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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWV913-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 09:01:01 AM UTC 2026

% Result   : Unsatisfiable 19.68s 5.50s
% Output   : Refutation 21.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  521
% Syntax   : Number of formulae    : 1043 ( 257 unt;   0 typ;   0 def)
%            Number of atoms       : 2335 ( 598 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 19616 (1204   ~;1292   |;   0   &;17120   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   79 (  77 usr;   6 con; 0-9 aty)
%            Number of variables   : 4000 (   0   ^;4000   !;   0   ?;4000   :)

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

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

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

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

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

thf(v_t_decl,type,
    v_t: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(class_Lattices_Olower__semilattice_decl,type,
    class_Lattices_Olower__semilattice: $i > $o ).

thf(c_Finite__Set_Ofun__left__comm__idem_decl,type,
    c_Finite__Set_Ofun__left__comm__idem: $i > $i > $i > $o ).

thf(c_Lattices_Olower__semilattice__class_Oinf_decl,type,
    c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).

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

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

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

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

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

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

thf(c_Finite__Set_Ofold1_decl,type,
    c_Finite__Set_Ofold1: $i > $i > $i > $i ).

thf(c_Finite__Set_Ofold1Set_decl,type,
    c_Finite__Set_Ofold1Set: $i > $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

thf(c_Fun_Oinj__on_decl,type,
    c_Fun_Oinj__on: $i > $i > $i > $i > $o ).

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

thf(c_Set_Ovimage_decl,type,
    c_Set_Ovimage: $i > $i > $i > $i ).

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

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

thf(c_Orderings_Olinorder_decl,type,
    c_Orderings_Olinorder: $i > $i > $i > $o ).

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

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

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

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

thf(c_SetInterval_Oord_OatLeastAtMost_decl,type,
    c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).

thf(c_Orderings_Oorder_decl,type,
    c_Orderings_Oorder: $i > $i > $i > $o ).

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

thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3_decl,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_decl,type,
    v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2: $i > $i > $i > $i > $i ).

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

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

thf(v_sko__Hoare__Mirabelle__Xconseq12__1_decl,type,
    v_sko__Hoare__Mirabelle__Xconseq12__1: $i > $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xconseq12__2_decl,type,
    v_sko__Hoare__Mirabelle__Xconseq12__2: $i > $i > $i > $i > $i ).

thf(c_OrderedGroup_Oab__semigroup__mult_decl,type,
    c_OrderedGroup_Oab__semigroup__mult: $i > $i > $o ).

thf(v_sko__Hoare__Mirabelle__Xconseq2__1_decl,type,
    v_sko__Hoare__Mirabelle__Xconseq2__1: $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xconseq2__2_decl,type,
    v_sko__Hoare__Mirabelle__Xconseq2__2: $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1_decl,type,
    v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1: $i > $i > $i > $i > $i ).

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

thf(class_Lattices_Odistrib__lattice_decl,type,
    class_Lattices_Odistrib__lattice: $i > $o ).

thf(v_sko__Hoare__Mirabelle__Xconseq1__1_decl,type,
    v_sko__Hoare__Mirabelle__Xconseq1__1: $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xconseq1__2_decl,type,
    v_sko__Hoare__Mirabelle__Xconseq1__2: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1_decl,type,
    c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2_decl,type,
    c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2: $i > $i > $i ).

thf(c_Nitpick_Osko__Nitpick__XEx1__def__1__3_decl,type,
    c_Nitpick_Osko__Nitpick__XEx1__def__1__3: $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xconseq12__3_decl,type,
    v_sko__Hoare__Mirabelle__Xconseq12__3: $i > $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xescape__1_decl,type,
    v_sko__Hoare__Mirabelle__Xescape__1: $i > $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xescape__2_decl,type,
    v_sko__Hoare__Mirabelle__Xescape__2: $i > $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3_decl,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_decl,type,
    v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2: $i > $i > $i > $i > $i ).

thf(c_Hoare__Mirabelle_Ohoare__valids_decl,type,
    c_Hoare__Mirabelle_Ohoare__valids: $i > $i > $i > $o ).

thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1_decl,type,
    v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1: $i > $i > $i > $i > $i ).

thf(225,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_in ) ) @ hBOOL )
      | ( ( E @ ( B @ hAPP ) )
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).

thf(1036,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ c_in ) ) @ hBOOL )
      | ( ( E @ ( B @ hAPP ) )
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(429,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).

thf(1501,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(355,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( F @ ( E @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 ) ) ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_2) ).

thf(1337,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( F @ ( E @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 ) ) ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(41,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

thf(629,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(370,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

thf(1369,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(408,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

thf(1454,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(488,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).

thf(1633,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(166,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

thf(909,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Nitpick_Osko__Nitpick__XEx1__def__1__3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).

thf(941,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Nitpick_Osko__Nitpick__XEx1__def__1__3 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(338,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Oorder ) ) )
      | ( B = C )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Oneq__le__trans_0) ).

thf(1295,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Oorder ) ) )
      | ( B = C )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(312,axiom,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).

thf(1237,plain,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(139,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).

thf(846,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(198,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).

thf(977,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(211,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).

thf(1005,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(471,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(1596,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(63,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_Onot__less__iff__gr__or__eq_1) ).

thf(683,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(439,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(1522,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(403,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).

thf(1443,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(481,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( E @ ( D @ ( G @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( G @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__3 ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_1) ).

thf(1618,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( E @ ( D @ ( G @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( G @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__3 ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(207,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

thf(994,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(384,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ ( E @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_0) ).

thf(1401,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ ( E @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(459,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(1569,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(297,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(1205,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(469,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C = D )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

thf(1591,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C = D )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(269,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Oorder ) ) )
      | ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Oantisym__conv_0) ).

thf(1142,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Oorder ) ) )
      | ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(153,axiom,
    tc_bool @ class_Orderings_Obot,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(878,plain,
    tc_bool @ class_Orderings_Obot,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(400,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

thf(1437,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(423,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( C @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).

thf(1486,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( C @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(22,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(582,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(101,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).

thf(762,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(34,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( C @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).

thf(614,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( C @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(513,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ c_COMBB ) ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I3_J_0) ).

thf(1692,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ c_COMBB ) ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(345,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( C = B )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_OneqE_0) ).

thf(1310,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( C = B )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(330,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).

thf(1275,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(310,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(1233,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(124,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__left__commute_0) ).

thf(814,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(491,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( F @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__I_0) ).

thf(1640,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( F @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(410,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).

thf(1458,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(58,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

thf(670,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(323,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

thf(1260,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(70,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( G @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 ) ) ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_1) ).

thf(698,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( G @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 ) ) ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(94,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).

thf(747,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(168,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( C @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI_0) ).

