CSE_E---1.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SWV898-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n028.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May  5 05:27:41 PM UTC 2026

% Result   : Unsatisfiable 1.12s 1.67s
% Output   : CNFRefutation 1.18s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named 631)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_MGT__Body_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | ~ c_Finite__Set_Ofinite(X2,tc_Com_Opname)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MGT__Body_0) ).

cnf(cls_conjecture_3,negated_conjecture,
    ~ c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

cnf(cls_inv__into__comp_0,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X6,X5),X7) = hAPP(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(X1,X3,X6,X4),c_Hilbert__Choice_Oinv__into(c_Set_Oimage(X3,X1,X6,X4),X2,X4,X5),X4,X6,X5),X7)
    | ~ c_in(X7,c_Set_Oimage(X2,c_Set_Oimage(X3,X1,X6,X4),X4,X5),X5)
    | ~ c_Fun_Oinj__on(X3,X1,X6,X4)
    | ~ c_Fun_Oinj__on(X2,c_Set_Oimage(X3,X1,X6,X4),X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__comp_0) ).

cnf(cls_conjecture_2,negated_conjecture,
    c_lessequals(v_F,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

cnf(cls_image__subset__iff_2,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | ~ c_in(hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X2,X5,X1,X3,X4)),X5,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_2) ).

cnf(cls_image__subsetI_1,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | ~ c_in(hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X2,X5,X1,X3,X4)),X5,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subsetI_1) ).

cnf(cls_image__cong_1,axiom,
    ( c_Set_Oimage(X1,X2,X4,X5) = c_Set_Oimage(X3,X2,X4,X5)
    | hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X3,X4,X5)) != hAPP(X3,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X3,X4,X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__cong_1) ).

cnf(cls_bij__betw__trans_0,axiom,
    ( c_Fun_Obij__betw(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6,X7,X5,X4)
    | ~ c_Fun_Obij__betw(X1,X8,X7,X3,X4)
    | ~ c_Fun_Obij__betw(X2,X6,X8,X5,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__betw__trans_0) ).

cnf(cls_o__assoc_0,axiom,
    c_Fun_Ocomp(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X5,X7,X6) = c_Fun_Ocomp(c_Fun_Ocomp(X1,X2,X5,X7,X4),X3,X4,X7,X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).

cnf(cls_finite__range__imageI_0,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(X1,X2,X3,X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X4),X4)
    | ~ c_Finite__Set_Ofinite(c_Set_Oimage(X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__range__imageI_0) ).

cnf(cls_o__inv__o__cancel_0,axiom,
    ( c_Fun_Ocomp(c_Fun_Ocomp(X1,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X2,X4),X2,X5,X4),X3,X4,X5,X2) = X1
    | ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__inv__o__cancel_0) ).

cnf(cls_o__inv__distrib_0,axiom,
    ( c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Fun_Ocomp(X2,X3,X4,X5,X1),X1,X5) = c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X3,X1,X4),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X2,X4,X5),X4,X1,X5)
    | ~ c_Fun_Obij(X3,X1,X4)
    | ~ c_Fun_Obij(X2,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__inv__distrib_0) ).

cnf(cls_comp__cong_0,axiom,
    ( hAPP(c_Fun_Ocomp(X1,X2,X7,X8,X9),X3) = hAPP(c_Fun_Ocomp(X4,X5,X10,X8,X11),X6)
    | hAPP(X1,hAPP(X2,X3)) != hAPP(X4,hAPP(X5,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).

cnf(cls_inj__on__imageI_0,axiom,
    ( c_Fun_Oinj__on(X1,c_Set_Oimage(X2,X3,X4,X5),X5,X6)
    | ~ c_Fun_Oinj__on(c_Fun_Ocomp(X1,X2,X5,X6,X4),X3,X4,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__imageI_0) ).

cnf(cls_comp__inj__on_0,axiom,
    ( c_Fun_Oinj__on(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6,X5,X4)
    | ~ c_Fun_Oinj__on(X1,c_Set_Oimage(X2,X6,X5,X3),X3,X4)
    | ~ c_Fun_Oinj__on(X2,X6,X5,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__inj__on_0) ).

cnf(cls_o__eq__dest_0,axiom,
    ( hAPP(X1,hAPP(X2,X9)) = hAPP(X6,hAPP(X7,X9))
    | c_Fun_Ocomp(X1,X2,X3,X4,X5) != c_Fun_Ocomp(X6,X7,X8,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).

cnf(cls_inj__on__Un_3,axiom,
    ( c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
    | c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X4,X5),tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).

cnf(cls_o__eq__id__dest_0,axiom,
    ( hAPP(X1,hAPP(X2,X7)) = hAPP(X6,X7)
    | c_Fun_Ocomp(X1,X2,X3,X4,X5) != c_Fun_Ocomp(c_Fun_Oid(X4),X6,X4,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__id__dest_0) ).

cnf(cls_bij__betw__inv__into_0,axiom,
    ( c_Fun_Obij__betw(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5,X1,X4,X3)
    | ~ c_Fun_Obij__betw(X2,X1,X5,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__betw__inv__into_0) ).

cnf(cls_finite__subset__image_2,axiom,
    ( X1 = c_Set_Oimage(X2,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X3,X1,X2,X4,X5),X4,X5)
    | ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Finite__Set_Ofinite(X1,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_2) ).

cnf(cls_subset__image__iff_1,axiom,
    ( X1 = c_Set_Oimage(X2,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X3,X1,X2,X4,X5),X4,X5)
    | ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_1) ).

cnf(cls_range__composition_0,axiom,
    c_Set_Oimage(c_COMBB(X1,X2,X3,X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X4) = c_Set_Oimage(X1,c_Set_Oimage(X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X3),X3,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__composition_0) ).

cnf(cls_finite__subset__image_0,axiom,
    ( c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X1,X2,X3,X4,X5),X1,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,c_Set_Oimage(X3,X1,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_0) ).

cnf(cls_vimage__compose_0,axiom,
    c_Set_Ovimage(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6,X5,X4) = c_Set_Ovimage(X2,c_Set_Ovimage(X1,X6,X3,X4),X5,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__compose_0) ).

cnf(cls_image__compose_0,axiom,
    c_Set_Oimage(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6,X5,X4) = c_Set_Oimage(X1,c_Set_Oimage(X2,X6,X5,X3),X3,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__compose_0) ).

cnf(cls_image__image_0,axiom,
    c_Set_Oimage(X1,c_Set_Oimage(X2,X3,X4,X5),X5,X6) = c_Set_Oimage(c_COMBB(X1,X2,X5,X6,X4),X3,X4,X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).

cnf(cls_subset__image__iff_0,axiom,
    ( c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X1,X2,X3,X4,X5),X1,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,c_Set_Oimage(X3,X1,X4,X5),tc_fun(X5,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_0) ).

cnf(cls_le__fun__def_1,axiom,
    ( c_lessequals(X2,X3,tc_fun(X4,X1))
    | ~ class_HOL_Oord(X1)
    | ~ c_lessequals(hAPP(X2,c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1(X2,X3,X4,X1)),hAPP(X3,c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1(X2,X3,X4,X1)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__fun__def_1) ).

cnf(cls_le__funI_0,axiom,
    ( c_lessequals(X2,X3,tc_fun(X4,X1))
    | ~ class_HOL_Oord(X1)
    | ~ c_lessequals(hAPP(X2,c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1(X2,X3,X4,X1)),hAPP(X3,c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1(X2,X3,X4,X1)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funI_0) ).

cnf(cls_finite__subset__image_1,axiom,
    ( c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X1,X2,X3,X4,X5),X4)
    | ~ c_lessequals(X2,c_Set_Oimage(X3,X1,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_1) ).

cnf(cls_inv__into__injective_0,axiom,
    ( X5 = X6
    | hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5) != hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X6)
    | ~ c_in(X6,c_Set_Oimage(X2,X1,X3,X4),X4)
    | ~ c_in(X5,c_Set_Oimage(X2,X1,X3,X4),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__injective_0) ).

cnf(cls_inj__on__insert_1,axiom,
    ( ~ c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5),X5)
    | ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).

cnf(cls_inj__iff_1,axiom,
    ( c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3)
    | c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),X2,X3,X1,X1) != c_Fun_Oid(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__iff_1) ).

cnf(cls_image__subset__iff_1,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X2,X5,X1,X3,X4),X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_1) ).

cnf(cls_image__subsetI_0,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X2,X5,X1,X3,X4),X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subsetI_0) ).

cnf(cls_image__diff__subset_0,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).

cnf(cls_image__Int__subset_0,axiom,
    c_lessequals(c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).

cnf(cls_image__cong_0,axiom,
    ( c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X5,X2,X3,X4)
    | c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X5,X3,X4),X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__cong_0) ).

cnf(cls_surj__iff_1,axiom,
    ( c_Fun_Osurj(X1,X2,X3)
    | c_Fun_Ocomp(X1,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),X2,X3,X3) != c_Fun_Oid(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surj__iff_1) ).

cnf(cls_weak__coinduct__image_0,axiom,
    ( c_in(hAPP(X1,X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_lessequals(c_Set_Oimage(X1,X5,X6,X4),hAPP(X3,c_Set_Oimage(X1,X5,X6,X4)),tc_fun(X4,tc_bool))
    | ~ c_in(X2,X5,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weak__coinduct__image_0) ).

cnf(cls_card__bij__eq_0,axiom,
    ( c_Finite__Set_Ocard(X1,X2) = c_Finite__Set_Ocard(X3,X4)
    | ~ c_Finite__Set_Ofinite(X3,X4)
    | ~ c_Finite__Set_Ofinite(X1,X2)
    | ~ c_lessequals(c_Set_Oimage(X5,X3,X4,X2),X1,tc_fun(X2,tc_bool))
    | ~ c_Fun_Oinj__on(X5,X3,X4,X2)
    | ~ c_lessequals(c_Set_Oimage(X6,X1,X2,X4),X3,tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X6,X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__bij__eq_0) ).

cnf(cls_bij__comp_0,axiom,
    ( c_Fun_Obij(c_Fun_Ocomp(X1,X2,X3,X4,X5),X5,X4)
    | ~ c_Fun_Obij(X1,X3,X4)
    | ~ c_Fun_Obij(X2,X5,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__comp_0) ).

cnf(cls_comp__surj_0,axiom,
    ( c_Fun_Osurj(c_Fun_Ocomp(X1,X2,X3,X4,X5),X5,X4)
    | ~ c_Fun_Osurj(X1,X3,X4)
    | ~ c_Fun_Osurj(X2,X5,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__surj_0) ).

cnf(cls_inj__on__insert_2,axiom,
    ( c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5)
    | c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5),X5)
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).

cnf(cls_ATP__Linkup_OCOMBB__def_0,axiom,
    hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).

cnf(cls_COMBB__def_0,axiom,
    hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).

cnf(cls_o__apply_0,axiom,
    hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).

cnf(cls_o__eq__dest__lhs_0,axiom,
    hAPP(X1,hAPP(X2,X3)) = hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).

cnf(cls_inj__on__Un_2,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X4,X5),tc_fun(X5,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).

cnf(cls_inj__iff_0,axiom,
    ( c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),X2,X3,X1,X1) = c_Fun_Oid(X1)
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__iff_0) ).

cnf(cls_inj__image__Compl__subset_0,axiom,
    ( c_lessequals(c_Set_Oimage(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3,X4),c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(X1,X2,X3,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__Compl__subset_0) ).

cnf(cls_inj__image__subset__iff_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).

cnf(cls_bij__betw__def_1,axiom,
    ( c_Set_Oimage(X1,X2,X3,X4) = X5
    | ~ c_Fun_Obij__betw(X1,X2,X5,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__betw__def_1) ).

cnf(cls_bij__betw__def_0,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Obij__betw(X1,X2,X5,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__betw__def_0) ).

cnf(cls_inj__on__image__set__diff_0,axiom,
    ( c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(X3,X6,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X6,tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X6,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).

cnf(cls_inj__on__image__Int_0,axiom,
    ( c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(X3,X6,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X6,tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X6,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).

cnf(cls_bij__betw__def_2,axiom,
    ( c_Fun_Obij__betw(X1,X2,c_Set_Oimage(X1,X2,X3,X4),X3,X4)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__betw__def_2) ).

cnf(cls_image__surj__f__inv__f_0,axiom,
    ( c_Set_Oimage(X1,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),X4,X3,X2),X2,X3) = X4
    | ~ c_Fun_Osurj(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__surj__f__inv__f_0) ).

cnf(cls_Un__Int__crazy_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).

cnf(cls_vimage__subsetI_0,axiom,
    ( c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),X5,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).

cnf(cls_image__set__diff_0,axiom,
    ( c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).

cnf(cls_image__Int_0,axiom,
    ( c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).

cnf(cls_inv__into__into_0,axiom,
    ( c_in(hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5),X1,X3)
    | ~ c_in(X5,c_Set_Oimage(X2,X1,X3,X4),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__into_0) ).

cnf(cls_bij__betw__same__card_0,axiom,
    ( c_Finite__Set_Ocard(X1,X2) = c_Finite__Set_Ocard(X3,X4)
    | ~ c_Fun_Obij__betw(X5,X1,X3,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__betw__same__card_0) ).

cnf(cls_surj__iff_0,axiom,
    ( c_Fun_Ocomp(X1,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),X2,X3,X3) = c_Fun_Oid(X3)
    | ~ c_Fun_Osurj(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surj__iff_0) ).

cnf(cls_f__inv__into__f_0,axiom,
    ( hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),X5)) = X5
    | ~ c_in(X5,c_Set_Oimage(X1,X2,X3,X4),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f__inv__into__f_0) ).

cnf(cls_surj__Compl__image__subset_0,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(X1,X2,X3,X4),tc_fun(X4,tc_bool)),c_Set_Oimage(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool))
    | ~ c_Fun_Osurj(X1,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surj__Compl__image__subset_0) ).

cnf(cls_MGT__BodyN_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X2)),X1,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MGT__BodyN_0) ).

cnf(cls_vimage__insert_0,axiom,
    c_Set_Ovimage(X1,c_Set_Oinsert(X2,X3,X4),X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).

cnf(cls_image__inv__f__f_0,axiom,
    ( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),c_Set_Oimage(X2,X4,X1,X3),X3,X1) = X4
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__inv__f__f_0) ).

cnf(cls_inv__image__comp_0,axiom,
    ( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),c_Set_Oimage(X2,X4,X1,X3),X3,X1) = X4
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__image__comp_0) ).

cnf(cls_inv__into__image__cancel_0,axiom,
    ( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),c_Set_Oimage(X2,X5,X3,X4),X4,X3) = X5
    | ~ c_lessequals(X5,X1,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__image__cancel_0) ).

cnf(cls_vimage__code_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).

cnf(cls_inj__image__subset__iff_1,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).

cnf(cls_inj__on__inv__into_0,axiom,
    ( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5,X4,X3)
    | ~ c_lessequals(X5,c_Set_Oimage(X2,X1,X3,X4),tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__inv__into_0) ).

cnf(cls_endo__inj__surj_0,axiom,
    ( c_Set_Oimage(X1,X2,X3,X3) = X2
    | ~ c_Fun_Oinj__on(X1,X2,X3,X3)
    | ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X3),X2,tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).

cnf(cls_image__vimage__subset_0,axiom,
    c_lessequals(c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4),X2,tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).

cnf(cls_vimage__subset__eq_1,axiom,
    ( c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),X5,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_Fun_Obij(X1,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subset__eq_1) ).

cnf(cls_vimage__subset__eq_0,axiom,
    ( c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(c_Set_Ovimage(X2,X1,X4,X5),X3,tc_fun(X4,tc_bool))
    | ~ c_Fun_Obij(X2,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subset__eq_0) ).

cnf(cls_vimage__subsetD_0,axiom,
    ( c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(c_Set_Ovimage(X2,X1,X4,X5),X3,tc_fun(X4,tc_bool))
    | ~ c_Fun_Osurj(X2,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetD_0) ).

cnf(cls_vimage__singleton__eq_0,axiom,
    ( hAPP(X1,X2) = X3
    | ~ c_in(X2,c_Set_Ovimage(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).

cnf(cls_vimage__Diff_0,axiom,
    c_Set_Ovimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).

cnf(cls_vimage__Un_0,axiom,
    c_Set_Ovimage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).

cnf(cls_vimage__Int_0,axiom,
    c_Set_Ovimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).

cnf(cls_image__Un_0,axiom,
    c_Set_Oimage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).

cnf(cls_inj__image__mem__iff_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
    | ~ c_Fun_Oinj__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).

cnf(cls_image__vimage__eq_0,axiom,
    c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).

cnf(cls_inj__on__Un__image__eq__iff_0,axiom,
    ( X2 = X5
    | c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X5,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).

cnf(cls_subset__insert__iff_4,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).

cnf(cls_surj__f__inv__f_0,axiom,
    ( hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),X4)) = X4
    | ~ c_Fun_Osurj(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surj__f__inv__f_0) ).

cnf(cls_diff__single__insert_0,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_in(X2,X1,X4)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).

cnf(cls_subset__insert__iff_3,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_in(X2,X1,X4)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

cnf(cls_inj__image__eq__iff_0,axiom,
    ( X2 = X5
    | c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X5,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).

cnf(cls_inj__vimage__image__eq_0,axiom,
    ( c_Set_Ovimage(X1,c_Set_Oimage(X1,X2,X3,X4),X3,X4) = X2
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).

cnf(cls_id__o_0,axiom,
    c_Fun_Ocomp(c_Fun_Oid(X1),X2,X1,X1,X3) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__o_0) ).

cnf(cls_o__id_0,axiom,
    c_Fun_Ocomp(X1,c_Fun_Oid(X2),X2,X3,X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__id_0) ).

cnf(cls_finite__imageD_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Fun_Oinj__on(X3,X1,X2,X4)
    | ~ c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).

cnf(cls_vimage__mono_0,axiom,
    ( c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),c_Set_Ovimage(X1,X5,X3,X4),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).

cnf(cls_image__mono_0,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).

cnf(cls_subset__image__iff_2,axiom,
    ( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).

cnf(cls_bij__vimage__eq__inv__image_0,axiom,
    ( c_Set_Ovimage(X1,X2,X3,X4) = c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X1,X3,X4),X2,X4,X3)
    | ~ c_Fun_Obij(X1,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__vimage__eq__inv__image_0) ).

cnf(cls_finite__surj__inj_0,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X3)
    | ~ c_lessequals(X2,c_Set_Oimage(X1,X2,X3,X3),tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).

cnf(cls_vimage__code_1,axiom,
    ( hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5))
    | ~ hBOOL(hAPP(X2,hAPP(X1,X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).

cnf(cls_inj__image__mem__iff_1,axiom,
    ( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
    | ~ c_in(X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).

cnf(cls_inj__imp__surj__inv_0,axiom,
    ( c_Fun_Osurj(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),X3,X1)
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__imp__surj__inv_0) ).

cnf(cls_inv__f__f_0,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),hAPP(X2,X4)) = X4
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__f__f_0) ).

cnf(cls_inv__f__eq_0,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),hAPP(X1,X4)) = X4
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__f__eq_0) ).

cnf(cls_MGF__lemma1_1,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | ~ c_Com_OWT(X2)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MGF__lemma1_1) ).

cnf(cls_eq__card__imp__inj__on_0,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) != c_Finite__Set_Ocard(X2,X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__card__imp__inj__on_0) ).

cnf(cls_vimage__singleton__eq_1,axiom,
    c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(hAPP(X2,X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).

cnf(cls_image__subset__iff_0,axiom,
    ( c_in(hAPP(X1,X2),X3,X4)
    | ~ c_in(X2,X5,X6)
    | ~ c_lessequals(c_Set_Oimage(X1,X5,X6,X4),X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

cnf(cls_subset__insert__iff_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | ~ c_in(X2,X1,X3)
    | ~ c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).

cnf(cls_map__le__trans_0,axiom,
    ( c_Map_Omap__le(X1,X2,X3,X4)
    | ~ c_Map_Omap__le(X5,X2,X3,X4)
    | ~ c_Map_Omap__le(X1,X5,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__trans_0) ).

cnf(cls_inv__into__f__f_0,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),hAPP(X2,X5)) = X5
    | ~ c_in(X5,X1,X3)
    | ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__f__f_0) ).

cnf(cls_inv__into__f__eq_0,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X2,X4,X3,X5),hAPP(X4,X1)) = X1
    | ~ c_in(X1,X2,X3)
    | ~ c_Fun_Oinj__on(X4,X2,X3,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__f__eq_0) ).

cnf(cls_finite__vimageI_0,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Ovimage(X1,X2,X3,X4),X3)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4)
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).

cnf(cls_inv__inv__eq_0,axiom,
    ( c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X2,X1),X1,X2) = X3
    | ~ c_Fun_Obij(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__inv__eq_0) ).

cnf(cls_surj__imp__inj__inv_0,axiom,
    ( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X1)
    | ~ c_Fun_Osurj(X2,X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surj__imp__inj__inv_0) ).

