0, cls_sup__eq__bot__eq2_0, cls_com_Osimps_I37_J_0, cls_com_Osimps_I10_J_0, cls_Un__upper2_0, cls_conseq_2, cls_triple_Orecs_0, cls_UN__Un_0, cls_com_Osimps_I38_J_0, cls_Sup__singleton_0, cls_UN__constant_0, cls_not__None__eq_1, cls_com_Osimps_I48_J_0, cls_com_Osimps_I60_J_0, cls_hoare__derivs_Ointros_I6_J_0, cls_evalc_OWhileFalse_0, cls_com_Osimps_I6_J_0, cls_UnCI_0, cls_escape_0, cls_com_Osimps_I20_J_0, cls_complete__lattice_OInf__empty_0, cls_subset__iff_0, cls_insert__code_2, cls_com_Osimps_I58_J_0, clsarity_fun__HOL_Oord, cls_evalc_OSkip_0, cls_Diff__idemp_0, cls_subset__empty_0, cls_com_Osimps_I40_J_0, cls_com_Osimps_I21_J_0, cls_WTs__elim__cases_I8_J_0, cls_singleton__iff_1, cls_atLeastatMost__empty__iff_1, cls_rev__predicate1D_0, cls_le__iff__diff__le__0_0, cls_insert__Diff__single_0, cls_com_Osimps_I57_J_0, cls_image__insert_0, cls_com_Osimps_I64_J_0, cls_Suc__neq__Zero_0, cls_SUP1__iff_2, cls_atLeastatMost__empty__iff2_0, cls_COMBB__def__raw_0, cls_WT_OCall_0, cls_com_Osimps_I7_J_0, cls_Sup__binary_0, cls_the_Osimps_0, cls_doubleton__eq__iff_2, cls_evalc__elim__cases_I5_J_0, cls_UN__subset__iff_0, cls_diff__single__insert_0, cls_com_Osimps_I51_J_0, cls_evaln_OBody_0, clsarity_bool__Lattices_Oupper__semilattice, cls_evaln__elim__cases_I6_J_0, cls_Un__insert__left_0, cls_com_Osimps_I59_J_0, cls_subset__insert__iff_3, clsarity_nat__Orderings_Obot, cls_evaln_OSemi_0, cls_com__det_0, cls_set__eq__subset_2, cls_Un__mono_0, cls_insert__subset_1, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_com_Osimps_I50_J_0, cls_ex__in__conv_0, cls_sup__commute_0, cls_evalc_OBody_0, cls_evaln__elim__cases_I5_J_0, cls_Un__subset__iff_2, clsarity_fun__Lattices_Olattice, cls_com_Osimps_I69_J_0, cls_COMBK__def__raw_0, cls_linorder__linear_0, cls_Un__empty_0, cls_conseq12_2, cls_order__antisym_0, cls_com_Osimps_I2_J_0, cls_image__empty_0, cls_com_Osimps_I68_J_0, cls_evaln_OIfFalse_0, cls_com_Osimps_I46_J_0, cls_insert__is__Un_0, cls_com_Osimps_I19_J_0, cls_order__trans_0, cls_subset__trans_0, cls_atLeastAtMost__singleton_0, cls_double__diff_0, cls_com_Osimps_I3_J_1, cls_insertI1_0, cls_DiffI_0, cls_evaln_OWhileTrue_0, cls_le__supE_0, cls_empty__not__insert_0, cls_sup__assoc_0, cls_insert__Diff1_0, cls_image__constant__conv_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, clsarity_bool__Orderings_Opreorder, cls_singleton__conv_0, cls_diff__self_0, cls_Nitpick_OEx1__def_2, cls_hoare__derivs_Oinsert_0, cls_com_Osimps_I67_J_0, cls_the__eq__trivial_0, cls_empty__subsetI_0, cls_com_Osimps_I70_J_0, cls_doubleton__eq__iff_0, cls_Un__absorb1_0, cls_hoare__derivs_OIf_0, cls_Diff__insert2_0, cls_Sup__upper_0, cls_sup__least_0, cls_com_Osimps_I17_J_0, cls_image__