thf(913,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( C @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(432,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).

thf(1507,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(304,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ c_COMBB ) ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I1_J_0) ).

thf(1222,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ c_COMBB ) ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(293,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_1) ).

thf(1196,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(380,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).

thf(1391,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(76,axiom,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_Set_Oinsert @ c_Finite__Set_Ofun__left__comm__idem ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__left__comm__idem__insert_0) ).

thf(709,plain,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_Set_Oinsert @ c_Finite__Set_Ofun__left__comm__idem ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(136,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).

thf(841,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(495,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).

thf(1650,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(365,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).

thf(1359,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(417,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).

thf(1475,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(368,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(1366,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(442,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__insert_0) ).

thf(1529,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(437,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).

thf(1518,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(50,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

thf(651,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(109,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).

thf(782,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(402,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(1441,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(473,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).

thf(1601,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(378,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Oeq__iff_2) ).

thf(1386,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(307,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).

thf(1228,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(421,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(1482,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(320,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_fequal ) @ c_Collect ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).

thf(1254,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_fequal ) @ c_Collect ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(486,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( D @ ( A @ ( C @ ( B @ c_Set_Oimage ) ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

thf(1628,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( D @ ( A @ ( C @ ( B @ c_Set_Oimage ) ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(520,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__subset__iff_0) ).

thf(1709,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(339,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

thf(1298,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(81,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

thf(719,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(325,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).

thf(1264,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(24,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(587,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofun__left__comm__idem ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__left__comm__idem__inf_0) ).

thf(542,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofun__left__comm__idem ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(233,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_fequal ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

thf(1055,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_fequal ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(83,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ofold1 ) ) )
        = F )
      | ~ ( C @ ( B @ ( A @ c_Orderings_Olinorder ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_OMax__singleton_0) ).

thf(724,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ofold1 ) ) )
        = F )
      | ~ ( C @ ( B @ ( A @ c_Orderings_Olinorder ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(434,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
      = ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).

thf(1511,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
      = ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(170,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( E @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ c_COMBB ) ) ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I3_J_1) ).

thf(917,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( E @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ c_COMBB ) ) ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(96,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weaken_0) ).

thf(751,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(346,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

thf(1313,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(332,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).

thf(1279,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(448,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).

thf(1545,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(125,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

thf(817,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(142,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_Oless__linear_0) ).

thf(853,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(246,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).

thf(1087,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(271,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(1147,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(317,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(1247,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(477,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Olinorder ) ) )
      | ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv1_0) ).

thf(1609,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Olinorder ) ) )
      | ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(104,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__binary_0) ).

thf(770,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(309,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( c_Com_Ocom_OSKIP @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).

thf(1232,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( c_Com_Ocom_OSKIP @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(348,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_OleD_0) ).

thf(1319,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(518,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).

thf(1704,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(413,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( C @ ( B @ ( E @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
       != ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).

thf(1465,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( C @ ( B @ ( E @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
       != ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(341,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(1302,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(406,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

thf(1450,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(48,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_The ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OThe__psimp_0) ).

thf(646,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_The ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(178,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).

thf(937,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(507,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

thf(1677,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(120,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).

thf(806,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(231,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).

thf(1051,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(424,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).

thf(1489,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(390,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(1415,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(509,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( C @ ( D @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_1) ).

thf(1682,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( C @ ( D @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(267,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( A @ ( C @ ( D @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( A @ ( C @ ( E @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).

thf(1136,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( A @ ( C @ ( D @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( A @ ( C @ ( E @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(133,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).

thf(834,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(287,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Fun_Oinj__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).

thf(1183,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Fun_Oinj__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(334,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

thf(1283,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(200,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = B )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).

thf(981,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = B )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(301,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( F @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

thf(1215,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( F @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(67,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_Finite__Set_Ofinite ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UN_0) ).

thf(692,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_Finite__Set_Ofinite ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(88,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Oorder ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Ole__less_1) ).

thf(734,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Oorder ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(188,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(956,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(148,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

thf(866,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(240,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

thf(1072,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(361,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(1351,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(204,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).

thf(988,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(398,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( F @ ( D @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( F @ ( E @ c_lessequals ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).

thf(1433,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( F @ ( D @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( F @ ( E @ c_lessequals ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(386,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).

thf(1405,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(295,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( B @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( B @ ( D @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).

thf(1201,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( B @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( B @ ( D @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(281,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(1169,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(65,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( A @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).

thf(687,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( A @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(260,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

thf(1119,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(483,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).

thf(1622,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(515,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).

thf(1697,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(315,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( C @ c_in ) ) @ hBOOL )
      | ( ( E @ ( A @ ( D @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
        = ( E @ ( A @ ( D @ ( B @ c_Set_Oimage ) ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

thf(1242,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( C @ c_in ) ) @ hBOOL )
      | ( ( E @ ( A @ ( D @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
        = ( E @ ( A @ ( D @ ( B @ c_Set_Oimage ) ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(171,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(920,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(61,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( I @ ( C @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).

thf(678,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( I @ ( C @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(3,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(529,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold1SetE_0) ).

thf(793,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(173,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

thf(925,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(343,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

thf(1306,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(294,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( B @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
      = ( F @ ( C @ ( E @ ( E @ ( C @ ( B @ ( D @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).

thf(1199,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( B @ ( E @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
      = ( F @ ( C @ ( E @ ( E @ ( C @ ( B @ ( D @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(122,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).

thf(810,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
     != c_Com_Ocom_OSKIP ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).

thf(534,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
     != c_Com_Ocom_OSKIP ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(238,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = B )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).

thf(1067,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = B )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(79,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).

thf(714,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(489,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).

thf(1636,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(229,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( A @ c_Collect ) @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectD_0) ).

thf(1047,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( A @ c_Collect ) @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(278,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).

thf(1163,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(160,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A @ ( B @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMax ) @ c_in ) ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__in_0) ).

thf(894,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A @ ( B @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMax ) @ c_in ) ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(128,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

thf(825,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(262,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

thf(1123,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(283,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).

thf(1174,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(126,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_0) ).

thf(820,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(112,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(788,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(85,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

thf(729,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(218,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ c_COMBB ) ) ) ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UN__distrib_0) ).

thf(1021,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ c_COMBB ) ) ) ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).

thf(778,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(227,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ c_COMBB ) ) ) ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_1) ).

thf(1042,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ c_COMBB ) ) ) ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(185,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).

thf(952,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(363,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__subset__iff_1) ).

thf(1355,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(464,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).

thf(1580,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(302,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ononempty__iff_2) ).

thf(1217,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(28,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).

thf(598,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(13,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) )
       != ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__eq__iff_0) ).