cnf(cls_vimageD_0,axiom,
    ( c_in(hAPP(X1,X2),X3,X4)
    | ~ c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).

cnf(cls_vimageE_0,axiom,
    ( c_in(hAPP(X1,X2),X3,X4)
    | ~ c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_0) ).

cnf(cls_bij__image__Compl__eq_0,axiom,
    ( c_Set_Oimage(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3,X4) = c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(X1,X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_Fun_Obij(X1,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__image__Compl__eq_0) ).

cnf(cls_finite__surj_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).

cnf(cls_inj__on__iff__eq__card_0,axiom,
    ( c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) = c_Finite__Set_Ocard(X2,X3)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff__eq__card_0) ).

cnf(cls_image__insert_0,axiom,
    c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).

cnf(cls_distrib__inf__le_0,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1),c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).

cnf(cls_distrib__sup__le_0,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).

cnf(cls_card__image_0,axiom,
    ( c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) = c_Finite__Set_Ocard(X2,X3)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image_0) ).

cnf(cls_insert__image_0,axiom,
    ( c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) = c_Set_Oimage(X1,X3,X4,X5)
    | ~ c_in(X2,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

cnf(cls_finite__vimage__iff_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_Set_Ovimage(X3,X1,X4,X2),X4)
    | ~ c_Fun_Obij(X3,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimage__iff_0) ).

cnf(cls_finite__vimageD_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Fun_Osurj(X3,X4,X2)
    | ~ c_Finite__Set_Ofinite(c_Set_Ovimage(X3,X1,X4,X2),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimageD_0) ).

cnf(cls_inj__on__Un_0,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).

cnf(cls_inj__on__Un_1,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X5,X2,tc_fun(X3,tc_bool)),X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).

cnf(cls_vimage__Compl_0,axiom,
    c_Set_Ovimage(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X4,X3) = c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(X1,X2,X4,X3),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).

cnf(cls_doubleton__eq__iff_0,axiom,
    ( X1 = X5
    | X1 = X4
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

cnf(cls_doubleton__eq__iff_1,axiom,
    ( X2 = X4
    | X1 = X4
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

cnf(cls_doubleton__eq__iff_2,axiom,
    ( X1 = X5
    | X2 = X5
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

cnf(cls_doubleton__eq__iff_3,axiom,
    ( X2 = X4
    | X2 = X5
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

cnf(cls_Diff__insert2_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

cnf(cls_surj__image__vimage__eq_0,axiom,
    ( c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4) = X2
    | ~ c_Fun_Osurj(X1,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surj__image__vimage__eq_0) ).

cnf(cls_inj__on__insert_0,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X5,X2,X3),X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).

cnf(cls_Un__Int__assoc__eq_0,axiom,
    ( c_lessequals(X4,X1,tc_fun(X3,tc_bool))
    | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).

cnf(cls_inj__on__diff_0,axiom,
    ( c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).

cnf(cls_map__le__antisym_0,axiom,
    ( X1 = X2
    | ~ c_Map_Omap__le(X2,X1,X3,X4)
    | ~ c_Map_Omap__le(X1,X2,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__antisym_0) ).

cnf(cls_hoare__derivs_Oinsert_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).

cnf(cls_finite__Diff__insert_0,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).

cnf(cls_subset__inj__on_0,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X5,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).

cnf(cls_bij__imp__bij__inv_0,axiom,
    ( c_Fun_Obij(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),X3,X1)
    | ~ c_Fun_Obij(X2,X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__imp__bij__inv_0) ).

cnf(cls_insert__Diff_0,axiom,
    ( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
    | ~ c_in(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

cnf(cls_insert__Diff__single_0,axiom,
    c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X1,X2,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

cnf(cls_map__le__implies__dom__le_0,axiom,
    ( c_lessequals(c_Map_Odom(X1,X2,X3),c_Map_Odom(X4,X2,X3),tc_fun(X2,tc_bool))
    | ~ c_Map_Omap__le(X1,X4,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__implies__dom__le_0) ).

cnf(cls_card__Diff__singleton__if_1,axiom,
    ( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Finite__Set_Ocard(X1,X3)
    | c_in(X2,X1,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__singleton__if_1) ).

cnf(cls_rangeI_0,axiom,
    c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).

cnf(cls_vimageI_0,axiom,
    ( c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)
    | ~ c_in(hAPP(X2,X1),X3,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI_0) ).

cnf(cls_vimageI2_0,axiom,
    ( c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)
    | ~ c_in(hAPP(X2,X1),X3,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).

cnf(cls_vimage__eq_1,axiom,
    ( c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)
    | ~ c_in(hAPP(X2,X1),X3,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).

cnf(cls_map__le__def_0,axiom,
    ( hAPP(X1,X2) = hAPP(X3,X2)
    | ~ c_in(X2,c_Map_Odom(X1,X4,X5),X4)
    | ~ c_Map_Omap__le(X1,X3,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__def_0) ).

cnf(cls_imageI_0,axiom,
    ( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
    | ~ c_in(X2,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).

cnf(cls_image__eqI_0,axiom,
    ( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
    | ~ c_in(X2,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).

cnf(cls_image__iff_2,axiom,
    ( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
    | ~ c_in(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).

cnf(cls_rev__image__eqI_0,axiom,
    ( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
    | ~ c_in(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

cnf(cls_finite__Diff__insert_1,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).

cnf(cls_finite__UNIV__inj__surj_0,axiom,
    ( c_Fun_Osurj(X1,X2,X2)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X2)
    | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV__inj__surj_0) ).

cnf(cls_Diff__mono_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

cnf(cls_Un__mono_0,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).

cnf(cls_Int__mono_0,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).

cnf(cls_Diff__insert_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

cnf(cls_finite__vimage__iff_1,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Ovimage(X1,X2,X3,X4),X3)
    | ~ c_Finite__Set_Ofinite(X2,X4)
    | ~ c_Fun_Obij(X1,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimage__iff_1) ).

cnf(cls_Diff__Int2_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).

cnf(cls_Un__Diff_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).

cnf(cls_Un__Int__distrib2_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).

cnf(cls_Diff__Int__distrib2_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

cnf(cls_Int__Un__distrib2_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).

cnf(cls_Diff__Un_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).

cnf(cls_Diff__Int_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).

cnf(cls_Un__Int__distrib_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).

cnf(cls_Diff__Int__distrib_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

cnf(cls_Int__Un__distrib_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).

cnf(cls_bijI_0,axiom,
    ( c_Fun_Obij(X1,X2,X3)
    | ~ c_Fun_Osurj(X1,X2,X3)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bijI_0) ).

cnf(cls_bij__def_2,axiom,
    ( c_Fun_Obij(X1,X2,X3)
    | ~ c_Fun_Osurj(X1,X2,X3)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__def_2) ).

cnf(cls_inj__on__contraD_0,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_in(X3,X4,X5)
    | ~ c_in(X2,X4,X5)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).

cnf(cls_inj__on__iff_0,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_in(X3,X4,X5)
    | ~ c_in(X2,X4,X5)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).

cnf(cls_inj__on__def_0,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_in(X3,X4,X5)
    | ~ c_in(X2,X4,X5)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).

cnf(cls_inj__onD_0,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6)
    | ~ c_in(X3,X4,X5)
    | ~ c_in(X2,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).

cnf(cls_atLeastatMost__subset__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).

cnf(cls_atLeastatMost__subset__iff_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X4,X2,X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X4,X2,X1),c_SetInterval_Oord__class_OatLeastAtMost(X5,X3,X1),tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).

cnf(cls_derivs__insertD_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_0) ).

cnf(cls_Diff__subset__conv_1,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

cnf(cls_Diff__subset__conv_0,axiom,
    ( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

cnf(cls_subset__singletonD_0,axiom,
    ( X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

cnf(cls_sup1E_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X3,X2))
    | ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).

cnf(cls_Un__Int__assoc__eq_1,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X4,X1,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).

cnf(cls_atLeastLessThan__subset__iff_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(X4,X2,X1),c_SetInterval_Oord__class_OatLeastLessThan(X5,X3,X1),tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_1) ).

cnf(cls_atLeastLessThan__subset__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X4,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),c_SetInterval_Oord__class_OatLeastLessThan(X2,X5,X1),tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_0) ).

cnf(cls_inf1E_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).

cnf(cls_inf1E_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).

cnf(cls_ivl__disj__un_I6_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I6_J_0) ).

cnf(cls_doubleton__eq__iff_4,axiom,
    c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

cnf(cls_finite__imageI_0,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).

cnf(cls_ivl__disj__un_I17_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I17_J_0) ).

cnf(cls_ivl__disj__un_I21_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I21_J_0) ).

cnf(cls_injD_0,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).

cnf(cls_MGF__lemma1_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
    | ~ c_Com_OWT(X2)
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MGF__lemma1_0) ).

cnf(cls_insert__inter__insert_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

cnf(cls_finite__UNIV__surj__inj_0,axiom,
    ( c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X2)
    | ~ c_Fun_Osurj(X1,X2,X2)
    | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV__surj__inj_0) ).

cnf(cls_Int__insert__left_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
    | ~ c_in(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

cnf(cls_Int__insert__right_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_in(X2,X1,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).

cnf(cls_double__diff_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X3
    | ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).

cnf(cls_Un__least_0,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).

cnf(cls_Un__subset__iff_2,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

cnf(cls_Int__greatest_0,axiom,
    ( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).

cnf(cls_Int__subset__iff_2,axiom,
    ( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).

cnf(cls_atLeastatMost__subset__iff_3,axiom,
    ( c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1),tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_lessequals(X4,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).

cnf(cls_Int__Diff_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).

cnf(cls_Un__assoc_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

cnf(cls_Int__assoc_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

cnf(cls_Un__left__commute_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

cnf(cls_Int__left__commute_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

cnf(cls_empty__is__image_0,axiom,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oimage(X2,X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

cnf(cls_image__is__empty_0,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

cnf(cls_Diff__insert__absorb_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2
    | c_in(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

cnf(cls_insert__Diff__if_1,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)
    | c_in(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

cnf(cls_Un__subset__iff_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

cnf(cls_Un__subset__iff_1,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

cnf(cls_Int__subset__iff_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).

cnf(cls_Int__subset__iff_1,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).

cnf(cls_ivl__diff_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X4,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__diff_0) ).

cnf(cls_sup__inf__distrib2_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).

cnf(cls_inf__sup__distrib2_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).

cnf(cls_sup__inf__distrib1_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).

cnf(cls_inf__sup__distrib1_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).

cnf(cls_UnE_0,axiom,
    ( c_in(X1,X2,X3)
    | c_in(X1,X4,X3)
    | ~ c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).

cnf(cls_inf1I_0,axiom,
    ( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4))
    | ~ hBOOL(hAPP(X2,X4))
    | ~ hBOOL(hAPP(X1,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).

cnf(cls_single__Diff__lessThan_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),c_SetInterval_Oord__class_OlessThan(X2,X1),tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__Diff__lessThan_0) ).

cnf(cls_Compl__subset__Compl__iff_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).

cnf(cls_subset__insert_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_in(X4,X1,X3)
    | ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).

cnf(cls_subset__insert__iff_1,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_in(X4,X1,X3)
    | ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

cnf(cls_singletonE_0,axiom,
    ( X1 = X2
    | ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).

cnf(cls_insert__code_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | X3 = X2
    | ~ hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

cnf(cls_MGF_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | ~ c_Com_OWT(X1)
    | ~ c_Com_OWT__bodies
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MGF_0) ).

cnf(cls_insert__mono_0,axiom,
    ( c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).

cnf(cls_surj__range_0,axiom,
    ( c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))
    | ~ c_Fun_Osurj(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surj__range_0) ).

cnf(cls_DiffE_1,axiom,
    ( ~ c_in(X1,X2,X3)
    | ~ c_in(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).

cnf(cls_Compl__Un_0,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Un_0) ).

cnf(cls_Compl__Int_0,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Int_0) ).

cnf(cls_insert__subset_2,axiom,
    ( c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
    | ~ c_in(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

cnf(cls_Un__insert__left_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

cnf(cls_Un__insert__right_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

cnf(cls_bij__def_0,axiom,
    ( c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
    | ~ c_Fun_Obij(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__def_0) ).

cnf(cls_Un__Diff__Int_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).

cnf(cls_sup1CI_1,axiom,
    ( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
    | ~ hBOOL(hAPP(X1,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).

cnf(cls_sup1CI_0,axiom,
    ( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
    | ~ hBOOL(hAPP(X2,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).

cnf(cls_DiffE_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).

cnf(cls_IntE_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).

cnf(cls_IntE_1,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).

cnf(cls_Int__iff_2,axiom,
    ( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).

cnf(cls_IntI_0,axiom,
    ( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).

cnf(cls_weak__coinduct_0,axiom,
    ( c_in(X1,c_Inductive_Ocomplete__lattice__class_Ogfp(X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_lessequals(X4,hAPP(X2,X4),tc_fun(X3,tc_bool))
    | ~ c_in(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weak__coinduct_0) ).

cnf(cls_insert__subset_1,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Set_Oinsert(X4,X1,X3),X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

cnf(cls_subset__insert_1,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | c_in(X2,X1,X4)
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).

cnf(cls_subset__insert__iff_2,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | c_in(X2,X1,X4)
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

cnf(cls_atLeastatMost__subset__iff_2,axiom,
    ( c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1),tc_fun(X1,tc_bool))
    | c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).

cnf(cls_Diff__partition_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X2
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).

cnf(cls_DiffI_0,axiom,
    ( c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)
    | c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).

cnf(cls_Diff__iff_2,axiom,
    ( c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)
    | c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

cnf(cls_insert__Diff1_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool))
    | ~ c_in(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

cnf(cls_insert__subset_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

cnf(cls_Compl__anti__mono_0,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).

cnf(cls_Compl__subset__Compl__iff_1,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).

cnf(cls_insert__is__Un_0,axiom,
    c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

cnf(cls_le__sup__iff_2,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

cnf(cls_sup__least_0,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).

cnf(cls_le__supI_0,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).

cnf(cls_inf__greatest_0,axiom,
    ( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).

cnf(cls_le__inf__iff_2,axiom,
    ( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).

cnf(cls_le__infI_0,axiom,
    ( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).

cnf(cls_disjoint__eq__subset__Compl_1,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_1) ).

cnf(cls_Compl__Diff__eq_0,axiom,
    c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Diff__eq_0) ).

cnf(cls_disjoint__iff__not__equal_0,axiom,
    ( ~ c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).

cnf(cls_singleton__inject_0,axiom,
    ( X1 = X3
    | c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

cnf(cls_ivl__disj__un_I1_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),c_SetInterval_Oord__class_OgreaterThan(X2,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeast(X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I1_J_0) ).

cnf(cls_ivl__disj__un_I2_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(X2,X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatMost(X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I2_J_0) ).

cnf(cls_finite__dom__map__of_0,axiom,
    c_Finite__Set_Ofinite(c_Map_Odom(c_Map_Omap__of(X1,X2,X3),X2,X3),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__dom__map__of_0) ).

cnf(cls_sup__assoc_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

cnf(cls_inf__sup__aci_I6_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

cnf(cls_inf__assoc_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

cnf(cls_inf__sup__aci_I2_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

cnf(cls_sup__left__commute_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

cnf(cls_inf__sup__aci_I7_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

cnf(cls_inf__left__commute_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

cnf(cls_inf__sup__aci_I3_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

cnf(cls_derivs__insertD_1,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X4,X2,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).

cnf(cls_vimage__UNIV_0,axiom,
    c_Set_Ovimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).

cnf(cls_vimage__empty_0,axiom,
    c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).

cnf(cls_image__empty_0,axiom,
    c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).

cnf(cls_empty__is__image_1,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).

cnf(cls_ivl__disj__int_I11_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I11_J_0) ).

cnf(cls_ivl__disj__int_I15_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I15_J_0) ).

cnf(cls_insert__commute_0,axiom,
    c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

cnf(cls_subset__trans_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).

cnf(cls_le__eqI_1,axiom,
    ( c_lessequals(X3,X2,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
    | ~ c_lessequals(X5,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).

cnf(cls_le__eqI_0,axiom,
    ( c_lessequals(X5,X4,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).

cnf(cls_ivl__disj__un_I14_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeast(X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeast(X2,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I14_J_0) ).

cnf(cls_ivl__disj__un_I13_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThan(X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeast(X2,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I13_J_0) ).

cnf(cls_ivl__disj__un_I8_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(X2,X1),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OlessThan(X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I8_J_0) ).

cnf(cls_ivl__disj__un_I10_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(X2,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatMost(X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I10_J_0) ).

cnf(cls_Int__insert__left_1,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool))
    | c_in(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

cnf(cls_Int__insert__right_1,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool))
    | c_in(X2,X1,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

cnf(cls_le__sup__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

cnf(cls_le__supE_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).

cnf(cls_le__sup__iff_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

cnf(cls_le__supE_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).

cnf(cls_le__inf__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

cnf(cls_le__infE_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).

cnf(cls_le__inf__iff_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).

cnf(cls_le__infE_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).

cnf(cls_disjoint__eq__subset__Compl_0,axiom,
    ( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_0) ).

cnf(cls_insertE_0,axiom,
    ( c_in(X1,X2,X3)
    | X1 = X4
    | ~ c_in(X1,c_Set_Oinsert(X4,X2,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

cnf(cls_inv__id_0,axiom,
    c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Fun_Oid(X1),X1,X1) = c_Fun_Oid(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__id_0) ).

cnf(cls_Diff__idemp_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

cnf(cls_Un__Diff__cancel2_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

cnf(cls_Un__Diff__cancel_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).

cnf(cls_Un__left__absorb_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

cnf(cls_Int__left__absorb_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

cnf(cls_subset__insertI2_0,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

cnf(cls_subset__Compl__self__eq_1,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_1) ).

cnf(cls_finite__Diff2_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).

cnf(cls_inj__on__empty_0,axiom,
    c_Fun_Oinj__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).

cnf(cls_UnCI_1,axiom,
    ( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_in(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).

cnf(cls_UnCI_0,axiom,
    ( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_in(X1,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).

cnf(cls_insert__code_2,axiom,
    ( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
    | ~ hBOOL(hAPP(X2,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

cnf(cls_Max__mono_0,axiom,
    ( c_lessequals(c_Finite__Set_Olinorder__class_OMax(X2,X1),c_Finite__Set_Olinorder__class_OMax(X3,X1),X1)
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | ~ c_lessequals(X2,X3,tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__mono_0) ).

cnf(cls_Min__antimono_0,axiom,
    ( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X1),c_Finite__Set_Olinorder__class_OMin(X3,X1),X1)
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Finite__Set_Ofinite(X2,X1)
    | ~ c_lessequals(X3,X2,tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__antimono_0) ).

cnf(cls_evalc_OBody_0,axiom,
    ( c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1),X2,X3)
    | ~ c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OBody_0) ).

cnf(cls_sup__eq__neg__inf_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__neg__inf_0) ).

cnf(cls_inf__eq__neg__sup_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__neg__sup_0) ).

cnf(cls_ComplD_0,axiom,
    ( ~ c_in(X1,X2,X3)
    | ~ c_in(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplD_0) ).

cnf(cls_insert__ident_0,axiom,
    ( c_in(X1,X4,X3)
    | c_in(X1,X2,X3)
    | X2 = X4
    | c_Set_Oinsert(X1,X2,X3) != c_Set_Oinsert(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

cnf(cls_weaken_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_lessequals(X2,X4,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weaken_0) ).

cnf(cls_thin_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_lessequals(X4,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_thin_0) ).

cnf(cls_finite__Un_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).

cnf(cls_finite__Un_1,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).

cnf(cls_greaterThan__subset__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OgreaterThan(X3,X1),c_SetInterval_Oord__class_OgreaterThan(X2,X1),tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThan__subset__iff_0) ).

cnf(cls_lessThan__subset__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OlessThan(X2,X1),c_SetInterval_Oord__class_OlessThan(X3,X1),tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__subset__iff_0) ).

cnf(cls_atMost__subset__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OatMost(X2,X1),c_SetInterval_Oord__class_OatMost(X3,X1),tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__subset__iff_0) ).

cnf(cls_atLeast__subset__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OatLeast(X3,X1),c_SetInterval_Oord__class_OatLeast(X2,X1),tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__subset__iff_0) ).

cnf(cls_singleton__iff_1,axiom,
    c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

cnf(cls_set__mp_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).

cnf(cls_subsetD_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).

cnf(cls_set__rev__mp_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_in(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

cnf(cls_subset__iff_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).

cnf(cls_subset__Compl__self__eq_0,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).

cnf(cls_insert__dom_0,axiom,
    ( c_Set_Oinsert(X2,c_Map_Odom(X1,X5,X4),X5) = c_Map_Odom(X1,X5,X4)
    | hAPP(X1,X2) != c_Option_Ooption_OSome(X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__dom_0) ).

cnf(cls_card__eq__UNIV__imp__eq__UNIV_0,axiom,
    ( X1 = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
    | c_Finite__Set_Ocard(X1,X2) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__UNIV__imp__eq__UNIV_0) ).