ident_0, cls_atLeastatMost__subset__iff_0, cls_sup1E_0, cls_WTs__elim__cases_I3_J_0, cls_subset__refl_0, cls_Max__singleton_0, cls_WTs__elim__cases_I5_J_1, cls_singletonE_0, clsarity_nat__Orderings_Opreorder, clsarity_nat__Lattices_Olattice, cls_DiffE_0, cls_conseq2_1, cls_image__iff_2, cls_insertCI_0, cls_complete__lattice_OSup__binary_0, cls_Un__Diff__cancel_0, cls_complete__lattice_OInf__insert_0, cls_image__Un_0, cls_insert__Diff_0, cls_not__Some__eq_1, cls_image__diff__subset_0, cls_sup1CI_1, cls_complete__lattice_OInf__binary_0, cls_COMBS__def__raw_0, cls_com_Osimps_I34_J_0, cls_right__minus__eq_1, cls_order__eq__iff_2, cls_bot1E_0, cls_weaken_0, cls_Body1_0, cls_evalc_OWhileTrue_0, cls_hoare__derivs_Ointros_I6_J_2, cls_le__supI2_0, cls_fold1__singleton_0, cls_Un__Diff__cancel2_0, cls_Collect__def_0, cls_WT_OBody_0, cls_UN__constant_1, cls_insert__mono_0, cls_eval__eq_1, cls_o__eq__dest_0, cls_Un__assoc_0, cls_empty__fold1SetE_0, cls_bex__empty_0, cls_inf__sup__ord_I4_J_0, cls_o__eq__dest__lhs_0, cls_com_Osimps_I42_J_0, cls_Diff__mono_0, cls_nat_Oinject_0, cls_order__antisym__conv_0, cls_com_Osimps_I2_J_1, cls_UnE_0, cls_subset__insertI2_0, cls_doubleton__eq__iff_3, cls_conseq_1, cls_atLeastatMost__empty__iff_0, cls_complete__lattice_Odual__complete__lattice_0, cls_com_Osimps_I13_J_0, cls_Un__absorb_0, clsarity_bool__Lattices_Olattice, cls_subset__insert__iff_4, cls_com_Osimps_I49_J_0, cls_evaln__Suc_0, clsarity_bool__Lattices_Obounded__lattice, cls_bot__empty__eq_0, cls_eq__eqI_0, cls_nat_Osimps_I2_J_0, cls_Zero__neq__Suc_0, cls_com_Osimps_I12_J_0, cls_complete__lattice_OInf__lower_0, cls_com_Osimps_I36_J_0, cls_le__eqI_0, cls_WT_OIf_0, cls_sup__left__idem_0, cls_complete__lattice_OSup__insert_0, cls_thin_0, cls_subsetD_0, cls_Body__triple__valid__Suc_0, cls_insert__not__empty_0, cls_le__sup__iff_2, clsarity_fun__Lattices_Obounded__lattice, cls_insert__subset_2, cls_com_Osimps_I35_J_0, cls_evaln__elim__cases_I6_J_1, cls_le__supI1_0, cls_o__def_0, clsarity_fun__Complete__Lattice_Ocomplete__lattice, cls_insert__absorb2_0, cls_sup__fun__eq_0, cls_UNION__empty__conv_I1_J_0, cls_subset__singletonD_0, cls_com_Osimps_I52_J_0, cls_UN__I_0, cls_doubleton__eq__iff_1, cls_UN__extend__simps_I2_J_0, cls_fun__diff__def_0, cls_Sup__insert_0, cls_diff__0__right_0, cls_xt1_I6_J_0, cls_subset__insert__iff_0, cls_empty_0, cls_complete__lattice_OInf__singleton_0, cls_Sup__empty_0, cls_Nitpick_OEx1__def_3, cls_nat_Osimps_I3_J_0, clsarity_bool__Complete__Lattice_Ocomplete__lattice, cls_Diff__empty_0, cls_Un__left__absorb_0, cls_evaln__evalc_0, cls_empty__Collect__eq_0, cls_atLeastatMost__subset__iff_1, cls_comp__cong_0, cls_evalc__elim__cases_I5_J_2, cls_inf__sup__ord_I3_J_0, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_inf__sup__aci_I5_J_0, cls_singleton__inject_0, cls_triple_Oinject_0, cls_Un__empty_1, cls_subset__insert_0, cls_sup__idem_0, cls_evaln_OIfTrue_0, clsarity_nat__Lattices_Oupper__semilattice, cls_emptyE_0, cls_eq__eqI_1, cls_com_Osimps_I4_J_1, cls_evaln__elim__cases_I1_J_0, cls_insert__def_0, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_UN__upper_0, cls_Un__least_0, cls_option_Osimps_I3_J_0, cls_sup1CI_0, cls_Loop_0, cls_conseq2_0, cls_hoare__derivs_Ointros_I6_J_1, cls_sup__ge2_0, clsarity_fun__Orderings_Opreorder, cls_atLeastatMost__empty__iff2_1, cls_triple_Osplit_0, cls_n__not__Suc__n_0, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_fold1Set__sing_0, cls_com_Osimps_I41_J_0, cls_insertCI_1, cls_complete__lattice_OSup__upper_0, cls_Nitpick_OThe__psimp_0, cls_image__eqI_0, cls_eq__iff__diff__eq__0_1, cls_image__subset__iff_0, cls_class__ringb_Osubr0__iff_1, cls_doubleton__eq__iff_4, cls_Body__triple__valid__0_0, cls_insert__code_0, cls_le__eqI_1, cls_subset__insertI_0, cls_le__iff__diff__le__0_1, cls_DiffE_1, cls_complete__lattice_OSup__empty_0, cls_Diff__subset__conv_1, cls_conseq12_0, cls_triple_Osplit__asm_0, cls_evalc_OIfFalse_0, cls_Diff__partition_0, cls_UNION__empty__conv_I2_J_0, cls_sup__bot__left_0, cls_insert__image_0, cls_evaln__elim__cases_I5_J_2, cls_COMBI__def_0, cls_eq__iff__diff__eq__0_0, cls_insert__commute_0, cls_insert__iff_2, cls_image__image_0, cls_Diff__insert__absorb_0, cls_evalc__elim__cases_I5_J_1, cls_com_Osimps_I16_J_0, cls_com_Osimps_I15_J_0, cls_class__ringb_Osubr0__iff_0, clsarity_nat__Orderings_Oorder, cls_image__compose_0, cls_image__is__empty_0, cls_UN__insert_0, cls_Un__insert__right_0, cls_com_Osimps_I2_J_2, cls_equalityE_0, cls_com_Osimps_I63_J_0, cls_com_Osimps_I11_J_0, cls_cut_0, clsarity_fun__HOL_Ominus, cls_triple__valid__def2_0, cls_com_Osimps_I53_J_0, cls_com_Osimps_I39_J_0, cls_imageI_0, cls_WT_OLocal_0, cls_com_Osimps_I4_J_0, cls_evalc_OIfTrue_0, cls_o__apply_0, cls_sup__absorb1_0, cls_Body__triple__valid__Suc_1, cls_ball__empty_0, cls_UN__empty2_0, cls_empty__Diff_0, cls_o__assoc_0, cls_com_Osimps_I71_J_0, cls_subset__insert__iff_1, cls_escape_1, cls_singleton__conv2_0, cls_com_Osimps_I62_J_0, cls_While_0, cls_Diff__subset_0, cls_conseq1_0, cls_predicate1D_0, clsarity_nat__HOL_Ominus, cls_com_Osimps_I7_J_2
% 9.63/3.23  % No. of inferences in proof: 939
% 9.63/3.23  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2705 ms resp. 2166 ms w/o parsing
% 10.66/3.41  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.66/3.41  % [INFO] 	 Killing All external provers ... 
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