thf(561,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) )
       != ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(502,axiom,
    tc_bool @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(1666,plain,
    tc_bool @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(393,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).

thf(1423,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(15,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(566,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(39,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_Oneq__iff_1) ).

thf(625,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(154,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__commute_0) ).

thf(879,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(452,axiom,
    tc_bool @ class_Lattices_Oupper__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

thf(1555,plain,
    tc_bool @ class_Lattices_Oupper__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(285,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

thf(1178,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(56,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(665,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(511,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).

thf(1687,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(484,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(1624,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(158,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) )
      = ( E @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).

thf(889,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) )
      = ( E @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(276,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_0) ).

thf(1159,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(299,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( C @ c_Orderings_Olinorder ) ) )
      | ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv1_1) ).

thf(1210,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( C @ c_Orderings_Olinorder ) ) )
      | ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(99,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(757,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(77,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).

thf(710,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(461,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(1573,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(214,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( C @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_OatLeastatMost__empty_0) ).

thf(1012,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( C @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(254,axiom,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).

thf(1106,plain,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(1,negated_conjecture,
    ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_t @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_t @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(522,plain,
    ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_t @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_t @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(131,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(830,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(243,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

thf(1079,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(221,axiom,
    tc_bool @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(1027,plain,
    tc_bool @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_fequal ) @ c_The ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__sym__eq__trivial_0) ).

thf(551,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_fequal ) @ c_The ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(264,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( F @ ( D @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( F @ ( E @ c_lessequals ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
        = ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).

thf(1128,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( F @ ( D @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( F @ ( E @ c_lessequals ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
        = ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(151,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).

thf(874,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(183,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(948,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(216,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).

thf(1017,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(237,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
     != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

thf(1064,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
     != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(257,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

thf(1111,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(467,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(1587,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(394,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).

thf(1425,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(250,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_escape_0) ).

thf(1096,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(458,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ c_Collect ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_0) ).

thf(1567,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ c_Collect ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(426,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

thf(1493,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(366,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) )
      = ( E @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).

thf(1361,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) )
      = ( E @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(499,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(1659,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(337,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( B = C )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).

thf(1292,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( B = C )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(97,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__Un_0) ).

thf(753,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(6,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).

thf(537,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(404,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).

thf(1446,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(493,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

thf(1644,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(156,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(884,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(352,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).

thf(1329,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(222,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).

thf(1028,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(244,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).

thf(1082,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(163,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I4_J_0) ).

thf(901,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(241,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).

thf(1075,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(298,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( F @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( E @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ c_COMBB ) ) ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert__distrib_0) ).

thf(1207,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( F @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( E @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ c_COMBB ) ) ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(25,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(590,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(478,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

thf(1612,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(226,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

thf(1039,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(195,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(970,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(38,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( C @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).

thf(622,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( C @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(208,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = ( D @ ( A @ hAPP ) @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).

thf(997,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = ( D @ ( A @ hAPP ) @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(72,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

thf(701,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(326,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__upper_0) ).

thf(1266,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(291,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(1192,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(235,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).

thf(1060,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(82,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

thf(721,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(210,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_0) ).

thf(1002,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(350,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

thf(1324,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(258,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(1114,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(468,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(1588,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(202,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).

thf(985,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(272,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).

thf(1150,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( B @ ( D @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(419,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(1478,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(407,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMax ) @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMax ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__mono_0) ).

thf(1451,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMax ) @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMax ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(90,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).

thf(738,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(446,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ c_Collect ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).

thf(1539,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ c_Collect ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(409,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( A @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_lessequals ) ) )
      | ~ ( F @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).

thf(1456,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( A @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_lessequals ) ) )
      | ~ ( F @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(376,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_Olinear_0) ).

thf(1382,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(265,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Olinorder__class_OMin ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__singleton_0) ).

thf(1131,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Olinorder__class_OMin ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(51,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Obounded__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

thf(654,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Obounded__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(201,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

thf(984,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(167,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_thin_0) ).

thf(911,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(16,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(569,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(396,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( C @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_0) ).

thf(1429,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( C @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(30,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(605,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(381,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).

thf(1393,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(314,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).

thf(1241,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ hAPP ) )
        = ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_HOL_Ominus ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).

thf(633,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ hAPP ) )
        = ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_HOL_Ominus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(456,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).

thf(1563,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(232,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).

thf(1054,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(335,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).

thf(1286,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(501,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

thf(1663,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(480,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( E @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ c_COMBB ) ) ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I5_J_0) ).

thf(1616,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( E @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ c_COMBB ) ) ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(105,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ofold1 ) ) )
        = ( A @ ( C @ ( D @ c_Finite__Set_Ofold1 ) ) @ ( A @ ( B @ ( D @ c_Finite__Set_Ofold1 ) ) @ ( D @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ ( D @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__Un_0) ).

thf(773,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ c_Finite__Set_Ofold1 ) ) )
        = ( A @ ( C @ ( D @ c_Finite__Set_Ofold1 ) ) @ ( A @ ( B @ ( D @ c_Finite__Set_Ofold1 ) ) @ ( D @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ ( D @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(54,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

thf(662,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(36,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( C @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).

thf(618,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( C @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(508,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( C @ ( B @ c_Collect ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectI_0) ).

thf(1680,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( C @ ( B @ c_Collect ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(253,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

thf(1103,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(329,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( G @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 ) ) ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).

thf(1273,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( G @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 ) ) ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(143,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).

thf(856,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(93,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(745,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofun__left__comm__idem ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__left__comm__idem__sup_0) ).

thf(573,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofun__left__comm__idem ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(66,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

thf(689,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(372,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( D @ hAPP ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert_0) ).

thf(1374,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( D @ hAPP ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(487,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ ( B @ c_Set_Oimage ) ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).

thf(1631,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( C @ ( B @ c_Set_Oimage ) ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(193,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).

thf(965,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(433,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).

thf(1510,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(87,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Ominus )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).

thf(732,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Ominus )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(379,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( E @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( E @ ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).

thf(1389,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( E @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( E @ ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(137,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

thf(843,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(482,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).

thf(1620,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(496,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( D @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( B @ ( A @ ( C @ c_Fun_Oinj__on ) ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).

thf(1652,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( D @ ( B @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( B @ ( A @ ( C @ c_Fun_Oinj__on ) ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(92,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).

thf(743,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(444,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

thf(1535,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(438,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).

thf(1520,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(23,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(584,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(274,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).

thf(1154,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(164,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( B @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 ) @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_0) ).

thf(904,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( B @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 ) @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(197,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__3 ) ) ) @ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_2) ).

thf(975,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__3 ) ) ) @ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(212,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).