cnf(cls_Diff__disjoint_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).

cnf(cls_le__infI1_0,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).

cnf(cls_le__infI2_0,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).

cnf(cls_le__supI1_0,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).

cnf(cls_le__supI2_0,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).

cnf(cls_evalc__elim__cases_I6_J_0,axiom,
    ( c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3)
    | ~ c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1),X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I6_J_0) ).

cnf(cls_vimage__id_0,axiom,
    c_Set_Ovimage(c_Fun_Oid(X1),X2,X1,X1) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__id_0) ).

cnf(cls_vimage__ident_0,axiom,
    c_Set_Ovimage(c_COMBI(X1),X2,X1,X1) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__ident_0) ).

cnf(cls_image__id_0,axiom,
    c_Set_Oimage(c_Fun_Oid(X1),X2,X1,X1) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__id_0) ).

cnf(cls_image__ident_0,axiom,
    c_Set_Oimage(c_COMBI(X1),X2,X1,X1) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__ident_0) ).

cnf(cls_inj__on__id_0,axiom,
    c_Fun_Oinj__on(c_Fun_Oid(X1),X2,X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__id_0) ).

cnf(cls_inj__on__id2_0,axiom,
    c_Fun_Oinj__on(c_COMBI(X1),X2,X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__id2_0) ).

cnf(cls_insert__iff_2,axiom,
    ( c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).

cnf(cls_insertCI_0,axiom,
    ( c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).

cnf(cls_map__le__refl_0,axiom,
    c_Map_Omap__le(X1,X1,X2,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__le__refl_0) ).

cnf(cls_equalityI_0,axiom,
    ( X1 = X2
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).

cnf(cls_set__eq__subset_2,axiom,
    ( X1 = X2
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

cnf(cls_ivl__disj__int_I8_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeast(X3,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I8_J_0) ).

cnf(cls_ivl__disj__int_I7_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThan(X3,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I7_J_0) ).

cnf(cls_ivl__disj__int_I2_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OlessThan(X2,X1),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I2_J_0) ).

cnf(cls_ivl__disj__int_I4_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OlessThan(X2,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I4_J_0) ).

cnf(cls_card__insert__if_0,axiom,
    ( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Finite__Set_Ocard(X2,X3)
    | ~ c_in(X1,X2,X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_0) ).

cnf(cls_insert__code_1,axiom,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

cnf(cls_atMost__Int__atLeast_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatMost(X2,X1),c_SetInterval_Oord__class_OatLeast(X2,X1),tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__Int__atLeast_0) ).

cnf(cls_Diff__triv_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).

cnf(cls_le__funD_0,axiom,
    ( c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1)
    | ~ class_HOL_Oord(X1)
    | ~ c_lessequals(X2,X4,tc_fun(X5,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).

cnf(cls_order__trans_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X4,X3,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

cnf(cls_xt1_I6_J_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X4,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

cnf(cls_neg__sup__eq__inf_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__sup__eq__inf_0) ).

cnf(cls_compl__sup_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup_0) ).

cnf(cls_neg__inf__eq__sup_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__inf__eq__sup_0) ).

cnf(cls_compl__inf_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf_0) ).

cnf(cls_Min__singleton_0,axiom,
    ( c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__singleton_0) ).

cnf(cls_Max__singleton_0,axiom,
    ( c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__singleton_0) ).

cnf(cls_subset__empty_0,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).

cnf(cls_Diff__subset_0,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

cnf(cls_Int__lower1_0,axiom,
    c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

cnf(cls_Int__lower2_0,axiom,
    c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

cnf(cls_Un__upper1_0,axiom,
    c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

cnf(cls_Un__upper2_0,axiom,
    c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

cnf(cls_neg__le__iff__le_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).

cnf(cls_cut_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut_0) ).

cnf(cls_Diff__Compl_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Compl_0) ).

cnf(cls_Diff__eq_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__eq_0) ).

cnf(cls_finite__compl_0,axiom,
    ( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__compl_0) ).

cnf(cls_greaterThan__subset__iff_1,axiom,
    ( c_lessequals(c_SetInterval_Oord__class_OgreaterThan(X2,X1),c_SetInterval_Oord__class_OgreaterThan(X3,X1),tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThan__subset__iff_1) ).

cnf(cls_atMost__subset__iff_1,axiom,
    ( c_lessequals(c_SetInterval_Oord__class_OatMost(X2,X1),c_SetInterval_Oord__class_OatMost(X3,X1),tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__subset__iff_1) ).

cnf(cls_atLeast__subset__iff_1,axiom,
    ( c_lessequals(c_SetInterval_Oord__class_OatLeast(X2,X1),c_SetInterval_Oord__class_OatLeast(X3,X1),tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__subset__iff_1) ).

cnf(cls_lessThan__subset__iff_1,axiom,
    ( c_lessequals(c_SetInterval_Oord__class_OlessThan(X2,X1),c_SetInterval_Oord__class_OlessThan(X3,X1),tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__subset__iff_1) ).

cnf(cls_sup__left__idem_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

cnf(cls_inf__sup__aci_I8_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

cnf(cls_inf__left__idem_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

cnf(cls_inf__sup__aci_I4_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

cnf(cls_atLeastatMost__empty__iff2_0,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).

cnf(cls_atLeastatMost__empty__iff_0,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).

cnf(cls_insert__absorb2_0,axiom,
    c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

cnf(cls_bex__empty_0,axiom,
    ( ~ hBOOL(hAPP(X1,X2))
    | ~ c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).

cnf(cls_minus__le__iff_1,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).

cnf(cls_minus__le__iff_0,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).

cnf(cls_gfp__upperbound_0,axiom,
    ( c_lessequals(X2,c_Inductive_Ocomplete__lattice__class_Ogfp(X3,X1),X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ c_lessequals(X2,hAPP(X3,X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gfp__upperbound_0) ).

cnf(cls_le__minus__iff_1,axiom,
    ( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).

cnf(cls_le__minus__iff_0,axiom,
    ( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).

cnf(cls_finite__compl_1,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__compl_1) ).

cnf(cls_finite__Diff2_1,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).

cnf(cls_finite__Un_2,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X2,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_2) ).

cnf(cls_finite__UnI_0,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X2,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).

cnf(cls_bot1E_0,axiom,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

cnf(cls_Un__empty_2,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).

cnf(cls_compl__unique_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(X2,X1) = X3
    | ~ class_Lattices_Oboolean__algebra(X1)
    | c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__unique_0) ).

cnf(cls_domI_0,axiom,
    ( c_in(X2,c_Map_Odom(X1,X5,X4),X5)
    | hAPP(X1,X2) != c_Option_Ooption_OSome(X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_domI_0) ).

cnf(cls_finite__insert_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).

cnf(cls_subset__Un__eq_1,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

cnf(cls_Un__absorb2_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X1
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

cnf(cls_Un__absorb1_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

cnf(cls_Int__absorb2_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).

cnf(cls_Int__absorb1_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X2
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

cnf(cls_predicate1D_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X3,X2))
    | ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).

cnf(cls_rev__predicate1D_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool))
    | ~ hBOOL(hAPP(X3,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

cnf(cls_le__imp__neg__le_0,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).

cnf(cls_ball__empty_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).

cnf(cls_Min__le_0,axiom,
    ( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X1),X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_in(X3,X2,X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__le_0) ).

cnf(cls_Max__ge_0,axiom,
    ( c_lessequals(X2,c_Finite__Set_Olinorder__class_OMax(X3,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_in(X2,X3,X1)
    | ~ c_Finite__Set_Ofinite(X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__ge_0) ).

cnf(cls_asm_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_lessequals(X2,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_asm_0) ).

cnf(cls_Un__empty_0,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).

cnf(cls_Un__empty_1,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).

cnf(cls_finite__Diff_0,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).

cnf(cls_finite__Int_0,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).

cnf(cls_finite__Int_1,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).

cnf(cls_atMost__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_HOL_Oord(X1)
    | ~ c_in(X2,c_SetInterval_Oord__class_OatMost(X3,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__iff_0) ).

cnf(cls_atLeast__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_HOL_Oord(X1)
    | ~ c_in(X3,c_SetInterval_Oord__class_OatLeast(X2,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__iff_0) ).

cnf(cls_subset__insertI_0,axiom,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

cnf(cls_comm__monoid__add_Ononempty__iff_2,axiom,
    ( c_in(X1,X2,X3)
    | c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

cnf(cls_minus__diff__eq_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Ominus__class_Ominus(X3,X2,X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).

cnf(cls_order__eq__iff_2,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

cnf(cls_order__antisym_0,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

cnf(cls_order__antisym__conv_0,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

cnf(cls_ComplI_0,axiom,
    ( c_in(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3)
    | c_in(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).

cnf(cls_subset__empty_1,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).

cnf(cls_eq__eqI_1,axiom,
    ( X2 = X3
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

cnf(cls_eq__eqI_0,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

cnf(cls_Compl__partition2_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition2_0) ).

cnf(cls_Compl__disjoint2_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint2_0) ).

cnf(cls_Compl__partition_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition_0) ).

cnf(cls_Compl__disjoint_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint_0) ).

cnf(cls_atLeastLessThan__empty_0,axiom,
    ( c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).

cnf(cls_com__det_0,axiom,
    ( X1 = X2
    | ~ c_Natural_Oevalc(X3,X4,X1)
    | ~ c_Natural_Oevalc(X3,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com__det_0) ).

cnf(cls_atMost__iff_1,axiom,
    ( c_in(X2,c_SetInterval_Oord__class_OatMost(X3,X1),X1)
    | ~ class_HOL_Oord(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__iff_1) ).

cnf(cls_atLeast__iff_1,axiom,
    ( c_in(X2,c_SetInterval_Oord__class_OatLeast(X3,X1),X1)
    | ~ class_HOL_Oord(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__iff_1) ).

cnf(cls_sup__inf__absorb_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = X2
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

cnf(cls_inf__sup__absorb_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = X2
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

cnf(cls_inf__le1_0,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).

cnf(cls_inf__sup__ord_I1_J_0,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

cnf(cls_inf__le2_0,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).

cnf(cls_inf__sup__ord_I2_J_0,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

cnf(cls_sup__ge1_0,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

cnf(cls_inf__sup__ord_I3_J_0,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

cnf(cls_sup__ge2_0,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

cnf(cls_inf__sup__ord_I4_J_0,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

cnf(cls_atLeastAtMost__singleton_0,axiom,
    ( c_SetInterval_Oord__class_OatLeastAtMost(X2,X2,X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).

cnf(cls_ex__in__conv_0,axiom,
    ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

cnf(cls_empty__iff_0,axiom,
    ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).

cnf(cls_emptyE_0,axiom,
    ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).

cnf(cls_Compl__eq__Diff__UNIV_0,axiom,
    c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Diff__UNIV_0) ).

cnf(cls_insert__iff_1,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).

cnf(cls_insertI1_0,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).

cnf(cls_insertCI_1,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).

cnf(cls_finite__subset_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(X3,X2)
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).

cnf(cls_rev__finite__subset_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).

cnf(cls_empty__Diff_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

cnf(cls_Un__UNIV__left_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).

cnf(cls_Int__empty__left_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

cnf(cls_Diff__UNIV_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).

cnf(cls_Un__UNIV__right_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).

cnf(cls_Int__empty__right_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

cnf(cls_Un__commute_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).

cnf(cls_Int__commute_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).

cnf(cls_le__iff__sup_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

cnf(cls_le__iff__inf_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

cnf(cls_sup__absorb1_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X2
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

cnf(cls_le__iff__sup_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X3
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

cnf(cls_le__iff__inf_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

cnf(cls_inf__absorb2_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X3
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

cnf(cls_finite__insert_1,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).

cnf(cls_atLeastatMost__empty__iff2_1,axiom,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
    | c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).

cnf(cls_atLeastatMost__empty__iff_1,axiom,
    ( c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).

cnf(cls_diff__eq_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__eq_0) ).

cnf(cls_insert__absorb_0,axiom,
    ( c_Set_Oinsert(X1,X2,X3) = X2
    | ~ c_in(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

cnf(cls_bij__def_1,axiom,
    ( c_Fun_Osurj(X1,X2,X3)
    | ~ c_Fun_Obij(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__def_1) ).

cnf(cls_Min__in_0,axiom,
    ( c_in(c_Finite__Set_Olinorder__class_OMin(X2,X1),X2,X1)
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__in_0) ).

cnf(cls_Max__in_0,axiom,
    ( c_in(c_Finite__Set_Olinorder__class_OMax(X2,X1),X2,X1)
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__in_0) ).

cnf(cls_top1I_0,axiom,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).

cnf(cls_empty_0,axiom,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty_0) ).

cnf(cls_Un__empty__left_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

cnf(cls_Int__UNIV__left_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).

cnf(cls_Diff__empty_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

cnf(cls_Un__empty__right_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

cnf(cls_Int__UNIV__right_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).

cnf(cls_empty__subsetI_0,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

cnf(cls_subset__UNIV_0,axiom,
    c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).

cnf(cls_empty__not__insert_0,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

cnf(cls_insert__not__empty_0,axiom,
    c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

cnf(cls_Compl__eq__Compl__iff_0,axiom,
    ( X1 = X3
    | c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)) != c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).

cnf(cls_linorder__linear_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

cnf(cls_mem__def_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_in(X2,X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

cnf(cls_sup__commute_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).

cnf(cls_inf__sup__aci_I5_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

cnf(cls_inf__commute_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

cnf(cls_inf__sup__aci_I1_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

cnf(cls_Compl__UNIV__eq_0,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__UNIV__eq_0) ).

cnf(cls_Compl__empty__eq_0,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).

cnf(cls_finite__dom__body_0,axiom,
    c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__dom__body_0) ).

cnf(cls_double__complement_0,axiom,
    c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).

cnf(cls_UNIV__I_0,axiom,
    c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).

cnf(cls_inf__eq__top__eq1_0,axiom,
    ( X2 = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).

cnf(cls_sup__eq__bot__eq1_0,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

cnf(cls_inf__eq__top__eq2_0,axiom,
    ( X3 = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).

cnf(cls_sup__eq__bot__eq2_0,axiom,
    ( X3 = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

cnf(cls_Diff__cancel_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

cnf(cls_mem__def_1,axiom,
    ( c_in(X1,X2,X3)
    | ~ hBOOL(hAPP(X2,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

cnf(cls_compl__sup__top_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup__top_0) ).

cnf(cls_compl__inf__bot_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).

cnf(cls_sup__compl__top_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__compl__top_0) ).

cnf(cls_inf__compl__bot_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).

cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
    ( X1 = X2
    | ~ c_fequal(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

cnf(cls_UNIV__not__empty_0,axiom,
    c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).

cnf(cls_Compl__greaterThan_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OgreaterThan(X2,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatMost(X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__greaterThan_0) ).

cnf(cls_Compl__atMost_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OatMost(X2,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThan(X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__atMost_0) ).

cnf(cls_Compl__atLeast_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OatLeast(X2,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OlessThan(X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__atLeast_0) ).

cnf(cls_Compl__lessThan_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OlessThan(X2,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeast(X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__lessThan_0) ).

cnf(cls_Un__absorb_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

cnf(cls_Int__absorb_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

cnf(cls_equalityE_0,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).

cnf(cls_subset__refl_0,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).

cnf(cls_finite__UNIV_0,axiom,
    ( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).

cnf(cls_sup__top__left_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X2,X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).

cnf(cls_inf__bot__left_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

cnf(cls_sup__top__right_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Otop__class_Otop(X1),X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).

cnf(cls_inf__bot__right_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Obot__class_Obot(X1),X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

cnf(cls_sup__bot__left_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

cnf(cls_inf__top__left_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X2,X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).

cnf(cls_sup__bot__right_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Obot__class_Obot(X1),X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

cnf(cls_inf__top__right_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Otop__class_Otop(X1),X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).

cnf(cls_bot__least_0,axiom,
    ( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
    | ~ class_Orderings_Obot(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).

cnf(cls_top__greatest_0,axiom,
    ( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
    | ~ class_Orderings_Otop(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).

cnf(cls_finite_OemptyI_0,axiom,
    c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).

cnf(cls_sup__idem_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X2,X1) = X2
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

cnf(cls_inf__idem_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X2,X1) = X2
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

cnf(cls_order__eq__refl_0,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Opreorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

cnf(cls_order__eq__iff_0,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

cnf(cls_bij__id_0,axiom,
    c_Fun_Obij(c_Fun_Oid(X1),X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__id_0) ).

cnf(cls_surj__id_0,axiom,
    c_Fun_Osurj(c_Fun_Oid(X1),X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surj__id_0) ).

cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
    c_fequal(X1,X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

cnf(cls_greaterThan__eq__iff_0,axiom,
    ( X2 = X3
    | ~ class_Orderings_Olinorder(X1)
    | c_SetInterval_Oord__class_OgreaterThan(X2,X1) != c_SetInterval_Oord__class_OgreaterThan(X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThan__eq__iff_0) ).

cnf(cls_atMost__eq__iff_0,axiom,
    ( X2 = X3
    | ~ class_Orderings_Olinorder(X1)
    | c_SetInterval_Oord__class_OatMost(X2,X1) != c_SetInterval_Oord__class_OatMost(X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__eq__iff_0) ).

cnf(cls_atLeast__eq__iff_0,axiom,
    ( X2 = X3
    | ~ class_Orderings_Olinorder(X1)
    | c_SetInterval_Oord__class_OatLeast(X2,X1) != c_SetInterval_Oord__class_OatLeast(X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__eq__iff_0) ).

cnf(cls_lessThan__eq__iff_0,axiom,
    ( X2 = X3
    | ~ class_Orderings_Olinorder(X1)
    | c_SetInterval_Oord__class_OlessThan(X2,X1) != c_SetInterval_Oord__class_OlessThan(X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__eq__iff_0) ).

cnf(cls_neg__equal__iff__equal_0,axiom,
    ( X2 = X3
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).

cnf(cls_compl__eq__compl__iff_0,axiom,
    ( X2 = X3
    | ~ class_Lattices_Oboolean__algebra(X1)
    | c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).

cnf(cls_minus__equation__iff_1,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).

cnf(cls_minus__minus_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).

cnf(cls_double__compl_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).

cnf(cls_equation__minus__iff_1,axiom,
    ( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).

cnf(cls_equation__minus__iff_0,axiom,
    ( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).

cnf(cls_the_Osimps_0,axiom,
    hAPP(c_Option_Othe(X1),c_Option_Ooption_OSome(X2,X1)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the_Osimps_0) ).

cnf(cls_option_Oinject_0,axiom,
    ( X1 = X3
    | c_Option_Ooption_OSome(X1,X2) != c_Option_Ooption_OSome(X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Oinject_0) ).

cnf(cls_WT__bodiesD_0,axiom,
    ( c_Com_OWT(X2)
    | hAPP(c_Com_Obody,X1) != c_Option_Ooption_OSome(X2,tc_Com_Ocom)
    | ~ c_Com_OWT__bodies ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__bodiesD_0) ).

cnf(clsarity_fun__Finite__Set_Ofinite_Ofinite,axiom,
    ( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
    | ~ class_Finite__Set_Ofinite_Ofinite(X2)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).

cnf(cls_com_Osimps_I6_J_0,axiom,
    ( X1 = X2
    | hAPP(c_Com_Ocom_OBODY,X1) != hAPP(c_Com_Ocom_OBODY,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).

cnf(clsarity_fun__Orderings_Opreorder,axiom,
    ( class_Orderings_Opreorder(tc_fun(X1,X2))
    | ~ class_Orderings_Opreorder(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

cnf(clsarity_fun__Orderings_Obot,axiom,
    ( class_Orderings_Obot(tc_fun(X1,X2))
    | ~ class_Orderings_Obot(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

cnf(clsarity_fun__Orderings_Otop,axiom,
    ( class_Orderings_Otop(tc_fun(X1,X2))
    | ~ class_Orderings_Otop(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).

cnf(clsarity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
    ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).

cnf(clsarity_fun__HOL_Oord,axiom,
    ( class_HOL_Oord(tc_fun(X1,X2))
    | ~ class_HOL_Oord(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

cnf(clsarity_fun__Lattices_Obounded__lattice,axiom,
    ( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
    | ~ class_Lattices_Obounded__lattice(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

cnf(clsarity_fun__Lattices_Odistrib__lattice,axiom,
    ( class_Lattices_Odistrib__lattice(tc_fun(X1,X2))
    | ~ class_Lattices_Odistrib__lattice(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).

cnf(clsarity_fun__Lattices_Oupper__semilattice,axiom,
    ( class_Lattices_Oupper__semilattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

cnf(clsarity_fun__Lattices_Olower__semilattice,axiom,
    ( class_Lattices_Olower__semilattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

cnf(clsarity_fun__Lattices_Olattice,axiom,
    ( class_Lattices_Olattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

cnf(clsarity_fun__Lattices_Oboolean__algebra,axiom,
    ( class_Lattices_Oboolean__algebra(tc_fun(X1,X2))
    | ~ class_Lattices_Oboolean__algebra(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).

cnf(clsarity_fun__Orderings_Oorder,axiom,
    ( class_Orderings_Oorder(tc_fun(X1,X2))
    | ~ class_Orderings_Oorder(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

cnf(cls_compl__top__eq_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(X1),X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).

cnf(cls_compl__bot__eq_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(X1),X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).

cnf(cls_finite_0,axiom,
    ( c_Finite__Set_Ofinite(X2,X1)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).

cnf(cls_id__apply_0,axiom,
    hAPP(c_Fun_Oid(X1),X2) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__apply_0) ).

cnf(cls_COMBI__def_0,axiom,
    hAPP(c_COMBI(X1),X2) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def_0) ).

cnf(clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite,axiom,
    ( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X1))
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite) ).

cnf(cls_single__stateE_0,axiom,
    ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X1) != X1
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__stateE_0) ).

cnf(cls_state__not__singleton__def_1,axiom,
    ( c_Hoare__Mirabelle_Ostate__not__singleton
    | X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_state__not__singleton__def_1) ).

cnf(clsarity_nat__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

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

cnf(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
    class_Finite__Set_Ofinite_Ofinite(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).

cnf(clsarity_nat__Orderings_Obot,axiom,
    class_Orderings_Obot(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

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

cnf(clsarity_bool__Orderings_Otop,axiom,
    class_Orderings_Otop(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).

cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).

cnf(clsarity_nat__HOL_Oord,axiom,
    class_HOL_Oord(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

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

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

cnf(clsarity_nat__Lattices_Odistrib__lattice,axiom,
    class_Lattices_Odistrib__lattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).

cnf(clsarity_bool__Lattices_Odistrib__lattice,axiom,
    class_Lattices_Odistrib__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).

cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom,
    class_Lattices_Oupper__semilattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

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

cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
    class_Lattices_Olower__semilattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).

cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

cnf(clsarity_nat__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

cnf(clsarity_bool__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

cnf(clsarity_nat__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
    class_Lattices_Oboolean__algebra(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).

cnf(clsarity_nat__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

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

cnf(cls_conjecture_1,negated_conjecture,
    c_Com_OWT__bodies,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_Hoare__Mirabelle_Ostate__not__singleton,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(i_0_625,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | ~ c_Finite__Set_Ofinite(X2,tc_Com_Opname)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),X2,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    cls_MGT__Body_0,
    [final] ).

cnf(i_0_626,negated_conjecture,
    ~ c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),
    cls_conjecture_3,
    [final] ).

cnf(i_0_627,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X6,X5),X7) = hAPP(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(X1,X3,X6,X4),c_Hilbert__Choice_Oinv__into(c_Set_Oimage(X3,X1,X6,X4),X2,X4,X5),X4,X6,X5),X7)
    | ~ c_in(X7,c_Set_Oimage(X2,c_Set_Oimage(X3,X1,X6,X4),X4,X5),X5)
    | ~ c_Fun_Oinj__on(X3,X1,X6,X4)
    | ~ c_Fun_Oinj__on(X2,c_Set_Oimage(X3,X1,X6,X4),X4,X5) ),
    cls_inv__into__comp_0,
    [final] ).

cnf(i_0_628,negated_conjecture,
    c_lessequals(v_F,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),
    cls_conjecture_2,
    [final] ).

cnf(i_0_629,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | ~ c_in(hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X2,X5,X1,X3,X4)),X5,X4) ),
    cls_image__subset__iff_2,
    [final] ).

cnf(i_0_630,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | ~ c_in(hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X2,X5,X1,X3,X4)),X5,X4) ),
    cls_image__subsetI_1,
    [final] ).

cnf(i_0_631,axiom,
    ( c_Set_Oimage(X1,X2,X4,X5) = c_Set_Oimage(X3,X2,X4,X5)
    | hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X3,X4,X5)) != hAPP(X3,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X3,X4,X5)) ),
    cls_image__cong_1,
    [final] ).

cnf(i_0_632,axiom,
    ( c_Fun_Obij__betw(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6,X7,X5,X4)
    | ~ c_Fun_Obij__betw(X1,X8,X7,X3,X4)
    | ~ c_Fun_Obij__betw(X2,X6,X8,X5,X3) ),
    cls_bij__betw__trans_0,
    [final] ).

cnf(i_0_633,axiom,
    c_Fun_Ocomp(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X5,X7,X6) = c_Fun_Ocomp(c_Fun_Ocomp(X1,X2,X5,X7,X4),X3,X4,X7,X6),
    cls_o__assoc_0,
    [final] ).

cnf(i_0_634,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(X1,X2,X3,X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X4),X4)
    | ~ c_Finite__Set_Ofinite(c_Set_Oimage(X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X3),X3) ),
    cls_finite__range__imageI_0,
    [final] ).

cnf(i_0_635,axiom,
    ( c_Fun_Ocomp(c_Fun_Ocomp(X1,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X2,X4),X2,X5,X4),X3,X4,X5,X2) = X1
    | ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X4) ),
    cls_o__inv__o__cancel_0,
    [final] ).

cnf(i_0_636,axiom,
    ( c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Fun_Ocomp(X2,X3,X4,X5,X1),X1,X5) = c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X3,X1,X4),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X2,X4,X5),X4,X1,X5)
    | ~ c_Fun_Obij(X3,X1,X4)
    | ~ c_Fun_Obij(X2,X4,X5) ),
    cls_o__inv__distrib_0,
    [final] ).

cnf(i_0_637,axiom,
    ( hAPP(c_Fun_Ocomp(X1,X2,X7,X8,X9),X3) = hAPP(c_Fun_Ocomp(X4,X5,X10,X8,X11),X6)
    | hAPP(X1,hAPP(X2,X3)) != hAPP(X4,hAPP(X5,X6)) ),
    cls_comp__cong_0,
    [final] ).

cnf(i_0_638,axiom,
    ( c_Fun_Oinj__on(X1,c_Set_Oimage(X2,X3,X4,X5),X5,X6)
    | ~ c_Fun_Oinj__on(c_Fun_Ocomp(X1,X2,X5,X6,X4),X3,X4,X6) ),
    cls_inj__on__imageI_0,
    [final] ).

cnf(i_0_639,axiom,
    ( c_Fun_Oinj__on(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6,X5,X4)
    | ~ c_Fun_Oinj__on(X1,c_Set_Oimage(X2,X6,X5,X3),X3,X4)
    | ~ c_Fun_Oinj__on(X2,X6,X5,X3) ),
    cls_comp__inj__on_0,
    [final] ).

cnf(i_0_640,axiom,
    ( hAPP(X1,hAPP(X2,X9)) = hAPP(X6,hAPP(X7,X9))
    | c_Fun_Ocomp(X1,X2,X3,X4,X5) != c_Fun_Ocomp(X6,X7,X8,X4,X5) ),
    cls_o__eq__dest_0,
    [final] ).

cnf(i_0_641,axiom,
    ( c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
    | c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X4,X5),tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X4,X5) ),
    cls_inj__on__Un_3,
    [final] ).

cnf(i_0_642,axiom,
    ( hAPP(X1,hAPP(X2,X7)) = hAPP(X6,X7)
    | c_Fun_Ocomp(X1,X2,X3,X4,X5) != c_Fun_Ocomp(c_Fun_Oid(X4),X6,X4,X4,X5) ),
    cls_o__eq__id__dest_0,
    [final] ).

cnf(i_0_643,axiom,
    ( c_Fun_Obij__betw(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5,X1,X4,X3)
    | ~ c_Fun_Obij__betw(X2,X1,X5,X3,X4) ),
    cls_bij__betw__inv__into_0,
    [final] ).

cnf(i_0_644,axiom,
    ( X1 = c_Set_Oimage(X2,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X3,X1,X2,X4,X5),X4,X5)
    | ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Finite__Set_Ofinite(X1,X5) ),
    cls_finite__subset__image_2,
    [final] ).

cnf(i_0_645,axiom,
    ( X1 = c_Set_Oimage(X2,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X3,X1,X2,X4,X5),X4,X5)
    | ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool)) ),
    cls_subset__image__iff_1,
    [final] ).

cnf(i_0_646,axiom,
    c_Set_Oimage(c_COMBB(X1,X2,X3,X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X4) = c_Set_Oimage(X1,c_Set_Oimage(X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X3),X3,X4),
    cls_range__composition_0,
    [final] ).

cnf(i_0_647,axiom,
    ( c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X1,X2,X3,X4,X5),X1,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,c_Set_Oimage(X3,X1,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X5) ),
    cls_finite__subset__image_0,
    [final] ).

cnf(i_0_648,axiom,
    c_Set_Ovimage(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6,X5,X4) = c_Set_Ovimage(X2,c_Set_Ovimage(X1,X6,X3,X4),X5,X3),
    cls_vimage__compose_0,
    [final] ).

cnf(i_0_649,axiom,
    c_Set_Oimage(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6,X5,X4) = c_Set_Oimage(X1,c_Set_Oimage(X2,X6,X5,X3),X3,X4),
    cls_image__compose_0,
    [final] ).

cnf(i_0_650,axiom,
    c_Set_Oimage(X1,c_Set_Oimage(X2,X3,X4,X5),X5,X6) = c_Set_Oimage(c_COMBB(X1,X2,X5,X6,X4),X3,X4,X6),
    cls_image__image_0,
    [final] ).

cnf(i_0_651,axiom,
    ( c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X1,X2,X3,X4,X5),X1,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,c_Set_Oimage(X3,X1,X4,X5),tc_fun(X5,tc_bool)) ),
    cls_subset__image__iff_0,
    [final] ).

cnf(i_0_652,axiom,
    ( c_lessequals(X2,X3,tc_fun(X4,X1))
    | ~ class_HOL_Oord(X1)
    | ~ c_lessequals(hAPP(X2,c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1(X2,X3,X4,X1)),hAPP(X3,c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1(X2,X3,X4,X1)),X1) ),
    cls_le__fun__def_1,
    [final] ).

cnf(i_0_653,axiom,
    ( c_lessequals(X2,X3,tc_fun(X4,X1))
    | ~ class_HOL_Oord(X1)
    | ~ c_lessequals(hAPP(X2,c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1(X2,X3,X4,X1)),hAPP(X3,c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1(X2,X3,X4,X1)),X1) ),
    cls_le__funI_0,
    [final] ).

cnf(i_0_654,axiom,
    ( c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X1,X2,X3,X4,X5),X4)
    | ~ c_lessequals(X2,c_Set_Oimage(X3,X1,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X5) ),
    cls_finite__subset__image_1,
    [final] ).

cnf(i_0_655,axiom,
    ( X5 = X6
    | hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5) != hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X6)
    | ~ c_in(X6,c_Set_Oimage(X2,X1,X3,X4),X4)
    | ~ c_in(X5,c_Set_Oimage(X2,X1,X3,X4),X4) ),
    cls_inv__into__injective_0,
    [final] ).

cnf(i_0_656,axiom,
    ( ~ c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5),X5)
    | ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) ),
    cls_inj__on__insert_1,
    [final] ).

cnf(i_0_657,axiom,
    ( c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3)
    | c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),X2,X3,X1,X1) != c_Fun_Oid(X1) ),
    cls_inj__iff_1,
    [final] ).

cnf(i_0_658,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X2,X5,X1,X3,X4),X2,X3) ),
    cls_image__subset__iff_1,
    [final] ).

cnf(i_0_659,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X2,X5,X1,X3,X4),X2,X3) ),
    cls_image__subsetI_0,
    [final] ).

cnf(i_0_660,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
    cls_image__diff__subset_0,
    [final] ).

cnf(i_0_661,axiom,
    c_lessequals(c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
    cls_image__Int__subset_0,
    [final] ).

cnf(i_0_662,axiom,
    ( c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X5,X2,X3,X4)
    | c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X5,X3,X4),X2,X3) ),
    cls_image__cong_0,
    [final] ).

cnf(i_0_663,axiom,
    ( c_Fun_Osurj(X1,X2,X3)
    | c_Fun_Ocomp(X1,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),X2,X3,X3) != c_Fun_Oid(X3) ),
    cls_surj__iff_1,
    [final] ).

cnf(i_0_664,axiom,
    ( c_in(hAPP(X1,X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_lessequals(c_Set_Oimage(X1,X5,X6,X4),hAPP(X3,c_Set_Oimage(X1,X5,X6,X4)),tc_fun(X4,tc_bool))
    | ~ c_in(X2,X5,X6) ),
    cls_weak__coinduct__image_0,
    [final] ).

cnf(i_0_665,axiom,
    ( c_Finite__Set_Ocard(X1,X2) = c_Finite__Set_Ocard(X3,X4)
    | ~ c_Finite__Set_Ofinite(X3,X4)
    | ~ c_Finite__Set_Ofinite(X1,X2)
    | ~ c_lessequals(c_Set_Oimage(X5,X3,X4,X2),X1,tc_fun(X2,tc_bool))
    | ~ c_Fun_Oinj__on(X5,X3,X4,X2)
    | ~ c_lessequals(c_Set_Oimage(X6,X1,X2,X4),X3,tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X6,X1,X2,X4) ),
    cls_card__bij__eq_0,
    [final] ).

cnf(i_0_666,axiom,
    ( c_Fun_Obij(c_Fun_Ocomp(X1,X2,X3,X4,X5),X5,X4)
    | ~ c_Fun_Obij(X1,X3,X4)
    | ~ c_Fun_Obij(X2,X5,X3) ),
    cls_bij__comp_0,
    [final] ).

cnf(i_0_667,axiom,
    ( c_Fun_Osurj(c_Fun_Ocomp(X1,X2,X3,X4,X5),X5,X4)
    | ~ c_Fun_Osurj(X1,X3,X4)
    | ~ c_Fun_Osurj(X2,X5,X3) ),
    cls_comp__surj_0,
    [final] ).

cnf(i_0_668,axiom,
    ( c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5)
    | c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5),X5)
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5) ),
    cls_inj__on__insert_2,
    [final] ).

cnf(i_0_669,axiom,
    hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
    cls_ATP__Linkup_OCOMBB__def_0,
    [final] ).

cnf(i_0_670,axiom,
    hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
    cls_COMBB__def_0,
    [final] ).

cnf(i_0_671,axiom,
    hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
    cls_o__apply_0,
    [final] ).

cnf(i_0_672,axiom,
    hAPP(X1,hAPP(X2,X3)) = hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3),
    cls_o__eq__dest__lhs_0,
    [final] ).

cnf(i_0_673,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X4,X5),tc_fun(X5,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
    cls_inj__on__Un_2,
    [final] ).

cnf(i_0_674,axiom,
    ( c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),X2,X3,X1,X1) = c_Fun_Oid(X1)
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
    cls_inj__iff_0,
    [final] ).

cnf(i_0_675,axiom,
    ( c_lessequals(c_Set_Oimage(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3,X4),c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(X1,X2,X3,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    cls_inj__image__Compl__subset_0,
    [final] ).

cnf(i_0_676,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X5) ),
    cls_inj__image__subset__iff_0,
    [final] ).

cnf(i_0_677,axiom,
    ( c_Set_Oimage(X1,X2,X3,X4) = X5
    | ~ c_Fun_Obij__betw(X1,X2,X5,X3,X4) ),
    cls_bij__betw__def_1,
    [final] ).

cnf(i_0_678,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Obij__betw(X1,X2,X5,X3,X4) ),
    cls_bij__betw__def_0,
    [final] ).

cnf(i_0_679,axiom,
    ( c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(X3,X6,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X6,tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X6,X4,X5) ),
    cls_inj__on__image__set__diff_0,
    [final] ).

cnf(i_0_680,axiom,
    ( c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(X3,X6,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X6,tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X6,X4,X5) ),
    cls_inj__on__image__Int_0,
    [final] ).

cnf(i_0_681,axiom,
    ( c_Fun_Obij__betw(X1,X2,c_Set_Oimage(X1,X2,X3,X4),X3,X4)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
    cls_bij__betw__def_2,
    [final] ).

cnf(i_0_682,axiom,
    ( c_Set_Oimage(X1,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),X4,X3,X2),X2,X3) = X4
    | ~ c_Fun_Osurj(X1,X2,X3) ),
    cls_image__surj__f__inv__f_0,
    [final] ).

cnf(i_0_683,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Un__Int__crazy_0,
    [final] ).

cnf(i_0_684,axiom,
    ( c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),X5,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    cls_vimage__subsetI_0,
    [final] ).

cnf(i_0_685,axiom,
    ( c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    cls_image__set__diff_0,
    [final] ).

cnf(i_0_686,axiom,
    ( c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    cls_image__Int_0,
    [final] ).

cnf(i_0_687,axiom,
    ( c_in(hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5),X1,X3)
    | ~ c_in(X5,c_Set_Oimage(X2,X1,X3,X4),X4) ),
    cls_inv__into__into_0,
    [final] ).

cnf(i_0_688,axiom,
    ( c_Finite__Set_Ocard(X1,X2) = c_Finite__Set_Ocard(X3,X4)
    | ~ c_Fun_Obij__betw(X5,X1,X3,X2,X4) ),
    cls_bij__betw__same__card_0,
    [final] ).

cnf(i_0_689,axiom,
    ( c_Fun_Ocomp(X1,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),X2,X3,X3) = c_Fun_Oid(X3)
    | ~ c_Fun_Osurj(X1,X2,X3) ),
    cls_surj__iff_0,
    [final] ).

cnf(i_0_690,axiom,
    ( hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),X5)) = X5
    | ~ c_in(X5,c_Set_Oimage(X1,X2,X3,X4),X4) ),
    cls_f__inv__into__f_0,
    [final] ).

cnf(i_0_691,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(X1,X2,X3,X4),tc_fun(X4,tc_bool)),c_Set_Oimage(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool))
    | ~ c_Fun_Osurj(X1,X3,X4) ),
    cls_surj__Compl__image__subset_0,
    [final] ).

cnf(i_0_692,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,X2)),X1,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
    cls_MGT__BodyN_0,
    [final] ).

cnf(i_0_693,axiom,
    c_Set_Ovimage(X1,c_Set_Oinsert(X2,X3,X4),X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
    cls_vimage__insert_0,
    [final] ).

cnf(i_0_694,axiom,
    ( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),c_Set_Oimage(X2,X4,X1,X3),X3,X1) = X4
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
    cls_image__inv__f__f_0,
    [final] ).

cnf(i_0_695,axiom,
    ( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),c_Set_Oimage(X2,X4,X1,X3),X3,X1) = X4
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
    cls_inv__image__comp_0,
    [final] ).

cnf(i_0_696,axiom,
    ( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),c_Set_Oimage(X2,X5,X3,X4),X4,X3) = X5
    | ~ c_lessequals(X5,X1,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
    cls_inv__into__image__cancel_0,
    [final] ).

cnf(i_0_697,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
    cls_vimage__code_0,
    [final] ).

cnf(i_0_698,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    cls_inj__image__subset__iff_1,
    [final] ).

cnf(i_0_699,axiom,
    ( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5,X4,X3)
    | ~ c_lessequals(X5,c_Set_Oimage(X2,X1,X3,X4),tc_fun(X4,tc_bool)) ),
    cls_inj__on__inv__into_0,
    [final] ).

cnf(i_0_700,axiom,
    ( c_Set_Oimage(X1,X2,X3,X3) = X2
    | ~ c_Fun_Oinj__on(X1,X2,X3,X3)
    | ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X3),X2,tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_endo__inj__surj_0,
    [final] ).

cnf(i_0_701,axiom,
    c_lessequals(c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4),X2,tc_fun(X4,tc_bool)),
    cls_image__vimage__subset_0,
    [final] ).

cnf(i_0_702,axiom,
    ( c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),X5,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_Fun_Obij(X1,X3,X4) ),
    cls_vimage__subset__eq_1,
    [final] ).

cnf(i_0_703,axiom,
    ( c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(c_Set_Ovimage(X2,X1,X4,X5),X3,tc_fun(X4,tc_bool))
    | ~ c_Fun_Obij(X2,X4,X5) ),
    cls_vimage__subset__eq_0,
    [final] ).

cnf(i_0_704,axiom,
    ( c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(c_Set_Ovimage(X2,X1,X4,X5),X3,tc_fun(X4,tc_bool))
    | ~ c_Fun_Osurj(X2,X4,X5) ),
    cls_vimage__subsetD_0,
    [final] ).

cnf(i_0_705,axiom,
    ( hAPP(X1,X2) = X3
    | ~ c_in(X2,c_Set_Ovimage(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),X5) ),
    cls_vimage__singleton__eq_0,
    [final] ).

cnf(i_0_706,axiom,
    c_Set_Ovimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
    cls_vimage__Diff_0,
    [final] ).

cnf(i_0_707,axiom,
    c_Set_Ovimage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
    cls_vimage__Un_0,
    [final] ).

cnf(i_0_708,axiom,
    c_Set_Ovimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
    cls_vimage__Int_0,
    [final] ).

cnf(i_0_709,axiom,
    c_Set_Oimage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),
    cls_image__Un_0,
    [final] ).