thf(1007,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(68,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(694,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(152,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(875,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(129,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(826,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(20,axiom,
    ! [B: $i,A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( B @ ( A @ c_Com_Ocom_OSemi ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).

thf(577,plain,
    ! [B: $i,A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( B @ ( A @ c_Com_Ocom_OSemi ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(189,axiom,
    ! [B: $i,A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Nitpick_Osko__Nitpick__XEx1__def__1__3 ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).

thf(958,plain,
    ! [B: $i,A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Nitpick_Osko__Nitpick__XEx1__def__1__3 ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(385,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( G @ ( A @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( F @ ( E @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_OatLeastatMost__subset__iff_3) ).

thf(1403,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( G @ ( A @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( F @ ( E @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(321,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).

thf(1256,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(306,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).

thf(1226,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(46,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(641,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(519,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).

thf(1707,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(328,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(1271,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(33,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( C @ ( B @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( B @ ( B @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( C @ ( B @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).

thf(611,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( C @ ( B @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( B @ ( B @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( C @ ( B @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(313,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__2 ) @ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__1 ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq2_1) ).

thf(1239,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__2 ) @ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__1 ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(353,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

thf(1332,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(247,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

thf(1090,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(322,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

thf(1258,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(506,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(1675,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(59,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = E )
      | ( B = E )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

thf(672,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = E )
      | ( B = E )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(268,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(1139,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(430,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(1503,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(234,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__2 ) @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__1 ) @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq1_1) ).

thf(1058,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__2 ) @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__1 ) @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(255,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(1107,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(490,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( C @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).

thf(1638,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( C @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(305,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_2) ).

thf(1224,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(292,axiom,
    ( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
    = ( t_a @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).

thf(1194,plain,
    ( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
    = ( t_a @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(333,axiom,
    tc_bool @ class_HOL_Ominus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).

thf(1282,plain,
    tc_bool @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(110,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).

thf(784,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(440,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).

thf(1524,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(89,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).

thf(736,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(360,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(1349,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(205,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(990,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(447,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(1542,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(512,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( C @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).

thf(1690,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( C @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(146,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(863,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(102,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = E )
      | ( C = D )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

thf(764,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = E )
      | ( C = D )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(199,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(979,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(62,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

thf(681,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(387,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

thf(1408,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(425,axiom,
    ! [B: $i,A: $i] : ( A @ ( B @ ( A @ c_fequal ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

thf(1492,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( A @ c_fequal ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(474,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).

thf(1603,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(35,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(616,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(261,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ hAPP ) @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).

thf(1122,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ hAPP ) @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(460,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( F @ ( E @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 ) ) ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).

thf(1571,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( F @ ( E @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 ) ) ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(373,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).

thf(1376,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(401,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Ofold1 ) ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).

thf(1439,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Ofold1 ) ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(503,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).

thf(1667,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(415,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

thf(1471,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(42,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Set_Ocontents ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_contents__eq_0) ).

thf(631,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Set_Ocontents ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(356,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( B @ ( E @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

thf(1339,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( B @ ( E @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(144,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_2) ).

thf(858,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( B @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(32,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( C @ ( A @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__belowI_0) ).

thf(609,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( C @ ( A @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(117,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__2 ) @ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__1 ) @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq2_0) ).

thf(799,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__2 ) @ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__1 ) @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(169,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( G @ ( D @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( F @ ( E @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( F @ ( E @ ( D @ c_Com_Ocom_OSemi ) @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comp_0) ).

thf(915,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( G @ ( D @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( F @ ( E @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( F @ ( E @ ( D @ c_Com_Ocom_OSemi ) @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(358,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

thf(1344,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(57,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

thf(668,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(176,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( B = E )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

thf(932,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( B = E )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(140,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(848,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(71,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

thf(700,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(453,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

thf(1556,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(411,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

thf(1460,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(382,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( A @ c_Orderings_Oorder ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_OatLeastatMost__empty__iff_0) ).

thf(1396,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( A @ c_Orderings_Oorder ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(190,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( F @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( F @ ( C @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__iff_2) ).

thf(959,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( F @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( F @ ( C @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(149,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

thf(868,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(108,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(780,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(215,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).

thf(1015,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(284,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

thf(1176,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(209,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( F @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( F @ ( C @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__I_0) ).

thf(1000,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( F @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( F @ ( C @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(418,axiom,
    tc_bool @ class_HOL_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(1477,plain,
    tc_bool @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(318,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).

thf(1250,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(427,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ c_COMBB ) ) ) ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_1) ).

thf(1496,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ c_COMBB ) ) ) ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(141,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(851,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(64,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).

thf(685,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(282,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__absorb_0) ).

thf(1171,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(470,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) )
      = ( E @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).

thf(1594,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) )
      = ( E @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(516,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv2_0) ).

thf(1699,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(44,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( E @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ c_COMBB ) ) ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I1_J_1) ).

thf(636,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( E @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ c_COMBB ) ) ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(316,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(1245,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(514,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).

thf(1694,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(172,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Oantisym_0) ).

thf(922,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(60,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = ( D @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).

thf(675,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = ( D @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(342,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut_0) ).

thf(1304,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(280,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).

thf(1166,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(296,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_asm_0) ).

thf(1203,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(181,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( E @ ( C @ ( D @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).

thf(944,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( E @ ( C @ ( D @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(115,axiom,
    tc_bool @ class_Lattices_Obounded__lattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

thf(795,plain,
    tc_bool @ class_Lattices_Obounded__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(55,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).

thf(663,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(392,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

thf(1420,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(510,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Orderings_Oorder ) ) )
      | ( ( C @ ( B @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_OatLeastAtMost__singleton_0) ).

thf(1684,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Orderings_Oorder ) ) )
      | ( ( C @ ( B @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(331,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__sound_0) ).

thf(1277,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(123,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).

thf(812,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

thf(749,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(179,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).

thf(939,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(270,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

thf(1145,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(553,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(134,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).

thf(836,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(230,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).

thf(1049,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(266,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).

thf(1134,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(49,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ c_Orderings_Oorder ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_OatLeastatMost__empty__iff_1) ).

thf(648,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ c_Orderings_Oorder ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) )
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(194,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(968,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(286,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(1181,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(78,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).

thf(712,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(21,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( A @ ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).

thf(580,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( A @ ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(220,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).

thf(1025,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(239,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Odistrib__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).

thf(1070,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Odistrib__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(75,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(707,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(494,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( B @ c_Collect ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).

thf(1647,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( B @ c_Collect ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(251,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( D
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( B @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Ofold1 ) ) )
        = ( B @ ( D @ ( A @ c_Finite__Set_Ofold1 ) ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__insert_0) ).

thf(1098,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( D
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( B @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Ofold1 ) ) )
        = ( B @ ( D @ ( A @ c_Finite__Set_Ofold1 ) ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(449,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMin ) @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__antimono_0) ).

thf(1547,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMin ) @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(106,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).

thf(776,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(436,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

thf(1516,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(472,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).

thf(1598,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( B @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(74,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(705,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(275,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A @ ( B @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_in ) ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__in_0) ).

thf(1156,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A @ ( B @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_in ) ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(186,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(954,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(319,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

thf(1252,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(308,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( F @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( F @ ( F @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ c_COMBB ) ) ) ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UN_0) ).

thf(1230,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( F @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( F @ ( F @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ c_COMBB ) ) ) ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(422,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_Orderings_Oorder ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Oeq__iff_0) ).

thf(1484,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_Orderings_Oorder ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(340,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(1300,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(113,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( E @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).

thf(791,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( E @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(289,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Oorder ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Ole__neq__trans_0) ).

thf(1186,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Oorder ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(80,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).

thf(717,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(324,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).

thf(1262,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(808,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(47,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).

thf(643,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(303,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

thf(1220,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(521,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( F @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( F @ ( F @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ c_COMBB ) ) ) ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__UN_0) ).

thf(1711,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( F @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( F @ ( F @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ c_COMBB ) ) ) ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(428,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).

thf(1499,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(8,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).

thf(544,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(165,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( C @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).

thf(907,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( C @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(73,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(703,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(517,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( B @ ( E @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( E @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).

thf(1702,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( B @ ( E @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( E @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(395,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) )
      | ( D @ ( E @ ( E @ ( D @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Finite__Set_Ofun__left__comm__idem ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__left__comm__idem_Ofun__left__comm__idem__apply_0) ).

thf(1427,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) )
      | ( D @ ( E @ ( E @ ( D @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Finite__Set_Ofun__left__comm__idem ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(84,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(727,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(504,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).

thf(1670,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(17,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Finite__Set_Ofold1 ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold1Set ) ) @ c_The ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__def_0) ).

thf(571,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Finite__Set_Ofold1 ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold1Set ) ) @ c_The ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(52,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( E @ c_in ) ) @ hBOOL )
      | ( ( E @ ( C @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).

thf(656,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( E @ c_in ) ) @ hBOOL )
      | ( ( E @ ( C @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(219,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(1023,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(362,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).

thf(1353,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(29,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
       != ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).

thf(600,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
       != ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(466,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).

thf(1585,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(249,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(1094,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(371,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
      = ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).

thf(1372,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
      = ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(27,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(595,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(40,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).

thf(627,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(12,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
       != ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).

thf(556,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
       != ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(451,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

thf(1553,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(349,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(1321,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(2,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).

thf(524,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(100,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).

thf(759,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(159,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__left__comm__idem_Ofun__left__idem_0) ).

thf(891,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(263,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_Onot__le_0) ).

thf(1126,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(256,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).

thf(1108,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(347,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

thf(1316,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(245,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__ac_I1_J_0) ).

thf(1084,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(497,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = ( D @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).

thf(1654,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = ( D @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(389,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(1412,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(405,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(1448,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(290,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(1189,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(213,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_OleI_0) ).

thf(1010,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(462,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
        = ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).

thf(1575,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
        = ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(336,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv3_0) ).

thf(1289,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(138,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ ( E @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).

thf(844,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ ( E @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(351,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__Diff__lessThan_0) ).

thf(1326,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(191,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ~ ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).

thf(961,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
      | ~ ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(192,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

thf(963,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(357,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Oorder ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Oless__le_2) ).

thf(1341,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Oorder ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(236,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

thf(1062,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(454,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
     != ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

thf(1558,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
     != ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(182,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(946,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(252,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(1101,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(86,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(731,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).

thf(786,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(223,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = ( D @ ( A @ hAPP ) @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).

thf(1030,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = ( D @ ( A @ hAPP ) @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(175,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

thf(929,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(344,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ c_COMBB ) ) ) ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I5_J_0) ).

thf(1308,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ c_COMBB ) ) ) ) @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(242,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).

thf(1077,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(300,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).

thf(1212,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(476,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( G @ ( A @ c_Orderings_Oorder ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( F @ ( E @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_OatLeastatMost__subset__iff_2) ).

thf(1607,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( G @ ( A @ c_Orderings_Oorder ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( F @ ( E @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(435,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

thf(1513,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(132,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

thf(832,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Collect ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).

thf(549,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Collect ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(228,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).

thf(1045,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(162,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__2 ) @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__1 ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq1_0) ).

thf(899,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__2 ) @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__1 ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(500,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).

thf(1661,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(277,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

thf(1161,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(479,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(1614,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(259,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( B @ c_Orderings_Oorder ) ) )
      | ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
        = ( A @ ( D @ ( C @ ( B @ c_SetInterval_Oord_OatLeastAtMost ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_OatLeastatMost__empty__iff2_1) ).

thf(1116,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( B @ c_Orderings_Oorder ) ) )
      | ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
        = ( A @ ( D @ ( C @ ( B @ c_SetInterval_Oord_OatLeastAtMost ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(37,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).

thf(620,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(492,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).

thf(1642,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(463,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).

thf(1578,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(184,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( F @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).

thf(950,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( F @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(485,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).

thf(1625,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(375,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ hAPP ) @ ( D @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).

thf(1380,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ hAPP ) @ ( D @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(441,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
      = ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).

thf(1527,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) )
      = ( E @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(505,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Oless__le_1) ).

thf(1673,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(147,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

thf(865,plain,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(420,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).

thf(1480,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(14,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(564,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(399,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty_0) ).

thf(1436,plain,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(118,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_Onot__le_1) ).

thf(801,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(367,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

thf(1363,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(498,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).

thf(1657,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(354,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).

thf(1335,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(455,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).

thf(1561,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(224,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

thf(1033,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(130,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( F @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_COMBB ) ) ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( B @ ( A @ ( D @ ( F @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I10_J_0) ).

thf(828,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( F @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_COMBB ) ) ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( B @ ( A @ ( D @ ( F @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(416,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(1473,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( C @ ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ c_lessequals ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).

thf(532,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( C @ ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ c_lessequals ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(69,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(696,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(279,axiom,
    tc_bool @ class_Lattices_Olower__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

thf(1165,plain,
    tc_bool @ class_Lattices_Olower__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(187,axiom,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).

thf(955,plain,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(359,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).

thf(1346,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(116,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

thf(796,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(161,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(897,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(388,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( A @ ( D @ hAPP ) @ hBOOL )
      | ( B @ ( B @ ( D @ c_Collect ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_2) ).