cnf(i_0_710,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
    | ~ c_Fun_Oinj__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X5) ),
    cls_inj__image__mem__iff_0,
    [final] ).

cnf(i_0_711,axiom,
    c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
    cls_image__vimage__eq_0,
    [final] ).

cnf(i_0_712,axiom,
    ( X2 = X5
    | c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X5,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),X3,X4) ),
    cls_inj__on__Un__image__eq__iff_0,
    [final] ).

cnf(i_0_713,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    cls_subset__insert__iff_4,
    [final] ).

cnf(i_0_714,axiom,
    ( hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),X4)) = X4
    | ~ c_Fun_Osurj(X1,X2,X3) ),
    cls_surj__f__inv__f_0,
    [final] ).

cnf(i_0_715,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_in(X2,X1,X4)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    cls_diff__single__insert_0,
    [final] ).

cnf(i_0_716,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_in(X2,X1,X4)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    cls_subset__insert__iff_3,
    [final] ).

cnf(i_0_717,axiom,
    ( X2 = X5
    | c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X5,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    cls_inj__image__eq__iff_0,
    [final] ).

cnf(i_0_718,axiom,
    ( c_Set_Ovimage(X1,c_Set_Oimage(X1,X2,X3,X4),X3,X4) = X2
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    cls_inj__vimage__image__eq_0,
    [final] ).

cnf(i_0_719,axiom,
    c_Fun_Ocomp(c_Fun_Oid(X1),X2,X1,X1,X3) = X2,
    cls_id__o_0,
    [final] ).

cnf(i_0_720,axiom,
    c_Fun_Ocomp(X1,c_Fun_Oid(X2),X2,X3,X2) = X1,
    cls_o__id_0,
    [final] ).

cnf(i_0_721,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Fun_Oinj__on(X3,X1,X2,X4)
    | ~ c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4) ),
    cls_finite__imageD_0,
    [final] ).

cnf(i_0_722,axiom,
    ( c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),c_Set_Ovimage(X1,X5,X3,X4),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X4,tc_bool)) ),
    cls_vimage__mono_0,
    [final] ).

cnf(i_0_723,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
    cls_image__mono_0,
    [final] ).

cnf(i_0_724,axiom,
    ( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_subset__image__iff_2,
    [final] ).

cnf(i_0_725,axiom,
    ( c_Set_Ovimage(X1,X2,X3,X4) = c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X1,X3,X4),X2,X4,X3)
    | ~ c_Fun_Obij(X1,X3,X4) ),
    cls_bij__vimage__eq__inv__image_0,
    [final] ).

cnf(i_0_726,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X3)
    | ~ c_lessequals(X2,c_Set_Oimage(X1,X2,X3,X3),tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_finite__surj__inj_0,
    [final] ).

cnf(i_0_727,axiom,
    ( hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5))
    | ~ hBOOL(hAPP(X2,hAPP(X1,X5))) ),
    cls_vimage__code_1,
    [final] ).

cnf(i_0_728,axiom,
    ( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
    | ~ c_in(X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    cls_inj__image__mem__iff_1,
    [final] ).

cnf(i_0_729,axiom,
    ( c_Fun_Osurj(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),X3,X1)
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
    cls_inj__imp__surj__inv_0,
    [final] ).

cnf(i_0_730,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),hAPP(X2,X4)) = X4
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
    cls_inv__f__f_0,
    [final] ).

cnf(i_0_731,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),hAPP(X1,X4)) = X4
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
    cls_inv__f__eq_0,
    [final] ).

cnf(i_0_732,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | ~ c_Com_OWT(X2)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    cls_MGF__lemma1_1,
    [final] ).

cnf(i_0_733,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) != c_Finite__Set_Ocard(X2,X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_eq__card__imp__inj__on_0,
    [final] ).

cnf(i_0_734,axiom,
    c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(hAPP(X2,X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3),X4),
    cls_vimage__singleton__eq_1,
    [final] ).

cnf(i_0_735,axiom,
    ( c_in(hAPP(X1,X2),X3,X4)
    | ~ c_in(X2,X5,X6)
    | ~ c_lessequals(c_Set_Oimage(X1,X5,X6,X4),X3,tc_fun(X4,tc_bool)) ),
    cls_image__subset__iff_0,
    [final] ).

cnf(i_0_736,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | ~ c_in(X2,X1,X3)
    | ~ c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool)) ),
    cls_subset__insert__iff_0,
    [final] ).

cnf(i_0_737,axiom,
    ( c_Map_Omap__le(X1,X2,X3,X4)
    | ~ c_Map_Omap__le(X5,X2,X3,X4)
    | ~ c_Map_Omap__le(X1,X5,X3,X4) ),
    cls_map__le__trans_0,
    [final] ).

cnf(i_0_738,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),hAPP(X2,X5)) = X5
    | ~ c_in(X5,X1,X3)
    | ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
    cls_inv__into__f__f_0,
    [final] ).

cnf(i_0_739,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X2,X4,X3,X5),hAPP(X4,X1)) = X1
    | ~ c_in(X1,X2,X3)
    | ~ c_Fun_Oinj__on(X4,X2,X3,X5) ),
    cls_inv__into__f__eq_0,
    [final] ).

cnf(i_0_740,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Ovimage(X1,X2,X3,X4),X3)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4)
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    cls_finite__vimageI_0,
    [final] ).

cnf(i_0_741,axiom,
    ( c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X2,X1),X1,X2) = X3
    | ~ c_Fun_Obij(X3,X2,X1) ),
    cls_inv__inv__eq_0,
    [final] ).

cnf(i_0_742,axiom,
    ( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X1)
    | ~ c_Fun_Osurj(X2,X1,X3) ),
    cls_surj__imp__inj__inv_0,
    [final] ).

cnf(i_0_743,axiom,
    ( c_in(hAPP(X1,X2),X3,X4)
    | ~ c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5) ),
    cls_vimageD_0,
    [final] ).

cnf(i_0_744,axiom,
    ( c_in(hAPP(X1,X2),X3,X4)
    | ~ c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5) ),
    cls_vimageE_0,
    [final] ).

cnf(i_0_745,axiom,
    ( c_Set_Oimage(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3,X4) = c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(X1,X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_Fun_Obij(X1,X3,X4) ),
    cls_bij__image__Compl__eq_0,
    [final] ).

cnf(i_0_746,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X4,X5) ),
    cls_finite__surj_0,
    [final] ).

cnf(i_0_747,axiom,
    ( c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) = c_Finite__Set_Ocard(X2,X3)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_inj__on__iff__eq__card_0,
    [final] ).

cnf(i_0_748,axiom,
    c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
    cls_image__insert_0,
    [final] ).

cnf(i_0_749,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1),c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_distrib__inf__le_0,
    [final] ).

cnf(i_0_750,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_distrib__sup__le_0,
    [final] ).

cnf(i_0_751,axiom,
    ( c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) = c_Finite__Set_Ocard(X2,X3)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
    cls_card__image_0,
    [final] ).

cnf(i_0_752,axiom,
    ( c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) = c_Set_Oimage(X1,X3,X4,X5)
    | ~ c_in(X2,X3,X4) ),
    cls_insert__image_0,
    [final] ).

cnf(i_0_753,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_Set_Ovimage(X3,X1,X4,X2),X4)
    | ~ c_Fun_Obij(X3,X4,X2) ),
    cls_finite__vimage__iff_0,
    [final] ).

cnf(i_0_754,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Fun_Osurj(X3,X4,X2)
    | ~ c_Finite__Set_Ofinite(c_Set_Ovimage(X3,X1,X4,X2),X4) ),
    cls_finite__vimageD_0,
    [final] ).

cnf(i_0_755,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),X3,X4) ),
    cls_inj__on__Un_0,
    [final] ).

cnf(i_0_756,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X5,X2,tc_fun(X3,tc_bool)),X3,X4) ),
    cls_inj__on__Un_1,
    [final] ).

cnf(i_0_757,axiom,
    c_Set_Ovimage(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X4,X3) = c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(X1,X2,X4,X3),tc_fun(X4,tc_bool)),
    cls_vimage__Compl_0,
    [final] ).

cnf(i_0_758,axiom,
    ( X1 = X5
    | X1 = X4
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    cls_doubleton__eq__iff_0,
    [final] ).

cnf(i_0_759,axiom,
    ( X2 = X4
    | X1 = X4
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    cls_doubleton__eq__iff_1,
    [final] ).

cnf(i_0_760,axiom,
    ( X1 = X5
    | X2 = X5
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    cls_doubleton__eq__iff_2,
    [final] ).

cnf(i_0_761,axiom,
    ( X2 = X4
    | X2 = X5
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    cls_doubleton__eq__iff_3,
    [final] ).

cnf(i_0_762,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)),
    cls_Diff__insert2_0,
    [final] ).

cnf(i_0_763,axiom,
    ( c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4) = X2
    | ~ c_Fun_Osurj(X1,X3,X4) ),
    cls_surj__image__vimage__eq_0,
    [final] ).

cnf(i_0_764,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X5,X2,X3),X3,X4) ),
    cls_inj__on__insert_0,
    [final] ).

cnf(i_0_765,axiom,
    ( c_lessequals(X4,X1,tc_fun(X3,tc_bool))
    | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    cls_Un__Int__assoc__eq_0,
    [final] ).

cnf(i_0_766,axiom,
    ( c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X4,X5) ),
    cls_inj__on__diff_0,
    [final] ).

cnf(i_0_767,axiom,
    ( X1 = X2
    | ~ c_Map_Omap__le(X2,X1,X3,X4)
    | ~ c_Map_Omap__le(X1,X2,X3,X4) ),
    cls_map__le__antisym_0,
    [final] ).

cnf(i_0_768,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
    cls_hoare__derivs_Oinsert_0,
    [final] ).

cnf(i_0_769,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)),X3) ),
    cls_finite__Diff__insert_0,
    [final] ).

cnf(i_0_770,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X5,X3,X4) ),
    cls_subset__inj__on_0,
    [final] ).

cnf(i_0_771,axiom,
    ( c_Fun_Obij(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),X3,X1)
    | ~ c_Fun_Obij(X2,X1,X3) ),
    cls_bij__imp__bij__inv_0,
    [final] ).

cnf(i_0_772,axiom,
    ( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
    | ~ c_in(X1,X2,X3) ),
    cls_insert__Diff_0,
    [final] ).

cnf(i_0_773,axiom,
    c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X1,X2,X3),
    cls_insert__Diff__single_0,
    [final] ).

cnf(i_0_774,axiom,
    ( c_lessequals(c_Map_Odom(X1,X2,X3),c_Map_Odom(X4,X2,X3),tc_fun(X2,tc_bool))
    | ~ c_Map_Omap__le(X1,X4,X2,X3) ),
    cls_map__le__implies__dom__le_0,
    [final] ).

cnf(i_0_775,axiom,
    ( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Finite__Set_Ocard(X1,X3)
    | c_in(X2,X1,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    cls_card__Diff__singleton__if_1,
    [final] ).

cnf(i_0_776,axiom,
    c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4),
    cls_rangeI_0,
    [final] ).

cnf(i_0_777,axiom,
    ( c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)
    | ~ c_in(hAPP(X2,X1),X3,X5) ),
    cls_vimageI_0,
    [final] ).

cnf(i_0_778,axiom,
    ( c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)
    | ~ c_in(hAPP(X2,X1),X3,X5) ),
    cls_vimageI2_0,
    [final] ).

cnf(i_0_779,axiom,
    ( c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)
    | ~ c_in(hAPP(X2,X1),X3,X5) ),
    cls_vimage__eq_1,
    [final] ).

cnf(i_0_780,axiom,
    ( hAPP(X1,X2) = hAPP(X3,X2)
    | ~ c_in(X2,c_Map_Odom(X1,X4,X5),X4)
    | ~ c_Map_Omap__le(X1,X3,X4,X5) ),
    cls_map__le__def_0,
    [final] ).

cnf(i_0_781,axiom,
    ( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
    | ~ c_in(X2,X3,X4) ),
    cls_imageI_0,
    [final] ).

cnf(i_0_782,axiom,
    ( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
    | ~ c_in(X2,X3,X4) ),
    cls_image__eqI_0,
    [final] ).

cnf(i_0_783,axiom,
    ( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
    | ~ c_in(X1,X2,X3) ),
    cls_image__iff_2,
    [final] ).

cnf(i_0_784,axiom,
    ( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
    | ~ c_in(X1,X2,X3) ),
    cls_rev__image__eqI_0,
    [final] ).

cnf(i_0_785,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4) ),
    cls_finite__Diff__insert_1,
    [final] ).

cnf(i_0_786,axiom,
    ( c_Fun_Osurj(X1,X2,X2)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X2)
    | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
    cls_finite__UNIV__inj__surj_0,
    [final] ).

cnf(i_0_787,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    cls_Diff__mono_0,
    [final] ).

cnf(i_0_788,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    cls_Un__mono_0,
    [final] ).

cnf(i_0_789,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    cls_Int__mono_0,
    [final] ).

cnf(i_0_790,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
    cls_Diff__insert_0,
    [final] ).

cnf(i_0_791,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Ovimage(X1,X2,X3,X4),X3)
    | ~ c_Finite__Set_Ofinite(X2,X4)
    | ~ c_Fun_Obij(X1,X3,X4) ),
    cls_finite__vimage__iff_1,
    [final] ).

cnf(i_0_792,axiom,
    c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
    cls_Diff__Int2_0,
    [final] ).

cnf(i_0_793,axiom,
    c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Un__Diff_0,
    [final] ).

cnf(i_0_794,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Un__Int__distrib2_0,
    [final] ).

cnf(i_0_795,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Diff__Int__distrib2_0,
    [final] ).

cnf(i_0_796,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Int__Un__distrib2_0,
    [final] ).

cnf(i_0_797,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Diff__Un_0,
    [final] ).

cnf(i_0_798,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Diff__Int_0,
    [final] ).

cnf(i_0_799,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Un__Int__distrib_0,
    [final] ).

cnf(i_0_800,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Diff__Int__distrib_0,
    [final] ).

cnf(i_0_801,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Int__Un__distrib_0,
    [final] ).

cnf(i_0_802,axiom,
    ( c_Fun_Obij(X1,X2,X3)
    | ~ c_Fun_Osurj(X1,X2,X3)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
    cls_bijI_0,
    [final] ).

cnf(i_0_803,axiom,
    ( c_Fun_Obij(X1,X2,X3)
    | ~ c_Fun_Osurj(X1,X2,X3)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
    cls_bij__def_2,
    [final] ).

cnf(i_0_804,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_in(X3,X4,X5)
    | ~ c_in(X2,X4,X5)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    cls_inj__on__contraD_0,
    [final] ).

cnf(i_0_805,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_in(X3,X4,X5)
    | ~ c_in(X2,X4,X5)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    cls_inj__on__iff_0,
    [final] ).

cnf(i_0_806,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_in(X3,X4,X5)
    | ~ c_in(X2,X4,X5)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    cls_inj__on__def_0,
    [final] ).

cnf(i_0_807,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6)
    | ~ c_in(X3,X4,X5)
    | ~ c_in(X2,X4,X5) ),
    cls_inj__onD_0,
    [final] ).

cnf(i_0_808,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1),tc_fun(X1,tc_bool)) ),
    cls_atLeastatMost__subset__iff_0,
    [final] ).

cnf(i_0_809,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X4,X2,X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X4,X2,X1),c_SetInterval_Oord__class_OatLeastAtMost(X5,X3,X1),tc_fun(X1,tc_bool)) ),
    cls_atLeastatMost__subset__iff_1,
    [final] ).

cnf(i_0_810,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
    cls_derivs__insertD_0,
    [final] ).

cnf(i_0_811,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    cls_Diff__subset__conv_1,
    [final] ).

cnf(i_0_812,axiom,
    ( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    cls_Diff__subset__conv_0,
    [final] ).

cnf(i_0_813,axiom,
    ( X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
    cls_subset__singletonD_0,
    [final] ).

cnf(i_0_814,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X3,X2))
    | ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
    cls_sup1E_0,
    [final] ).

cnf(i_0_815,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X4,X1,tc_fun(X3,tc_bool)) ),
    cls_Un__Int__assoc__eq_1,
    [final] ).

cnf(i_0_816,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(X4,X2,X1),c_SetInterval_Oord__class_OatLeastLessThan(X5,X3,X1),tc_fun(X1,tc_bool)) ),
    cls_atLeastLessThan__subset__iff_1,
    [final] ).

cnf(i_0_817,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X4,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),c_SetInterval_Oord__class_OatLeastLessThan(X2,X5,X1),tc_fun(X1,tc_bool)) ),
    cls_atLeastLessThan__subset__iff_0,
    [final] ).

cnf(i_0_818,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2)) ),
    cls_inf1E_0,
    [final] ).

cnf(i_0_819,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
    cls_inf1E_1,
    [final] ).

cnf(i_0_820,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_ivl__disj__un_I6_J_0,
    [final] ).

cnf(i_0_821,axiom,
    c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
    cls_doubleton__eq__iff_4,
    [final] ).

cnf(i_0_822,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_finite__imageI_0,
    [final] ).

cnf(i_0_823,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_ivl__disj__un_I17_J_0,
    [final] ).

cnf(i_0_824,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_ivl__disj__un_I21_J_0,
    [final] ).

cnf(i_0_825,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    cls_injD_0,
    [final] ).

cnf(i_0_826,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
    | ~ c_Com_OWT(X2)
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    cls_MGF__lemma1_0,
    [final] ).

cnf(i_0_827,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3),
    cls_insert__inter__insert_0,
    [final] ).

cnf(i_0_828,axiom,
    ( c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X2)
    | ~ c_Fun_Osurj(X1,X2,X2)
    | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
    cls_finite__UNIV__surj__inj_0,
    [final] ).

cnf(i_0_829,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
    | ~ c_in(X1,X4,X3) ),
    cls_Int__insert__left_0,
    [final] ).

cnf(i_0_830,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_in(X2,X1,X4) ),
    cls_Int__insert__right_0,
    [final] ).

cnf(i_0_831,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X3
    | ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
    cls_double__diff_0,
    [final] ).

cnf(i_0_832,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    cls_Un__least_0,
    [final] ).

cnf(i_0_833,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    cls_Un__subset__iff_2,
    [final] ).

cnf(i_0_834,axiom,
    ( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
    cls_Int__greatest_0,
    [final] ).

cnf(i_0_835,axiom,
    ( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
    cls_Int__subset__iff_2,
    [final] ).

cnf(i_0_836,axiom,
    ( c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1),tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_lessequals(X4,X2,X1) ),
    cls_atLeastatMost__subset__iff_3,
    [final] ).

cnf(i_0_837,axiom,
    c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Int__Diff_0,
    [final] ).

cnf(i_0_838,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Un__assoc_0,
    [final] ).

cnf(i_0_839,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Int__assoc_0,
    [final] ).

cnf(i_0_840,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Un__left__commute_0,
    [final] ).

cnf(i_0_841,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Int__left__commute_0,
    [final] ).

cnf(i_0_842,axiom,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oimage(X2,X3,X4,X1) ),
    cls_empty__is__image_0,
    [final] ).

cnf(i_0_843,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
    cls_image__is__empty_0,
    [final] ).

cnf(i_0_844,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2
    | c_in(X1,X2,X3) ),
    cls_Diff__insert__absorb_0,
    [final] ).

cnf(i_0_845,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)
    | c_in(X1,X4,X3) ),
    cls_insert__Diff__if_1,
    [final] ).

cnf(i_0_846,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
    cls_Un__subset__iff_0,
    [final] ).

cnf(i_0_847,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
    cls_Un__subset__iff_1,
    [final] ).

cnf(i_0_848,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    cls_Int__subset__iff_0,
    [final] ).

cnf(i_0_849,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    cls_Int__subset__iff_1,
    [final] ).

cnf(i_0_850,axiom,
    ( c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X4,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_ivl__diff_0,
    [final] ).

cnf(i_0_851,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    cls_sup__inf__distrib2_0,
    [final] ).

cnf(i_0_852,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    cls_inf__sup__distrib2_0,
    [final] ).

cnf(i_0_853,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    cls_sup__inf__distrib1_0,
    [final] ).

cnf(i_0_854,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    cls_inf__sup__distrib1_0,
    [final] ).

cnf(i_0_855,axiom,
    ( c_in(X1,X2,X3)
    | c_in(X1,X4,X3)
    | ~ c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3) ),
    cls_UnE_0,
    [final] ).

cnf(i_0_856,axiom,
    ( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4))
    | ~ hBOOL(hAPP(X2,X4))
    | ~ hBOOL(hAPP(X1,X4)) ),
    cls_inf1I_0,
    [final] ).

cnf(i_0_857,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),c_SetInterval_Oord__class_OlessThan(X2,X1),tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_single__Diff__lessThan_0,
    [final] ).

cnf(i_0_858,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    cls_Compl__subset__Compl__iff_0,
    [final] ).

cnf(i_0_859,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_in(X4,X1,X3)
    | ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
    cls_subset__insert_0,
    [final] ).

cnf(i_0_860,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_in(X4,X1,X3)
    | ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
    cls_subset__insert__iff_1,
    [final] ).

cnf(i_0_861,axiom,
    ( X1 = X2
    | ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    cls_singletonE_0,
    [final] ).

cnf(i_0_862,axiom,
    ( hBOOL(hAPP(X1,X2))
    | X3 = X2
    | ~ hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
    cls_insert__code_0,
    [final] ).

cnf(i_0_863,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
    | ~ c_Com_OWT(X1)
    | ~ c_Com_OWT__bodies
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    cls_MGF_0,
    [final] ).

cnf(i_0_864,axiom,
    ( c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
    cls_insert__mono_0,
    [final] ).

cnf(i_0_865,axiom,
    ( c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))
    | ~ c_Fun_Osurj(X1,X2,X3) ),
    cls_surj__range_0,
    [final] ).

cnf(i_0_866,axiom,
    ( ~ c_in(X1,X2,X3)
    | ~ c_in(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3) ),
    cls_DiffE_1,
    [final] ).

cnf(i_0_867,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Compl__Un_0,
    [final] ).

cnf(i_0_868,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Compl__Int_0,
    [final] ).

cnf(i_0_869,axiom,
    ( c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
    | ~ c_in(X1,X4,X3) ),
    cls_insert__subset_2,
    [final] ).

cnf(i_0_870,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3),
    cls_Un__insert__left_0,
    [final] ).

cnf(i_0_871,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X4),
    cls_Un__insert__right_0,
    [final] ).

cnf(i_0_872,axiom,
    ( c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3)
    | ~ c_Fun_Obij(X1,X2,X3) ),
    cls_bij__def_0,
    [final] ).

cnf(i_0_873,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1,
    cls_Un__Diff__Int_0,
    [final] ).

cnf(i_0_874,axiom,
    ( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
    | ~ hBOOL(hAPP(X1,X4)) ),
    cls_sup1CI_1,
    [final] ).

cnf(i_0_875,axiom,
    ( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
    | ~ hBOOL(hAPP(X2,X4)) ),
    cls_sup1CI_0,
    [final] ).

cnf(i_0_876,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3) ),
    cls_DiffE_0,
    [final] ).

cnf(i_0_877,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3) ),
    cls_IntE_0,
    [final] ).

cnf(i_0_878,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3) ),
    cls_IntE_1,
    [final] ).

cnf(i_0_879,axiom,
    ( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    cls_Int__iff_2,
    [final] ).

cnf(i_0_880,axiom,
    ( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    cls_IntI_0,
    [final] ).

cnf(i_0_881,axiom,
    ( c_in(X1,c_Inductive_Ocomplete__lattice__class_Ogfp(X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_lessequals(X4,hAPP(X2,X4),tc_fun(X3,tc_bool))
    | ~ c_in(X1,X4,X3) ),
    cls_weak__coinduct_0,
    [final] ).

cnf(i_0_882,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Set_Oinsert(X4,X1,X3),X2,tc_fun(X3,tc_bool)) ),
    cls_insert__subset_1,
    [final] ).

cnf(i_0_883,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | c_in(X2,X1,X4)
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    cls_subset__insert_1,
    [final] ).

cnf(i_0_884,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | c_in(X2,X1,X4)
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    cls_subset__insert__iff_2,
    [final] ).

cnf(i_0_885,axiom,
    ( c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1),tc_fun(X1,tc_bool))
    | c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_atLeastatMost__subset__iff_2,
    [final] ).

cnf(i_0_886,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X2
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_Diff__partition_0,
    [final] ).

cnf(i_0_887,axiom,
    ( c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)
    | c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    cls_DiffI_0,
    [final] ).

cnf(i_0_888,axiom,
    ( c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)
    | c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    cls_Diff__iff_2,
    [final] ).

cnf(i_0_889,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool))
    | ~ c_in(X1,X4,X3) ),
    cls_insert__Diff1_0,
    [final] ).

cnf(i_0_890,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
    cls_insert__subset_0,
    [final] ).

cnf(i_0_891,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
    cls_Compl__anti__mono_0,
    [final] ).

cnf(i_0_892,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
    cls_Compl__subset__Compl__iff_1,
    [final] ).

cnf(i_0_893,axiom,
    c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,tc_fun(X3,tc_bool)),
    cls_insert__is__Un_0,
    [final] ).

cnf(i_0_894,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_le__sup__iff_2,
    [final] ).

cnf(i_0_895,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_sup__least_0,
    [final] ).

cnf(i_0_896,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_le__supI_0,
    [final] ).

cnf(i_0_897,axiom,
    ( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_inf__greatest_0,
    [final] ).

cnf(i_0_898,axiom,
    ( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__inf__iff_2,
    [final] ).

cnf(i_0_899,axiom,
    ( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__infI_0,
    [final] ).

cnf(i_0_900,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    cls_disjoint__eq__subset__Compl_1,
    [final] ).

cnf(i_0_901,axiom,
    c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
    cls_Compl__Diff__eq_0,
    [final] ).

cnf(i_0_902,axiom,
    ( ~ c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_disjoint__iff__not__equal_0,
    [final] ).

cnf(i_0_903,axiom,
    ( X1 = X3
    | c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    cls_singleton__inject_0,
    [final] ).

cnf(i_0_904,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),c_SetInterval_Oord__class_OgreaterThan(X2,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeast(X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_ivl__disj__un_I1_J_0,
    [final] ).

cnf(i_0_905,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(X2,X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatMost(X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_ivl__disj__un_I2_J_0,
    [final] ).

cnf(i_0_906,axiom,
    c_Finite__Set_Ofinite(c_Map_Odom(c_Map_Omap__of(X1,X2,X3),X2,X3),X2),
    cls_finite__dom__map__of_0,
    [final] ).

cnf(i_0_907,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__assoc_0,
    [final] ).

cnf(i_0_908,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I6_J_0,
    [final] ).

cnf(i_0_909,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__assoc_0,
    [final] ).

cnf(i_0_910,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I2_J_0,
    [final] ).

cnf(i_0_911,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__left__commute_0,
    [final] ).

cnf(i_0_912,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I7_J_0,
    [final] ).

cnf(i_0_913,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__left__commute_0,
    [final] ).

cnf(i_0_914,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I3_J_0,
    [final] ).

cnf(i_0_915,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X4,X2,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
    cls_derivs__insertD_1,
    [final] ).

cnf(i_0_916,axiom,
    c_Set_Ovimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
    cls_vimage__UNIV_0,
    [final] ).

cnf(i_0_917,axiom,
    c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    cls_vimage__empty_0,
    [final] ).

cnf(i_0_918,axiom,
    c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    cls_image__empty_0,
    [final] ).

cnf(i_0_919,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1),
    cls_empty__is__image_1,
    [final] ).

cnf(i_0_920,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    cls_ivl__disj__int_I11_J_0,
    [final] ).

cnf(i_0_921,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    cls_ivl__disj__int_I15_J_0,
    [final] ).

cnf(i_0_922,axiom,
    c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
    cls_insert__commute_0,
    [final] ).

cnf(i_0_923,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    cls_subset__trans_0,
    [final] ).

cnf(i_0_924,axiom,
    ( c_lessequals(X3,X2,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
    | ~ c_lessequals(X5,X4,X1) ),
    cls_le__eqI_1,
    [final] ).

cnf(i_0_925,axiom,
    ( c_lessequals(X5,X4,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_le__eqI_0,
    [final] ).

cnf(i_0_926,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeast(X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeast(X2,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_ivl__disj__un_I14_J_0,
    [final] ).

cnf(i_0_927,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThan(X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeast(X2,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_ivl__disj__un_I13_J_0,
    [final] ).

cnf(i_0_928,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(X2,X1),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OlessThan(X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_ivl__disj__un_I8_J_0,
    [final] ).

cnf(i_0_929,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(X2,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatMost(X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_ivl__disj__un_I10_J_0,
    [final] ).

cnf(i_0_930,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool))
    | c_in(X1,X4,X3) ),
    cls_Int__insert__left_1,
    [final] ).

cnf(i_0_931,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool))
    | c_in(X2,X1,X4) ),
    cls_Int__insert__right_1,
    [final] ).

cnf(i_0_932,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X3,X1) ),
    cls_le__sup__iff_0,
    [final] ).

cnf(i_0_933,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X3,X1) ),
    cls_le__supE_0,
    [final] ).

cnf(i_0_934,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X1),X3,X1) ),
    cls_le__sup__iff_1,
    [final] ).

cnf(i_0_935,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X1),X3,X1) ),
    cls_le__supE_1,
    [final] ).

cnf(i_0_936,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
    cls_le__inf__iff_0,
    [final] ).

cnf(i_0_937,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
    cls_le__infE_0,
    [final] ).

cnf(i_0_938,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
    cls_le__inf__iff_1,
    [final] ).

cnf(i_0_939,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
    cls_le__infE_1,
    [final] ).

cnf(i_0_940,axiom,
    ( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_disjoint__eq__subset__Compl_0,
    [final] ).

cnf(i_0_941,axiom,
    ( c_in(X1,X2,X3)
    | X1 = X4
    | ~ c_in(X1,c_Set_Oinsert(X4,X2,X3),X3) ),
    cls_insertE_0,
    [final] ).

cnf(i_0_942,axiom,
    c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Fun_Oid(X1),X1,X1) = c_Fun_Oid(X1),
    cls_inv__id_0,
    [final] ).

cnf(i_0_943,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),
    cls_Diff__idemp_0,
    [final] ).

cnf(i_0_944,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
    cls_Un__Diff__cancel2_0,
    [final] ).

cnf(i_0_945,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
    cls_Un__Diff__cancel_0,
    [final] ).

cnf(i_0_946,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
    cls_Un__left__absorb_0,
    [final] ).

cnf(i_0_947,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
    cls_Int__left__absorb_0,
    [final] ).

cnf(i_0_948,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    cls_subset__insertI2_0,
    [final] ).

cnf(i_0_949,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
    cls_subset__Compl__self__eq_1,
    [final] ).

cnf(i_0_950,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    cls_finite__Diff2_0,
    [final] ).

cnf(i_0_951,axiom,
    c_Fun_Oinj__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3),
    cls_inj__on__empty_0,
    [final] ).

cnf(i_0_952,axiom,
    ( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_in(X1,X2,X4) ),
    cls_UnCI_1,
    [final] ).

cnf(i_0_953,axiom,
    ( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_in(X1,X3,X4) ),
    cls_UnCI_0,
    [final] ).

cnf(i_0_954,axiom,
    ( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
    | ~ hBOOL(hAPP(X2,X4)) ),
    cls_insert__code_2,
    [final] ).

cnf(i_0_955,axiom,
    ( c_lessequals(c_Finite__Set_Olinorder__class_OMax(X2,X1),c_Finite__Set_Olinorder__class_OMax(X3,X1),X1)
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | ~ c_lessequals(X2,X3,tc_fun(X1,tc_bool)) ),
    cls_Max__mono_0,
    [final] ).

cnf(i_0_956,axiom,
    ( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X1),c_Finite__Set_Olinorder__class_OMin(X3,X1),X1)
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Finite__Set_Ofinite(X2,X1)
    | ~ c_lessequals(X3,X2,tc_fun(X1,tc_bool)) ),
    cls_Min__antimono_0,
    [final] ).

cnf(i_0_957,axiom,
    ( c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1),X2,X3)
    | ~ c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3) ),
    cls_evalc_OBody_0,
    [final] ).

cnf(i_0_958,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_sup__eq__neg__inf_0,
    [final] ).

cnf(i_0_959,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_inf__eq__neg__sup_0,
    [final] ).

cnf(i_0_960,axiom,
    ( ~ c_in(X1,X2,X3)
    | ~ c_in(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3) ),
    cls_ComplD_0,
    [final] ).

cnf(i_0_961,axiom,
    ( c_in(X1,X4,X3)
    | c_in(X1,X2,X3)
    | X2 = X4
    | c_Set_Oinsert(X1,X2,X3) != c_Set_Oinsert(X1,X4,X3) ),
    cls_insert__ident_0,
    [final] ).

cnf(i_0_962,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_lessequals(X2,X4,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
    cls_weaken_0,
    [final] ).

cnf(i_0_963,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_lessequals(X4,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3) ),
    cls_thin_0,
    [final] ).

cnf(i_0_964,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2) ),
    cls_finite__Un_0,
    [final] ).

cnf(i_0_965,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)),X2) ),
    cls_finite__Un_1,
    [final] ).

cnf(i_0_966,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OgreaterThan(X3,X1),c_SetInterval_Oord__class_OgreaterThan(X2,X1),tc_fun(X1,tc_bool)) ),
    cls_greaterThan__subset__iff_0,
    [final] ).

cnf(i_0_967,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OlessThan(X2,X1),c_SetInterval_Oord__class_OlessThan(X3,X1),tc_fun(X1,tc_bool)) ),
    cls_lessThan__subset__iff_0,
    [final] ).

cnf(i_0_968,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OatMost(X2,X1),c_SetInterval_Oord__class_OatMost(X3,X1),tc_fun(X1,tc_bool)) ),
    cls_atMost__subset__iff_0,
    [final] ).

cnf(i_0_969,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OatLeast(X3,X1),c_SetInterval_Oord__class_OatLeast(X2,X1),tc_fun(X1,tc_bool)) ),
    cls_atLeast__subset__iff_0,
    [final] ).

cnf(i_0_970,axiom,
    c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),
    cls_singleton__iff_1,
    [final] ).

cnf(i_0_971,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    cls_set__mp_0,
    [final] ).

cnf(i_0_972,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    cls_subsetD_0,
    [final] ).

cnf(i_0_973,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_in(X1,X4,X3) ),
    cls_set__rev__mp_0,
    [final] ).

cnf(i_0_974,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    cls_subset__iff_0,
    [final] ).

cnf(i_0_975,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    cls_subset__Compl__self__eq_0,
    [final] ).

cnf(i_0_976,axiom,
    ( c_Set_Oinsert(X2,c_Map_Odom(X1,X5,X4),X5) = c_Map_Odom(X1,X5,X4)
    | hAPP(X1,X2) != c_Option_Ooption_OSome(X3,X4) ),
    cls_insert__dom_0,
    [final] ).

cnf(i_0_977,axiom,
    ( X1 = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
    | c_Finite__Set_Ocard(X1,X2) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
    cls_card__eq__UNIV__imp__eq__UNIV_0,
    [final] ).

cnf(i_0_978,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    cls_Diff__disjoint_0,
    [final] ).

cnf(i_0_979,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_le__infI1_0,
    [final] ).

cnf(i_0_980,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    cls_le__infI2_0,
    [final] ).

cnf(i_0_981,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__supI1_0,
    [final] ).

cnf(i_0_982,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_le__supI2_0,
    [final] ).

cnf(i_0_983,axiom,
    ( c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3)
    | ~ c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1),X2,X3) ),
    cls_evalc__elim__cases_I6_J_0,
    [final] ).

cnf(i_0_984,axiom,
    c_Set_Ovimage(c_Fun_Oid(X1),X2,X1,X1) = X2,
    cls_vimage__id_0,
    [final] ).

cnf(i_0_985,axiom,
    c_Set_Ovimage(c_COMBI(X1),X2,X1,X1) = X2,
    cls_vimage__ident_0,
    [final] ).

cnf(i_0_986,axiom,
    c_Set_Oimage(c_Fun_Oid(X1),X2,X1,X1) = X2,
    cls_image__id_0,
    [final] ).

cnf(i_0_987,axiom,
    c_Set_Oimage(c_COMBI(X1),X2,X1,X1) = X2,
    cls_image__ident_0,
    [final] ).

cnf(i_0_988,axiom,
    c_Fun_Oinj__on(c_Fun_Oid(X1),X2,X1,X1),
    cls_inj__on__id_0,
    [final] ).

cnf(i_0_989,axiom,
    c_Fun_Oinj__on(c_COMBI(X1),X2,X1,X1),
    cls_inj__on__id2_0,
    [final] ).

cnf(i_0_990,axiom,
    ( c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    cls_insert__iff_2,
    [final] ).

cnf(i_0_991,axiom,
    ( c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    cls_insertCI_0,
    [final] ).

cnf(i_0_992,axiom,
    c_Map_Omap__le(X1,X1,X2,X3),
    cls_map__le__refl_0,
    [final] ).

cnf(i_0_993,axiom,
    ( X1 = X2
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_equalityI_0,
    [final] ).

cnf(i_0_994,axiom,
    ( X1 = X2
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_set__eq__subset_2,
    [final] ).

cnf(i_0_995,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeast(X3,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    cls_ivl__disj__int_I8_J_0,
    [final] ).

cnf(i_0_996,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThan(X3,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    cls_ivl__disj__int_I7_J_0,
    [final] ).

cnf(i_0_997,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OlessThan(X2,X1),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    cls_ivl__disj__int_I2_J_0,
    [final] ).

cnf(i_0_998,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OlessThan(X2,X1),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    cls_ivl__disj__int_I4_J_0,
    [final] ).

cnf(i_0_999,axiom,
    ( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Finite__Set_Ocard(X2,X3)
    | ~ c_in(X1,X2,X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_card__insert__if_0,
    [final] ).

cnf(i_0_1000,axiom,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    cls_insert__code_1,
    [final] ).

cnf(i_0_1001,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatMost(X2,X1),c_SetInterval_Oord__class_OatLeast(X2,X1),tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_atMost__Int__atLeast_0,
    [final] ).

cnf(i_0_1002,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_Diff__triv_0,
    [final] ).

cnf(i_0_1003,axiom,
    ( c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1)
    | ~ class_HOL_Oord(X1)
    | ~ c_lessequals(X2,X4,tc_fun(X5,X1)) ),
    cls_le__funD_0,
    [final] ).

cnf(i_0_1004,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X4,X3,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_order__trans_0,
    [final] ).

cnf(i_0_1005,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X4,X3,X1) ),
    cls_xt1_I6_J_0,
    [final] ).

cnf(i_0_1006,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_neg__sup__eq__inf_0,
    [final] ).

cnf(i_0_1007,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_compl__sup_0,
    [final] ).

cnf(i_0_1008,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_neg__inf__eq__sup_0,
    [final] ).

cnf(i_0_1009,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_compl__inf_0,
    [final] ).

cnf(i_0_1010,axiom,
    ( c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    cls_Min__singleton_0,
    [final] ).

cnf(i_0_1011,axiom,
    ( c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    cls_Max__singleton_0,
    [final] ).

cnf(i_0_1012,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    cls_subset__empty_0,
    [final] ).

cnf(i_0_1013,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    cls_Diff__subset_0,
    [final] ).

cnf(i_0_1014,axiom,
    c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    cls_Int__lower1_0,
    [final] ).

cnf(i_0_1015,axiom,
    c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
    cls_Int__lower2_0,
    [final] ).

cnf(i_0_1016,axiom,
    c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Un__upper1_0,
    [final] ).

cnf(i_0_1017,axiom,
    c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Un__upper2_0,
    [final] ).

cnf(i_0_1018,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
    cls_neg__le__iff__le_0,
    [final] ).

cnf(i_0_1019,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3) ),
    cls_cut_0,
    [final] ).

cnf(i_0_1020,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
    cls_Diff__Compl_0,
    [final] ).

cnf(i_0_1021,axiom,
    c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Diff__eq_0,
    [final] ).

cnf(i_0_1022,axiom,
    ( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    cls_finite__compl_0,
    [final] ).

cnf(i_0_1023,axiom,
    ( c_lessequals(c_SetInterval_Oord__class_OgreaterThan(X2,X1),c_SetInterval_Oord__class_OgreaterThan(X3,X1),tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_greaterThan__subset__iff_1,
    [final] ).

cnf(i_0_1024,axiom,
    ( c_lessequals(c_SetInterval_Oord__class_OatMost(X2,X1),c_SetInterval_Oord__class_OatMost(X3,X1),tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_atMost__subset__iff_1,
    [final] ).

cnf(i_0_1025,axiom,
    ( c_lessequals(c_SetInterval_Oord__class_OatLeast(X2,X1),c_SetInterval_Oord__class_OatLeast(X3,X1),tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_atLeast__subset__iff_1,
    [final] ).

cnf(i_0_1026,axiom,
    ( c_lessequals(c_SetInterval_Oord__class_OlessThan(X2,X1),c_SetInterval_Oord__class_OlessThan(X3,X1),tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_lessThan__subset__iff_1,
    [final] ).

cnf(i_0_1027,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__left__idem_0,
    [final] ).

cnf(i_0_1028,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I8_J_0,
    [final] ).

cnf(i_0_1029,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__left__idem_0,
    [final] ).

cnf(i_0_1030,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I4_J_0,
    [final] ).

cnf(i_0_1031,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_atLeastatMost__empty__iff2_0,
    [final] ).

cnf(i_0_1032,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ c_lessequals(X2,X3,X1) ),
    cls_atLeastatMost__empty__iff_0,
    [final] ).

cnf(i_0_1033,axiom,
    c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
    cls_insert__absorb2_0,
    [final] ).