thf(1410,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( A @ ( D @ hAPP ) @ hBOOL )
      | ( B @ ( B @ ( D @ c_Collect ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(103,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
      | ( D
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( A @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_below__fold1__iff_0) ).

thf(767,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
      | ( D
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( A @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(157,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(886,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(174,axiom,
    tc_bool @ class_Lattices_Odistrib__lattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).

thf(928,plain,
    tc_bool @ class_Lattices_Odistrib__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(91,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_Onot__less__iff__gr__or__eq_0) ).

thf(740,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(273,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_Orderings_Olinorder ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_Onot__less__iff__gr__or__eq_2) ).

thf(1152,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_Orderings_Olinorder ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(374,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).

thf(1378,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(450,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(1550,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(364,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( F @ tc_fun ) @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( F @ tc_fun ) @ ( B @ ( B @ ( tc_bool @ ( F @ tc_fun ) @ ( C @ ( A @ ( E @ c_COMBB ) ) ) ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I10_J_0) ).

thf(1357,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( F @ tc_fun ) @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
      = ( tc_bool @ ( F @ tc_fun ) @ ( B @ ( B @ ( tc_bool @ ( F @ tc_fun ) @ ( C @ ( A @ ( E @ c_COMBB ) ) ) ) @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(206,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( A @ c_Collect ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_1) ).

thf(992,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( A @ c_Collect ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(127,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

thf(822,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(397,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( G @ ( A @ c_Orderings_Oorder ) ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( F @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( E @ ( D @ ( C @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ c_lessequals ) ) )
      | ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_OatLeastatMost__subset__iff_0) ).

thf(1431,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( G @ ( A @ c_Orderings_Oorder ) ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( F @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( E @ ( D @ ( C @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ c_lessequals ) ) )
      | ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(150,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).

thf(871,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(31,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( C @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__le_0) ).

thf(607,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( C @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(248,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

thf(1093,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(135,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

thf(839,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(311,axiom,
    tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).

thf(1236,plain,
    tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(203,axiom,
    tc_bool @ class_Lattices_Olattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(987,plain,
    tc_bool @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(327,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Ole__less_0) ).

thf(1268,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Oorder ) ) )
      | ~ ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(19,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMax ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__ge_0) ).

thf(575,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMax ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(443,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

thf(1532,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(145,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(860,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(377,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).

thf(1384,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(445,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

thf(1537,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(465,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

thf(1582,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(217,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(1019,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(431,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).

thf(1505,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(383,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( B @ ( E @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).

thf(1399,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( B @ ( E @ ( C @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(475,axiom,
    tc_bool @ class_Finite__Set_Ofinite_Ofinite,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).

thf(1606,plain,
    tc_bool @ class_Finite__Set_Ofinite_Ofinite,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(119,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

thf(803,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(369,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( G @ ( A @ c_Orderings_Oorder ) ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( F @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( E @ ( B @ ( D @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ c_lessequals ) ) )
      | ~ ( B @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_OatLeastatMost__subset__iff_1) ).

thf(1367,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( G @ ( A @ c_Orderings_Oorder ) ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( F @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( E @ ( B @ ( D @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ c_lessequals ) ) )
      | ~ ( B @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(177,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

thf(935,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(288,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).

thf(1184,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(45,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(639,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(98,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__2 ) ) ) @ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_0) ).

thf(755,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__2 ) ) ) @ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(155,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv2_1) ).

thf(882,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(412,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder_Onot__leE_0) ).

thf(1463,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(53,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( E @ ( B @ c_Orderings_Oorder ) ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( D @ ( C @ ( B @ c_SetInterval_Oord_OatLeastAtMost ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_OatLeastatMost__empty__iff2_0) ).

thf(659,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( E @ ( B @ c_Orderings_Oorder ) ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( D @ ( C @ ( B @ c_SetInterval_Oord_OatLeastAtMost ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(457,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
      | ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).

thf(1565,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
      | ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(26,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(592,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(414,axiom,
    ! [A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

thf(1468,plain,
    ! [A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(391,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Olinorder__class_OMax ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__singleton_0) ).