cnf(i_0_1034,axiom,
    ( ~ hBOOL(hAPP(X1,X2))
    | ~ c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
    cls_bex__empty_0,
    [final] ).

cnf(i_0_1035,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
    cls_minus__le__iff_1,
    [final] ).

cnf(i_0_1036,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
    cls_minus__le__iff_0,
    [final] ).

cnf(i_0_1037,axiom,
    ( c_lessequals(X2,c_Inductive_Ocomplete__lattice__class_Ogfp(X3,X1),X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ c_lessequals(X2,hAPP(X3,X2),X1) ),
    cls_gfp__upperbound_0,
    [final] ).

cnf(i_0_1038,axiom,
    ( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
    cls_le__minus__iff_1,
    [final] ).

cnf(i_0_1039,axiom,
    ( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
    cls_le__minus__iff_0,
    [final] ).

cnf(i_0_1040,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    cls_finite__compl_1,
    [final] ).

cnf(i_0_1041,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_finite__Diff2_1,
    [final] ).

cnf(i_0_1042,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X2,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    cls_finite__Un_2,
    [final] ).

cnf(i_0_1043,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X2,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    cls_finite__UnI_0,
    [final] ).

cnf(i_0_1044,axiom,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    cls_bot1E_0,
    [final] ).

cnf(i_0_1045,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_Un__empty_2,
    [final] ).

cnf(i_0_1046,axiom,
    ( c_HOL_Ouminus__class_Ouminus(X2,X1) = X3
    | ~ class_Lattices_Oboolean__algebra(X1)
    | c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
    cls_compl__unique_0,
    [final] ).

cnf(i_0_1047,axiom,
    ( c_in(X2,c_Map_Odom(X1,X5,X4),X5)
    | hAPP(X1,X2) != c_Option_Ooption_OSome(X3,X4) ),
    cls_domI_0,
    [final] ).

cnf(i_0_1048,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2) ),
    cls_finite__insert_0,
    [final] ).

cnf(i_0_1049,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2 ),
    cls_subset__Un__eq_1,
    [final] ).

cnf(i_0_1050,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X1
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
    cls_Un__absorb2_0,
    [final] ).

cnf(i_0_1051,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_Un__absorb1_0,
    [final] ).

cnf(i_0_1052,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_Int__absorb2_0,
    [final] ).

cnf(i_0_1053,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X2
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
    cls_Int__absorb1_0,
    [final] ).

cnf(i_0_1054,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X3,X2))
    | ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
    cls_predicate1D_0,
    [final] ).

cnf(i_0_1055,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool))
    | ~ hBOOL(hAPP(X3,X2)) ),
    cls_rev__predicate1D_0,
    [final] ).

cnf(i_0_1056,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_le__imp__neg__le_0,
    [final] ).

cnf(i_0_1057,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
    cls_ball__empty_0,
    [final] ).

cnf(i_0_1058,axiom,
    ( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X1),X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_in(X3,X2,X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    cls_Min__le_0,
    [final] ).

cnf(i_0_1059,axiom,
    ( c_lessequals(X2,c_Finite__Set_Olinorder__class_OMax(X3,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_in(X2,X3,X1)
    | ~ c_Finite__Set_Ofinite(X3,X1) ),
    cls_Max__ge_0,
    [final] ).

cnf(i_0_1060,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_lessequals(X2,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
    cls_asm_0,
    [final] ).

cnf(i_0_1061,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_Un__empty_0,
    [final] ).

cnf(i_0_1062,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_Un__empty_1,
    [final] ).

cnf(i_0_1063,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    cls_finite__Diff_0,
    [final] ).

cnf(i_0_1064,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    cls_finite__Int_0,
    [final] ).

cnf(i_0_1065,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_finite__Int_1,
    [final] ).

cnf(i_0_1066,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_HOL_Oord(X1)
    | ~ c_in(X2,c_SetInterval_Oord__class_OatMost(X3,X1),X1) ),
    cls_atMost__iff_0,
    [final] ).

cnf(i_0_1067,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_HOL_Oord(X1)
    | ~ c_in(X3,c_SetInterval_Oord__class_OatLeast(X2,X1),X1) ),
    cls_atLeast__iff_0,
    [final] ).

cnf(i_0_1068,axiom,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    cls_subset__insertI_0,
    [final] ).

cnf(i_0_1069,axiom,
    ( c_in(X1,X2,X3)
    | c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_comm__monoid__add_Ononempty__iff_2,
    [final] ).

cnf(i_0_1070,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Ominus__class_Ominus(X3,X2,X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    cls_minus__diff__eq_0,
    [final] ).

cnf(i_0_1071,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__eq__iff_2,
    [final] ).

cnf(i_0_1072,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__antisym_0,
    [final] ).

cnf(i_0_1073,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_order__antisym__conv_0,
    [final] ).

cnf(i_0_1074,axiom,
    ( c_in(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3)
    | c_in(X1,X2,X3) ),
    cls_ComplI_0,
    [final] ).

cnf(i_0_1075,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
    cls_subset__empty_1,
    [final] ).

cnf(i_0_1076,axiom,
    ( X2 = X3
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
    cls_eq__eqI_1,
    [final] ).

cnf(i_0_1077,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
    cls_eq__eqI_0,
    [final] ).

cnf(i_0_1078,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    cls_Compl__partition2_0,
    [final] ).

cnf(i_0_1079,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_Compl__disjoint2_0,
    [final] ).

cnf(i_0_1080,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    cls_Compl__partition_0,
    [final] ).

cnf(i_0_1081,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_Compl__disjoint_0,
    [final] ).

cnf(i_0_1082,axiom,
    ( c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_atLeastLessThan__empty_0,
    [final] ).

cnf(i_0_1083,axiom,
    ( X1 = X2
    | ~ c_Natural_Oevalc(X3,X4,X1)
    | ~ c_Natural_Oevalc(X3,X4,X2) ),
    cls_com__det_0,
    [final] ).

cnf(i_0_1084,axiom,
    ( c_in(X2,c_SetInterval_Oord__class_OatMost(X3,X1),X1)
    | ~ class_HOL_Oord(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_atMost__iff_1,
    [final] ).

cnf(i_0_1085,axiom,
    ( c_in(X2,c_SetInterval_Oord__class_OatLeast(X3,X1),X1)
    | ~ class_HOL_Oord(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_atLeast__iff_1,
    [final] ).

cnf(i_0_1086,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = X2
    | ~ class_Lattices_Olattice(X1) ),
    cls_sup__inf__absorb_0,
    [final] ).

cnf(i_0_1087,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = X2
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__absorb_0,
    [final] ).

cnf(i_0_1088,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__le1_0,
    [final] ).

cnf(i_0_1089,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__ord_I1_J_0,
    [final] ).

cnf(i_0_1090,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__le2_0,
    [final] ).

cnf(i_0_1091,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__ord_I2_J_0,
    [final] ).

cnf(i_0_1092,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__ge1_0,
    [final] ).

cnf(i_0_1093,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__ord_I3_J_0,
    [final] ).

cnf(i_0_1094,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__ge2_0,
    [final] ).

cnf(i_0_1095,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__ord_I4_J_0,
    [final] ).

cnf(i_0_1096,axiom,
    ( c_SetInterval_Oord__class_OatLeastAtMost(X2,X2,X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_atLeastAtMost__singleton_0,
    [final] ).

cnf(i_0_1097,axiom,
    ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    cls_ex__in__conv_0,
    [final] ).

cnf(i_0_1098,axiom,
    ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    cls_empty__iff_0,
    [final] ).

cnf(i_0_1099,axiom,
    ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    cls_emptyE_0,
    [final] ).

cnf(i_0_1100,axiom,
    c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
    cls_Compl__eq__Diff__UNIV_0,
    [final] ).

cnf(i_0_1101,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    cls_insert__iff_1,
    [final] ).

cnf(i_0_1102,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    cls_insertI1_0,
    [final] ).

cnf(i_0_1103,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    cls_insertCI_1,
    [final] ).

cnf(i_0_1104,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(X3,X2)
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
    cls_finite__subset_0,
    [final] ).

cnf(i_0_1105,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    cls_rev__finite__subset_0,
    [final] ).

cnf(i_0_1106,axiom,
    c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_empty__Diff_0,
    [final] ).

cnf(i_0_1107,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
    cls_Un__UNIV__left_0,
    [final] ).

cnf(i_0_1108,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_Int__empty__left_0,
    [final] ).

cnf(i_0_1109,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_Diff__UNIV_0,
    [final] ).

cnf(i_0_1110,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    cls_Un__UNIV__right_0,
    [final] ).

cnf(i_0_1111,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_Int__empty__right_0,
    [final] ).

cnf(i_0_1112,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),
    cls_Un__commute_0,
    [final] ).

cnf(i_0_1113,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
    cls_Int__commute_0,
    [final] ).

cnf(i_0_1114,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != X3 ),
    cls_le__iff__sup_1,
    [final] ).

cnf(i_0_1115,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != X2 ),
    cls_le__iff__inf_1,
    [final] ).

cnf(i_0_1116,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X2
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_sup__absorb1_0,
    [final] ).

cnf(i_0_1117,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X3
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__iff__sup_0,
    [final] ).

cnf(i_0_1118,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__iff__inf_0,
    [final] ).

cnf(i_0_1119,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X3
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_inf__absorb2_0,
    [final] ).

cnf(i_0_1120,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_finite__insert_1,
    [final] ).

cnf(i_0_1121,axiom,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
    | c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_atLeastatMost__empty__iff2_1,
    [final] ).

cnf(i_0_1122,axiom,
    ( c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_atLeastatMost__empty__iff_1,
    [final] ).

cnf(i_0_1123,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_diff__eq_0,
    [final] ).

cnf(i_0_1124,axiom,
    ( c_Set_Oinsert(X1,X2,X3) = X2
    | ~ c_in(X1,X2,X3) ),
    cls_insert__absorb_0,
    [final] ).

cnf(i_0_1125,axiom,
    ( c_Fun_Osurj(X1,X2,X3)
    | ~ c_Fun_Obij(X1,X2,X3) ),
    cls_bij__def_1,
    [final] ).

cnf(i_0_1126,axiom,
    ( c_in(c_Finite__Set_Olinorder__class_OMin(X2,X1),X2,X1)
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    cls_Min__in_0,
    [final] ).

cnf(i_0_1127,axiom,
    ( c_in(c_Finite__Set_Olinorder__class_OMax(X2,X1),X2,X1)
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    cls_Max__in_0,
    [final] ).

cnf(i_0_1128,axiom,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
    cls_top1I_0,
    [final] ).

cnf(i_0_1129,axiom,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2),
    cls_empty_0,
    [final] ).

cnf(i_0_1130,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
    cls_Un__empty__left_0,
    [final] ).

cnf(i_0_1131,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
    cls_Int__UNIV__left_0,
    [final] ).

cnf(i_0_1132,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    cls_Diff__empty_0,
    [final] ).

cnf(i_0_1133,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    cls_Un__empty__right_0,
    [final] ).

cnf(i_0_1134,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    cls_Int__UNIV__right_0,
    [final] ).

cnf(i_0_1135,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
    cls_empty__subsetI_0,
    [final] ).

cnf(i_0_1136,axiom,
    c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    cls_subset__UNIV_0,
    [final] ).

cnf(i_0_1137,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
    cls_empty__not__insert_0,
    [final] ).

cnf(i_0_1138,axiom,
    c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    cls_insert__not__empty_0,
    [final] ).

cnf(i_0_1139,axiom,
    ( X1 = X3
    | c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)) != c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X2,tc_bool)) ),
    cls_Compl__eq__Compl__iff_0,
    [final] ).

cnf(i_0_1140,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__linear_0,
    [final] ).

cnf(i_0_1141,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_in(X2,X1,X3) ),
    cls_mem__def_0,
    [final] ).

cnf(i_0_1142,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__commute_0,
    [final] ).

cnf(i_0_1143,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I5_J_0,
    [final] ).

cnf(i_0_1144,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__commute_0,
    [final] ).

cnf(i_0_1145,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I1_J_0,
    [final] ).

cnf(i_0_1146,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_Compl__UNIV__eq_0,
    [final] ).

cnf(i_0_1147,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
    cls_Compl__empty__eq_0,
    [final] ).

cnf(i_0_1148,axiom,
    c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
    cls_finite__dom__body_0,
    [final] ).

cnf(i_0_1149,axiom,
    c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    cls_double__complement_0,
    [final] ).

cnf(i_0_1150,axiom,
    c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2),
    cls_UNIV__I_0,
    [final] ).

cnf(i_0_1151,axiom,
    ( X2 = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
    cls_inf__eq__top__eq1_0,
    [final] ).

cnf(i_0_1152,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
    cls_sup__eq__bot__eq1_0,
    [final] ).

cnf(i_0_1153,axiom,
    ( X3 = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
    cls_inf__eq__top__eq2_0,
    [final] ).

cnf(i_0_1154,axiom,
    ( X3 = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
    cls_sup__eq__bot__eq2_0,
    [final] ).

cnf(i_0_1155,axiom,
    c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_Diff__cancel_0,
    [final] ).

cnf(i_0_1156,axiom,
    ( c_in(X1,X2,X3)
    | ~ hBOOL(hAPP(X2,X1)) ),
    cls_mem__def_1,
    [final] ).

cnf(i_0_1157,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_compl__sup__top_0,
    [final] ).

cnf(i_0_1158,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_compl__inf__bot_0,
    [final] ).

cnf(i_0_1159,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_sup__compl__top_0,
    [final] ).

cnf(i_0_1160,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_inf__compl__bot_0,
    [final] ).

cnf(i_0_1161,axiom,
    ( X1 = X2
    | ~ c_fequal(X1,X2,X3) ),
    cls_ATP__Linkup_Ofequal__imp__equal_0,
    [final] ).

cnf(i_0_1162,axiom,
    c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_UNIV__not__empty_0,
    [final] ).

cnf(i_0_1163,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OgreaterThan(X2,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatMost(X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_Compl__greaterThan_0,
    [final] ).

cnf(i_0_1164,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OatMost(X2,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThan(X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_Compl__atMost_0,
    [final] ).

cnf(i_0_1165,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OatLeast(X2,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OlessThan(X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_Compl__atLeast_0,
    [final] ).

cnf(i_0_1166,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OlessThan(X2,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeast(X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_Compl__lessThan_0,
    [final] ).

cnf(i_0_1167,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
    cls_Un__absorb_0,
    [final] ).

cnf(i_0_1168,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
    cls_Int__absorb_0,
    [final] ).

cnf(i_0_1169,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    cls_equalityE_0,
    [final] ).

cnf(i_0_1170,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    cls_subset__refl_0,
    [final] ).

cnf(i_0_1171,axiom,
    ( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    cls_finite__UNIV_0,
    [final] ).

cnf(i_0_1172,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X2,X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_sup__top__left_0,
    [final] ).

cnf(i_0_1173,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_inf__bot__left_0,
    [final] ).

cnf(i_0_1174,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Otop__class_Otop(X1),X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_sup__top__right_0,
    [final] ).

cnf(i_0_1175,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Obot__class_Obot(X1),X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_inf__bot__right_0,
    [final] ).

cnf(i_0_1176,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_sup__bot__left_0,
    [final] ).

cnf(i_0_1177,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X2,X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_inf__top__left_0,
    [final] ).

cnf(i_0_1178,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Obot__class_Obot(X1),X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_sup__bot__right_0,
    [final] ).

cnf(i_0_1179,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Otop__class_Otop(X1),X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_inf__top__right_0,
    [final] ).

cnf(i_0_1180,axiom,
    ( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
    | ~ class_Orderings_Obot(X1) ),
    cls_bot__least_0,
    [final] ).

cnf(i_0_1181,axiom,
    ( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
    | ~ class_Orderings_Otop(X1) ),
    cls_top__greatest_0,
    [final] ).

cnf(i_0_1182,axiom,
    c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
    cls_finite_OemptyI_0,
    [final] ).

cnf(i_0_1183,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X2,X1) = X2
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__idem_0,
    [final] ).

cnf(i_0_1184,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X2,X1) = X2
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__idem_0,
    [final] ).

cnf(i_0_1185,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Opreorder(X1) ),
    cls_order__eq__refl_0,
    [final] ).

cnf(i_0_1186,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_order__eq__iff_0,
    [final] ).

cnf(i_0_1187,axiom,
    c_Fun_Obij(c_Fun_Oid(X1),X1,X1),
    cls_bij__id_0,
    [final] ).

cnf(i_0_1188,axiom,
    c_Fun_Osurj(c_Fun_Oid(X1),X1,X1),
    cls_surj__id_0,
    [final] ).

cnf(i_0_1189,axiom,
    c_fequal(X1,X1,X2),
    cls_ATP__Linkup_Oequal__imp__fequal_0,
    [final] ).

cnf(i_0_1190,axiom,
    ( X2 = X3
    | ~ class_Orderings_Olinorder(X1)
    | c_SetInterval_Oord__class_OgreaterThan(X2,X1) != c_SetInterval_Oord__class_OgreaterThan(X3,X1) ),
    cls_greaterThan__eq__iff_0,
    [final] ).

cnf(i_0_1191,axiom,
    ( X2 = X3
    | ~ class_Orderings_Olinorder(X1)
    | c_SetInterval_Oord__class_OatMost(X2,X1) != c_SetInterval_Oord__class_OatMost(X3,X1) ),
    cls_atMost__eq__iff_0,
    [final] ).

cnf(i_0_1192,axiom,
    ( X2 = X3
    | ~ class_Orderings_Olinorder(X1)
    | c_SetInterval_Oord__class_OatLeast(X2,X1) != c_SetInterval_Oord__class_OatLeast(X3,X1) ),
    cls_atLeast__eq__iff_0,
    [final] ).

cnf(i_0_1193,axiom,
    ( X2 = X3
    | ~ class_Orderings_Olinorder(X1)
    | c_SetInterval_Oord__class_OlessThan(X2,X1) != c_SetInterval_Oord__class_OlessThan(X3,X1) ),
    cls_lessThan__eq__iff_0,
    [final] ).

cnf(i_0_1194,axiom,
    ( X2 = X3
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
    cls_neg__equal__iff__equal_0,
    [final] ).

cnf(i_0_1195,axiom,
    ( X2 = X3
    | ~ class_Lattices_Oboolean__algebra(X1)
    | c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
    cls_compl__eq__compl__iff_0,
    [final] ).

cnf(i_0_1196,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_minus__equation__iff_1,
    [final] ).

cnf(i_0_1197,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_minus__minus_0,
    [final] ).

cnf(i_0_1198,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_double__compl_0,
    [final] ).

cnf(i_0_1199,axiom,
    ( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_equation__minus__iff_1,
    [final] ).

cnf(i_0_1200,axiom,
    ( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_equation__minus__iff_0,
    [final] ).

cnf(i_0_1201,axiom,
    hAPP(c_Option_Othe(X1),c_Option_Ooption_OSome(X2,X1)) = X2,
    cls_the_Osimps_0,
    [final] ).

cnf(i_0_1202,axiom,
    ( X1 = X3
    | c_Option_Ooption_OSome(X1,X2) != c_Option_Ooption_OSome(X3,X2) ),
    cls_option_Oinject_0,
    [final] ).

cnf(i_0_1203,axiom,
    ( c_Com_OWT(X2)
    | hAPP(c_Com_Obody,X1) != c_Option_Ooption_OSome(X2,tc_Com_Ocom)
    | ~ c_Com_OWT__bodies ),
    cls_WT__bodiesD_0,
    [final] ).

cnf(i_0_1204,axiom,
    ( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
    | ~ class_Finite__Set_Ofinite_Ofinite(X2)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    clsarity_fun__Finite__Set_Ofinite_Ofinite,
    [final] ).

cnf(i_0_1205,axiom,
    ( X1 = X2
    | hAPP(c_Com_Ocom_OBODY,X1) != hAPP(c_Com_Ocom_OBODY,X2) ),
    cls_com_Osimps_I6_J_0,
    [final] ).

cnf(i_0_1206,axiom,
    ( class_Orderings_Opreorder(tc_fun(X1,X2))
    | ~ class_Orderings_Opreorder(X2) ),
    clsarity_fun__Orderings_Opreorder,
    [final] ).

cnf(i_0_1207,axiom,
    ( class_Orderings_Obot(tc_fun(X1,X2))
    | ~ class_Orderings_Obot(X2) ),
    clsarity_fun__Orderings_Obot,
    [final] ).

cnf(i_0_1208,axiom,
    ( class_Orderings_Otop(tc_fun(X1,X2))
    | ~ class_Orderings_Otop(X2) ),
    clsarity_fun__Orderings_Otop,
    [final] ).

cnf(i_0_1209,axiom,
    ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
    clsarity_fun__Complete__Lattice_Ocomplete__lattice,
    [final] ).

cnf(i_0_1210,axiom,
    ( class_HOL_Oord(tc_fun(X1,X2))
    | ~ class_HOL_Oord(X2) ),
    clsarity_fun__HOL_Oord,
    [final] ).