thf(1417,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Olinorder__class_OMax ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(196,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(972,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(1768,plain,
    $false,
    inference(e,[status(thm)],[1036,1501,1337,629,1369,1454,1633,909,941,1295,1237,846,977,1005,1596,683,1522,1443,1618,994,1401,1569,1205,1591,1142,878,1437,1486,582,762,614,1692,1310,1275,1233,814,1640,1458,670,1260,698,747,913,1507,1222,1196,1391,709,841,1650,1359,1475,1366,1529,1518,651,782,1441,1601,1386,1228,1482,1254,1628,1709,1298,719,1264,587,542,1055,724,1511,917,751,1313,1279,1545,817,853,1087,1147,1247,1609,770,1232,1319,1704,1465,1302,1450,646,937,1677,806,1051,1489,1415,1682,1136,834,1183,1283,981,1215,692,734,956,866,1072,1351,988,1433,1405,1201,1169,687,1119,1622,1697,1242,920,678,529,793,925,1306,1199,810,534,1067,714,1636,1047,1163,894,825,1123,1174,820,788,729,1021,778,1042,952,1355,1580,1217,598,561,1666,1423,566,625,879,1555,1178,665,1687,1624,889,1159,1210,757,710,1573,1012,1106,522,830,1079,1027,551,1128,874,948,1017,1064,1111,1587,1425,1096,1567,1493,1361,1659,1292,753,537,1446,1644,884,1329,1028,1082,901,1075,1207,590,1612,1039,970,622,997,701,1266,1192,1060,721,1002,1324,1114,1588,985,1150,1478,1451,738,1539,1456,1382,1131,654,984,911,569,1429,605,1393,1241,633,1563,1054,1286,1663,1616,773,662,618,1680,1103,1273,856,745,573,689,1374,1631,965,1510,732,1389,843,1620,1652,743,1535,1520,584,1154,904,975,1007,694,875,826,577,958,1403,1256,1226,641,1707,1271,611,1239,1332,1090,1258,1675,672,1139,1503,1058,1107,1638,1224,1194,1282,784,1524,736,1349,990,1542,1690,863,764,979,681,1408,1492,1603,616,1122,1571,1376,1439,1667,1471,631,1339,858,609,799,915,1344,668,932,848,700,1556,1460,1396,959,868,780,1015,1176,1000,1477,1250,1496,851,685,1171,1594,1699,636,1245,1694,922,675,1304,1166,1203,944,795,663,1420,1684,1277,812,749,939,1145,553,836,1049,1134,648,968,1181,712,580,1025,1070,707,1647,1098,1547,776,1516,1598,705,1156,954,1252,1230,1484,1300,791,1186,717,1262,808,643,1220,1711,1499,544,907,703,1702,1427,727,1670,571,656,1023,1353,600,1585,1094,1372,595,627,556,1553,1321,524,759,891,1126,1108,1316,1084,1654,1412,1448,1189,1010,1575,1289,844,1326,961,963,1341,1062,1558,946,1101,731,786,1030,929,1308,1077,1212,1607,1513,832,549,1045,899,1661,1161,1614,1116,620,1642,1578,950,1625,1380,1527,1673,865,1480,564,1436,801,1363,1657,1335,1561,1033,828,1473,532,696,1165,955,1346,796,897,1410,767,886,928,740,1152,1378,1550,1357,992,822,1431,871,607,1093,839,1236,987,1268,575,1532,860,1384,1537,1582,1019,1505,1399,1606,803,1367,935,1184,639,755,882,1463,659,1565,592,1468,1417,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWV913-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.39  % Computer : n015.cluster.edu
% 0.14/0.39  % Model    : x86_64 x86_64
% 0.14/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39  % Memory   : 8046.5625MB
% 0.14/0.39  % OS       : Linux 6.8.0-71-generic
% 0.14/0.39  % CPULimit : 300
% 0.14/0.39  % WCLimit  : 300
% 0.14/0.39  % DateTime : Sat Sep 26 15:12:29 UTC 2026
% 0.14/0.40  % CPUTime  : 
% 0.14/0.40  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.89/0.99  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.90/1.34  % [INFO] 	 Parsing done (355ms). 
% 1.90/1.36  % [INFO] 	 Running in sequential loop mode. 
% 2.97/1.74  % [INFO] 	 eprover registered as external prover. 
% 2.97/1.75  % [INFO] 	 Scanning for conjecture ... 
% 3.52/1.94  % [INFO] 	 Found a conjecture (or negated_conjecture) and 520 axioms. Running axiom selection ... 
% 4.48/2.16  % [INFO] 	 Axiom selection finished. Selected 520 axioms (removed 0 axioms). 
% 5.61/2.42  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 5.61/2.44  % [INFO] 	 Type checking passed. 
% 5.61/2.45  % [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 ... 
% 19.22/5.49  % External prover 'e' found a proof!
% 19.22/5.49  % [INFO] 	 Killing All external provers ... 
% 19.22/5.49  % Time passed: 4953ms (effective reasoning time: 4128ms)
% 19.68/5.50  % Axioms used in derivation (520): cls_inf__sup__absorb_0, cls_vimage__code_0, cls_inf__sup__aci_I2_J_0, cls_ab__semigroup__mult_Omult__left__commute_0, cls_atLeastatMost__subset__iff_2, cls_the__sym__eq__trivial_0, cls_Int__absorb2_0, cls_Int__Un__distrib_0, cls_order_Ole__less_0, clsarity_fun__Lattices_Olower__semilattice, cls_Diff__cancel_0, cls_INT__extend__simps_I4_J_0, cls_asm_0, cls_subset__insert_1, cls_Diff__iff_2, cls_UN__extend__simps_I3_J_1, cls_order_Oeq__iff_0, cls_bot__fun__eq_0, cls_order_OatLeastatMost__subset__iff_3, cls_UN__simps_I1_J_1, cls_sup__ge1_0, cls_insertE_0, cls_com_Osimps_I3_J_0, cls_Un__subset__iff_0, cls_order_Oantisym_0, cls_order__eq__iff_0, cls_equalityI_0, cls_insert__inter__insert_0, cls_inj__on__Un_2, cls_Un__Diff_0, cls_UN__simps_I3_J_1, cls_subset__empty_1, cls_subset__image__iff_2, cls_vimage__UN_0, cls_inj__on__image__Int_0, cls_empty__is__image_1, cls_image__mono_0, cls_Un__empty__left_0, cls_le__funD_0, cls_ab__semigroup__mult_Ofold1__Un_0, cls_finite__insert_0, cls_sup__bot__right_0, cls_insert__code_1, clsarity_bool__Lattices_Olower__semilattice, cls_le__SUPI_0, cls_inf__sup__aci_I6_J_0, cls_Un__upper1_0, cls_Un__commute_0, cls_UnCI_1, cls_distrib__sup__le_0, cls_Int__mono_0, cls_vimage__Diff_0, cls_UN__extend__simps_I5_J_0, cls_le__iff__inf_1, cls_complete__lattice_OSup__singleton_0, cls_conseq_0, cls_UN__extend__simps_I10_J_0, cls_fold1Set__sing_1, clsarity_fun__Orderings_Oorder, cls_finite__Un_2, cls_Diff__Un_0, cls_Int__insert__left_0, cls_triple_Oinject_1, cls_le__inf__iff_1, clsarity_bool__HOL_Ominus, cls_Diff__subset__conv_0, cls_Int__Un__distrib2_0, cls_mem__def_1, cls_linorder_Onot__less__iff__gr__or__eq_2, cls_Int__Collect_1, cls_ab__semigroup__mult_Omult__ac_I1_J_0, cls_Inf__lower_0, cls_insert__absorb_0, cls_empty__iff_0, cls_Min__le_0, cls_Int__subset__iff_2, cls_order_OatLeastatMost__subset__iff_0, cls_image__vimage__subset_0, cls_inj__on__image__set__diff_0, cls_derivs__insertD_1, cls_inf1E_1, cls_linorder_OleI_0, cls_Diff__triv_0, cls_insert__iff_1, cls_insert__subset_0, cls_sup__inf__distrib2_0, clsarity_fun__Lattices_Oupper__semilattice, cls_le__sup__iff_0, cls_inj__on__Un__image__eq__iff_0, cls_ab__semigroup__mult_Omult__commute_0, cls_inf__sup__distrib1_0, cls_Int__absorb1_0, cls_conseq12_1, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_inf__left__commute_0, cls_ord_OatLeastAtMost__iff_2, cls_COMBB__def_0, cls_UN__simps_I1_J_0, cls_subset__insert__iff_2, cls_fun__left__comm__idem_Ofun__left__comm__idem__apply_0, cls_hoare__derivs_OSkip_0, cls_contents__eq_0, cls_comm__monoid__add_Ononempty__iff_0, cls_CollectI_0, cls_linorder_OMax__singleton_0, cls_inf__commute_0, cls_Min__singleton_0, cls_Comp_0, cls_Un__left__commute_0, clsarity_bool__Finite__Set_Ofinite_Ofinite, cls_finite__insert_1, cls_linorder_Oantisym__conv2_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_finite__Int_1, cls_Int__empty__right_0, cls_fold1__def_0, cls_vimage__insert_0, cls_Collect__empty__eq_0, cls_inf__fun__eq_0, cls_Inf__singleton_0, cls_le__supI_0, cls_order_Oneq__le__trans_0, cls_CollectD_0, cls_linorder_OneqE_0, cls_Un__Int__distrib2_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_ab__semigroup__mult_Ononempty__iff_2, cls_UN__extend__simps_I1_J_0, cls_Un__subset__iff_1, cls_Inf__binary_0, cls_empty__is__image_0, cls_linorder_Oneq__iff_1, cls_linorder_Onot__less__iff__gr__or__eq_0, cls_rev__image__eqI_0, cls_inj__on__insert_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_inj__on__Un_3, cls_Int__UN__distrib_0, cls_UN__absorb_0, clsarity_fun__Orderings_Obot, cls_UN__simps_I3_J_0, cls_le__iff__sup_0, cls_UN__insert__distrib_0, cls_finite__Int_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, cls_linorder_Oantisym__conv2_1, cls_vimageI_0, cls_order_OatLeastatMost__empty_0, cls_lessThan__subset__iff_1, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_sup__eq__bot__eq2_0, cls_hoare__derivs_Ointros_I6_J_0, cls_UnCI_0, cls_Un__upper2_0, cls_Int__insert__right_1, cls_conseq_2, cls_UN__Un_0, cls_Max__mono_0, cls_Sup__singleton_0, cls_escape_0, cls_subset__iff_0, cls_insert__code_2, cls_order_OatLeastatMost__empty__iff_0, clsarity_fun__HOL_Oord, cls_Diff__idemp_0, cls_subset__empty_0, cls_rev__predicate1D_0, cls_insert__Diff__single_0, cls_lessThan__eq__iff_0, cls_UN__simps_I10_J_0, cls_singleton__iff_1, cls_atLeastatMost__empty__iff_1, cls_finite_0, cls_complete__lattice_OInf__empty_0, cls_image__insert_0, cls_UN__subset__iff_0, cls_SUP1__iff_2, cls_inf__absorb2_0, cls_atLeastatMost__empty__iff2_0, clsarity_bool__Lattices_Oupper__semilattice, cls_order_OatLeastatMost__empty__iff_1, cls_order_Ole__neq__trans_0, cls_linorder_Oantisym__conv1_1, cls_order_OatLeastAtMost__singleton_0, cls_vimage__Un_0, cls_finite__Diff_0, cls_diff__single__insert_0, clsarity_fun__Finite__Set_Ofinite_Ofinite, cls_Sup__binary_0, cls_Int__Collect_0, cls_Un__insert__left_0, cls_inf__sup__ord_I2_J_0, cls_order_Oantisym__conv_0, cls_doubleton__eq__iff_2, cls_vimage__singleton__eq_1, cls_subset__insert__iff_3, cls_Inf__insert_0, cls_linorder_Onot__less__iff__gr__or__eq_1, cls_UN__extend__simps_I1_J_1, cls_finite__UnI_0, cls_inf__sup__aci_I3_J_0, cls_set__eq__subset_2, cls_Un__mono_0, cls_Int__insert__left_1, cls_insert__subset_1, cls_Int__empty__left_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_order_Ole__less_1, cls_ex__in__conv_0, cls_sup__commute_0, cls_ivl__disj__int_I4_J_0, cls_finite__surj_0, cls_order_OatLeastatMost__subset__iff_1, cls_le__inf__iff_0, cls_Int__subset__iff_1, cls_image__UN_0, cls_Un__subset__iff_2, clsarity_fun__Lattices_Olattice, cls_linorder__linear_0, cls_Un__empty_0, cls_order__antisym_0, cls_order__trans_0, cls_ord_OatLeastAtMost__iff_1, cls_image__empty_0, cls_inf__le2_0, cls_insert__is__Un_0, cls_Int__assoc_0, cls_linorder_OleD_0, cls_order_OatLeastatMost__empty__iff2_0, cls_conseq12_2, cls_subset__trans_0, cls_atLeastAtMost__singleton_0, cls_double__diff_0, cls_com_Osimps_I3_J_1, cls_DiffI_0, cls_inj__on__insert_1, cls_le__supE_0, cls_empty__not__insert_0, cls_sup__assoc_0, cls_insert__Diff1_0, cls_lessThan__subset__iff_0, cls_Diff__Int__distrib2_0, cls_linorder_Oless__linear_0, cls_insertI1_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_Un__Int__crazy_0, clsarity_bool__Orderings_Opreorder, cls_Nitpick_OEx1__def_2, cls_fun__left__comm__idem__sup_0, cls_hoare__derivs_Oinsert_0, cls_empty__subsetI_0, cls_atLeastatMost__subset__iff_0, cls_linorder_Onot__le_1, cls_Un__absorb1_0, cls_Diff__insert2_0, cls_Int__commute_0, cls_Sup__upper_0, cls_sup__least_0, cls_comm__monoid__add_Ononempty__iff_1, cls_doubleton__eq__iff_0, cls_inf__sup__aci_I1_J_0, cls_sup1E_0, cls_distrib__inf__le_0, cls_subset__refl_0, cls_Max__singleton_0, cls_singletonE_0, cls_inj__on__iff_0, cls_image__diff__subset_0, cls_fun__left__comm__idem_Ofun__left__idem_0, cls_inj__on__empty_0, cls_DiffE_0, cls_Int__Diff_0, cls_conseq2_1, cls_image__iff_2, cls_insertCI_0, cls_complete__lattice_OSup__binary_0, cls_image__Int__subset_0, cls_le__inf__iff_2, cls_vimage__Int_0, cls_Un__Diff__cancel_0, cls_complete__lattice_OInf__insert_0, cls_image__Un_0, cls_insert__Diff_0, cls_sup1CI_1, cls_complete__lattice_OInf__binary_0, cls_below__fold1__iff_0, cls_le__infE_0, cls_order__eq__iff_2, cls_le__infI1_0, cls_bot1E_0, cls_weaken_0, cls_Int__absorb_0, cls_inf__assoc_0, cls_Int__lower2_0, cls_order_OatLeastatMost__empty__iff2_1, cls_insert__mono_0, cls_hoare__derivs_Ointros_I6_J_2, cls_le__supI2_0, cls_Un__assoc_0, cls_fold1__singleton_0, cls_Collect__def_0, cls_Un__Diff__cancel2_0, cls_Max__ge_0, cls_empty__fold1SetE_0, cls_bex__empty_0, cls_Diff__disjoint_0, cls_inf__sup__ord_I4_J_0, cls_linorder_Oantisym__conv1_0, cls_Diff__mono_0, 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% 19.68/5.50  % No. of inferences in proof: 1043
% 19.68/5.50  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4953 ms resp. 4128 ms w/o parsing
% 21.08/5.83  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 21.08/5.83  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------