cnf(i_0_1211,axiom,
    ( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
    | ~ class_Lattices_Obounded__lattice(X2) ),
    clsarity_fun__Lattices_Obounded__lattice,
    [final] ).

cnf(i_0_1212,axiom,
    ( class_Lattices_Odistrib__lattice(tc_fun(X1,X2))
    | ~ class_Lattices_Odistrib__lattice(X2) ),
    clsarity_fun__Lattices_Odistrib__lattice,
    [final] ).

cnf(i_0_1213,axiom,
    ( class_Lattices_Oupper__semilattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Oupper__semilattice,
    [final] ).

cnf(i_0_1214,axiom,
    ( class_Lattices_Olower__semilattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_1215,axiom,
    ( class_Lattices_Olattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Olattice,
    [final] ).

cnf(i_0_1216,axiom,
    ( class_Lattices_Oboolean__algebra(tc_fun(X1,X2))
    | ~ class_Lattices_Oboolean__algebra(X2) ),
    clsarity_fun__Lattices_Oboolean__algebra,
    [final] ).

cnf(i_0_1217,axiom,
    ( class_Orderings_Oorder(tc_fun(X1,X2))
    | ~ class_Orderings_Oorder(X2) ),
    clsarity_fun__Orderings_Oorder,
    [final] ).

cnf(i_0_1218,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(X1),X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_compl__top__eq_0,
    [final] ).

cnf(i_0_1219,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(X1),X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_compl__bot__eq_0,
    [final] ).

cnf(i_0_1220,axiom,
    ( c_Finite__Set_Ofinite(X2,X1)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    cls_finite_0,
    [final] ).

cnf(i_0_1221,axiom,
    hAPP(c_Fun_Oid(X1),X2) = X2,
    cls_id__apply_0,
    [final] ).

cnf(i_0_1222,axiom,
    hAPP(c_COMBI(X1),X2) = X2,
    cls_COMBI__def_0,
    [final] ).

cnf(i_0_1223,axiom,
    ( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X1))
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite,
    [final] ).

cnf(i_0_1224,axiom,
    ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X1) != X1
    | ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
    cls_single__stateE_0,
    [final] ).

cnf(i_0_1225,axiom,
    ( c_Hoare__Mirabelle_Ostate__not__singleton
    | X1 = X2 ),
    cls_state__not__singleton__def_1,
    [final] ).

cnf(i_0_1226,axiom,
    class_Orderings_Opreorder(tc_nat),
    clsarity_nat__Orderings_Opreorder,
    [final] ).

cnf(i_0_1227,axiom,
    class_Orderings_Opreorder(tc_bool),
    clsarity_bool__Orderings_Opreorder,
    [final] ).

cnf(i_0_1228,axiom,
    class_Finite__Set_Ofinite_Ofinite(tc_bool),
    clsarity_bool__Finite__Set_Ofinite_Ofinite,
    [final] ).

cnf(i_0_1229,axiom,
    class_Orderings_Obot(tc_nat),
    clsarity_nat__Orderings_Obot,
    [final] ).

cnf(i_0_1230,axiom,
    class_Orderings_Obot(tc_bool),
    clsarity_bool__Orderings_Obot,
    [final] ).

cnf(i_0_1231,axiom,
    class_Orderings_Otop(tc_bool),
    clsarity_bool__Orderings_Otop,
    [final] ).

cnf(i_0_1232,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_bool),
    clsarity_bool__Complete__Lattice_Ocomplete__lattice,
    [final] ).

cnf(i_0_1233,axiom,
    class_HOL_Oord(tc_nat),
    clsarity_nat__HOL_Oord,
    [final] ).

cnf(i_0_1234,axiom,
    class_HOL_Oord(tc_bool),
    clsarity_bool__HOL_Oord,
    [final] ).

cnf(i_0_1235,axiom,
    class_Lattices_Obounded__lattice(tc_bool),
    clsarity_bool__Lattices_Obounded__lattice,
    [final] ).

cnf(i_0_1236,axiom,
    class_Lattices_Odistrib__lattice(tc_nat),
    clsarity_nat__Lattices_Odistrib__lattice,
    [final] ).

cnf(i_0_1237,axiom,
    class_Lattices_Odistrib__lattice(tc_bool),
    clsarity_bool__Lattices_Odistrib__lattice,
    [final] ).

cnf(i_0_1238,axiom,
    class_Lattices_Oupper__semilattice(tc_nat),
    clsarity_nat__Lattices_Oupper__semilattice,
    [final] ).

cnf(i_0_1239,axiom,
    class_Lattices_Oupper__semilattice(tc_bool),
    clsarity_bool__Lattices_Oupper__semilattice,
    [final] ).

cnf(i_0_1240,axiom,
    class_Lattices_Olower__semilattice(tc_nat),
    clsarity_nat__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_1241,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    clsarity_bool__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_1242,axiom,
    class_Lattices_Olattice(tc_nat),
    clsarity_nat__Lattices_Olattice,
    [final] ).

cnf(i_0_1243,axiom,
    class_Lattices_Olattice(tc_bool),
    clsarity_bool__Lattices_Olattice,
    [final] ).

cnf(i_0_1244,axiom,
    class_Orderings_Olinorder(tc_nat),
    clsarity_nat__Orderings_Olinorder,
    [final] ).

cnf(i_0_1245,axiom,
    class_Lattices_Oboolean__algebra(tc_bool),
    clsarity_bool__Lattices_Oboolean__algebra,
    [final] ).

cnf(i_0_1246,axiom,
    class_Orderings_Oorder(tc_nat),
    clsarity_nat__Orderings_Oorder,
    [final] ).

cnf(i_0_1247,axiom,
    class_Orderings_Oorder(tc_bool),
    clsarity_bool__Orderings_Oorder,
    [final] ).

cnf(i_0_1248,negated_conjecture,
    c_Com_OWT__bodies,
    cls_conjecture_1,
    [final] ).

cnf(i_0_1249,negated_conjecture,
    c_Hoare__Mirabelle_Ostate__not__singleton,
    cls_conjecture_0,
    [final] ).

cnf(i_0_1250,axiom,
    X1 = X1 ).

cnf(i_0_1251,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1252,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1253,axiom,
    ( X1 != X2
    | c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).

cnf(i_0_1254,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).

cnf(i_0_1255,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).

cnf(i_0_1256,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).

cnf(i_0_1257,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X1,X3,X4,X5) = c_Hilbert__Choice_Oinv__into(X2,X3,X4,X5) ) ).

cnf(i_0_1258,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X1,X4,X5) = c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5) ) ).

cnf(i_0_1259,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X1,X5) = c_Hilbert__Choice_Oinv__into(X3,X4,X2,X5) ) ).

cnf(i_0_1260,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X5,X1) = c_Hilbert__Choice_Oinv__into(X3,X4,X5,X2) ) ).

cnf(i_0_1261,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X1,X3,X4,X5,X6) = c_Fun_Ocomp(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1262,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X1,X4,X5,X6) = c_Fun_Ocomp(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1263,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X1,X5,X6) = c_Fun_Ocomp(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1264,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X5,X1,X6) = c_Fun_Ocomp(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1265,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X5,X6,X1) = c_Fun_Ocomp(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1266,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_1267,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4) ) ).

cnf(i_0_1268,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X4) ) ).

cnf(i_0_1269,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2) ) ).

cnf(i_0_1270,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_1271,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_1272,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_1273,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_1274,axiom,
    ( X1 != X2
    | c_Fun_Oid(X1) = c_Fun_Oid(X2) ) ).

cnf(i_0_1275,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X1,X3,X4,X5) = c_Set_Ovimage(X2,X3,X4,X5) ) ).

cnf(i_0_1276,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X1,X4,X5) = c_Set_Ovimage(X3,X2,X4,X5) ) ).

cnf(i_0_1277,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X1,X5) = c_Set_Ovimage(X3,X4,X2,X5) ) ).

cnf(i_0_1278,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X5,X1) = c_Set_Ovimage(X3,X4,X5,X2) ) ).

cnf(i_0_1279,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).

cnf(i_0_1280,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).

cnf(i_0_1281,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).

cnf(i_0_1282,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).

cnf(i_0_1283,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).

cnf(i_0_1284,axiom,
    ( X1 != X2
    | c_HOL_Ouminus__class_Ouminus(X1,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3) ) ).

cnf(i_0_1285,axiom,
    ( X1 != X2
    | c_HOL_Ouminus__class_Ouminus(X3,X1) = c_HOL_Ouminus__class_Ouminus(X3,X2) ) ).

cnf(i_0_1286,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).

cnf(i_0_1287,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).

cnf(i_0_1288,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).

cnf(i_0_1289,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).

cnf(i_0_1290,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).

cnf(i_0_1291,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).

cnf(i_0_1292,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OlessThan(X1,X3) = c_SetInterval_Oord__class_OlessThan(X2,X3) ) ).

cnf(i_0_1293,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OlessThan(X3,X1) = c_SetInterval_Oord__class_OlessThan(X3,X2) ) ).

cnf(i_0_1294,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThan(X1,X3) = c_SetInterval_Oord__class_OgreaterThan(X2,X3) ) ).

cnf(i_0_1295,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThan(X3,X1) = c_SetInterval_Oord__class_OgreaterThan(X3,X2) ) ).

cnf(i_0_1296,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeast(X1,X3) = c_SetInterval_Oord__class_OatLeast(X2,X3) ) ).

cnf(i_0_1297,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeast(X3,X1) = c_SetInterval_Oord__class_OatLeast(X3,X2) ) ).

cnf(i_0_1298,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatMost(X1,X3) = c_SetInterval_Oord__class_OatMost(X2,X3) ) ).

cnf(i_0_1299,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatMost(X3,X1) = c_SetInterval_Oord__class_OatMost(X3,X2) ) ).

cnf(i_0_1300,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X1,X3) = c_Finite__Set_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_1301,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X3,X1) = c_Finite__Set_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_1302,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X1,X3) = c_Finite__Set_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_1303,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X3,X1) = c_Finite__Set_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_1304,axiom,
    ( X1 != X2
    | c_Option_Ooption_OSome(X1,X3) = c_Option_Ooption_OSome(X2,X3) ) ).

cnf(i_0_1305,axiom,
    ( X1 != X2
    | c_Option_Ooption_OSome(X3,X1) = c_Option_Ooption_OSome(X3,X2) ) ).

cnf(i_0_1306,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4) ) ).

cnf(i_0_1307,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X4) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) ) ).

cnf(i_0_1308,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2) ) ).

cnf(i_0_1309,axiom,
    ( X1 != X2
    | v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X1) = v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X2) ) ).

cnf(i_0_1310,axiom,
    ( X1 != X2
    | c_Map_Odom(X1,X3,X4) = c_Map_Odom(X2,X3,X4) ) ).

cnf(i_0_1311,axiom,
    ( X1 != X2
    | c_Map_Odom(X3,X1,X4) = c_Map_Odom(X3,X2,X4) ) ).

cnf(i_0_1312,axiom,
    ( X1 != X2
    | c_Map_Odom(X3,X4,X1) = c_Map_Odom(X3,X4,X2) ) ).

cnf(i_0_1313,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1314,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1315,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).

cnf(i_0_1316,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).

cnf(i_0_1317,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).

cnf(i_0_1318,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1319,axiom,
    ( X1 != X2
    | ~ c_Com_OWT(X1)
    | c_Com_OWT(X2) ) ).

cnf(i_0_1320,axiom,
    ( X1 != X2
    | ~ c_Map_Omap__le(X1,X3,X4,X5)
    | c_Map_Omap__le(X2,X3,X4,X5) ) ).

cnf(i_0_1321,axiom,
    ( X1 != X2
    | ~ c_Map_Omap__le(X3,X1,X4,X5)
    | c_Map_Omap__le(X3,X2,X4,X5) ) ).

cnf(i_0_1322,axiom,
    ( X1 != X2
    | ~ c_Map_Omap__le(X3,X4,X1,X5)
    | c_Map_Omap__le(X3,X4,X2,X5) ) ).

cnf(i_0_1323,axiom,
    ( X1 != X2
    | ~ c_Map_Omap__le(X3,X4,X5,X1)
    | c_Map_Omap__le(X3,X4,X5,X2) ) ).

cnf(i_0_1324,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_1325,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1326,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1327,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_1328,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oupper__semilattice(X1)
    | class_Lattices_Oupper__semilattice(X2) ) ).

cnf(i_0_1329,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | c_Finite__Set_Ofinite(X2,X3) ) ).

cnf(i_0_1330,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | c_Finite__Set_Ofinite(X3,X2) ) ).

cnf(i_0_1331,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | class_Lattices_Olower__semilattice(X2) ) ).

cnf(i_0_1332,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_1333,axiom,
    ( X1 != X2
    | ~ c_Natural_Oevalc(X1,X3,X4)
    | c_Natural_Oevalc(X2,X3,X4) ) ).

cnf(i_0_1334,axiom,
    ( X1 != X2
    | ~ c_Natural_Oevalc(X3,X1,X4)
    | c_Natural_Oevalc(X3,X2,X4) ) ).

cnf(i_0_1335,axiom,
    ( X1 != X2
    | ~ c_Natural_Oevalc(X3,X4,X1)
    | c_Natural_Oevalc(X3,X4,X2) ) ).

cnf(i_0_1336,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_1337,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1338,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oboolean__algebra(X1)
    | class_Lattices_Oboolean__algebra(X2) ) ).

cnf(i_0_1339,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_1340,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1341,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_1342,axiom,
    ( X1 != X2
    | ~ c_fequal(X1,X3,X4)
    | c_fequal(X2,X3,X4) ) ).

cnf(i_0_1343,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X1,X4)
    | c_fequal(X3,X2,X4) ) ).

cnf(i_0_1344,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X4,X1)
    | c_fequal(X3,X4,X2) ) ).

cnf(i_0_1345,axiom,
    ( X1 != X2
    | ~ c_in(X1,X3,X4)
    | c_in(X2,X3,X4) ) ).

cnf(i_0_1346,axiom,
    ( X1 != X2
    | ~ c_in(X3,X1,X4)
    | c_in(X3,X2,X4) ) ).

cnf(i_0_1347,axiom,
    ( X1 != X2
    | ~ c_in(X3,X4,X1)
    | c_in(X3,X4,X2) ) ).

cnf(i_0_1348,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite_Ofinite(X1)
    | class_Finite__Set_Ofinite_Ofinite(X2) ) ).

cnf(i_0_1349,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_1350,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_1351,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | class_OrderedGroup_Ogroup__add(X2) ) ).

cnf(i_0_1352,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_1353,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_1354,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_1355,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_1356,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_1357,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_1358,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_1359,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X1,X3,X4,X5,X6)
    | c_Fun_Obij__betw(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1360,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X1,X4,X5,X6)
    | c_Fun_Obij__betw(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1361,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X1,X5,X6)
    | c_Fun_Obij__betw(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1362,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X5,X1,X6)
    | c_Fun_Obij__betw(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1363,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X5,X6,X1)
    | c_Fun_Obij__betw(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1364,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij(X1,X3,X4)
    | c_Fun_Obij(X2,X3,X4) ) ).

cnf(i_0_1365,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij(X3,X1,X4)
    | c_Fun_Obij(X3,X2,X4) ) ).

cnf(i_0_1366,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij(X3,X4,X1)
    | c_Fun_Obij(X3,X4,X2) ) ).

cnf(i_0_1367,axiom,
    ( X1 != X2
    | ~ class_HOL_Oord(X1)
    | class_HOL_Oord(X2) ) ).

cnf(i_0_1368,axiom,
    ( X1 != X2
    | ~ c_Fun_Osurj(X1,X3,X4)
    | c_Fun_Osurj(X2,X3,X4) ) ).

cnf(i_0_1369,axiom,
    ( X1 != X2
    | ~ c_Fun_Osurj(X3,X1,X4)
    | c_Fun_Osurj(X3,X2,X4) ) ).

cnf(i_0_1370,axiom,
    ( X1 != X2
    | ~ c_Fun_Osurj(X3,X4,X1)
    | c_Fun_Osurj(X3,X4,X2) ) ).

cnf(i_0_1250_001,axiom,
    X1 = X1 ).

cnf(i_0_1251_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1252_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1253_004,axiom,
    ( X1 != X2
    | c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).

cnf(i_0_1254_005,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).

cnf(i_0_1255_006,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).

cnf(i_0_1256_007,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).

cnf(i_0_1257_008,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X1,X3,X4,X5) = c_Hilbert__Choice_Oinv__into(X2,X3,X4,X5) ) ).

cnf(i_0_1258_009,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X1,X4,X5) = c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5) ) ).

cnf(i_0_1259_010,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X1,X5) = c_Hilbert__Choice_Oinv__into(X3,X4,X2,X5) ) ).

cnf(i_0_1260_011,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X5,X1) = c_Hilbert__Choice_Oinv__into(X3,X4,X5,X2) ) ).

cnf(i_0_1261_012,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X1,X3,X4,X5,X6) = c_Fun_Ocomp(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1262_013,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X1,X4,X5,X6) = c_Fun_Ocomp(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1263_014,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X1,X5,X6) = c_Fun_Ocomp(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1264_015,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X5,X1,X6) = c_Fun_Ocomp(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1265_016,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X5,X6,X1) = c_Fun_Ocomp(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1266_017,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_1267_018,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4) ) ).

cnf(i_0_1268_019,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X4) ) ).

cnf(i_0_1269_020,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2) ) ).

cnf(i_0_1270_021,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_1271_022,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_1272_023,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_1273_024,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_1274_025,axiom,
    ( X1 != X2
    | c_Fun_Oid(X1) = c_Fun_Oid(X2) ) ).

cnf(i_0_1275_026,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X1,X3,X4,X5) = c_Set_Ovimage(X2,X3,X4,X5) ) ).

cnf(i_0_1276_027,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X1,X4,X5) = c_Set_Ovimage(X3,X2,X4,X5) ) ).

cnf(i_0_1277_028,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X1,X5) = c_Set_Ovimage(X3,X4,X2,X5) ) ).

cnf(i_0_1278_029,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X5,X1) = c_Set_Ovimage(X3,X4,X5,X2) ) ).

cnf(i_0_1279_030,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).

cnf(i_0_1280_031,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).

cnf(i_0_1281_032,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).

cnf(i_0_1282_033,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).

cnf(i_0_1283_034,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).

cnf(i_0_1284_035,axiom,
    ( X1 != X2
    | c_HOL_Ouminus__class_Ouminus(X1,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3) ) ).

cnf(i_0_1285_036,axiom,
    ( X1 != X2
    | c_HOL_Ouminus__class_Ouminus(X3,X1) = c_HOL_Ouminus__class_Ouminus(X3,X2) ) ).

cnf(i_0_1286_037,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).

cnf(i_0_1287_038,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).

cnf(i_0_1288_039,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).

cnf(i_0_1289_040,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).

cnf(i_0_1290_041,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).

cnf(i_0_1291_042,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).

cnf(i_0_1292_043,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OlessThan(X1,X3) = c_SetInterval_Oord__class_OlessThan(X2,X3) ) ).

cnf(i_0_1293_044,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OlessThan(X3,X1) = c_SetInterval_Oord__class_OlessThan(X3,X2) ) ).

cnf(i_0_1294_045,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThan(X1,X3) = c_SetInterval_Oord__class_OgreaterThan(X2,X3) ) ).

cnf(i_0_1295_046,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThan(X3,X1) = c_SetInterval_Oord__class_OgreaterThan(X3,X2) ) ).

cnf(i_0_1296_047,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeast(X1,X3) = c_SetInterval_Oord__class_OatLeast(X2,X3) ) ).

cnf(i_0_1297_048,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeast(X3,X1) = c_SetInterval_Oord__class_OatLeast(X3,X2) ) ).

cnf(i_0_1298_049,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatMost(X1,X3) = c_SetInterval_Oord__class_OatMost(X2,X3) ) ).

cnf(i_0_1299_050,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatMost(X3,X1) = c_SetInterval_Oord__class_OatMost(X3,X2) ) ).

cnf(i_0_1300_051,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X1,X3) = c_Finite__Set_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_1301_052,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X3,X1) = c_Finite__Set_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_1302_053,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X1,X3) = c_Finite__Set_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_1303_054,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X3,X1) = c_Finite__Set_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_1304_055,axiom,
    ( X1 != X2
    | c_Option_Ooption_OSome(X1,X3) = c_Option_Ooption_OSome(X2,X3) ) ).

cnf(i_0_1305_056,axiom,
    ( X1 != X2
    | c_Option_Ooption_OSome(X3,X1) = c_Option_Ooption_OSome(X3,X2) ) ).

cnf(i_0_1306_057,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4) ) ).

cnf(i_0_1307_058,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X4) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) ) ).

cnf(i_0_1308_059,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2) ) ).

cnf(i_0_1309_060,axiom,
    ( X1 != X2
    | v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X1) = v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X2) ) ).

cnf(i_0_1310_061,axiom,
    ( X1 != X2
    | c_Map_Odom(X1,X3,X4) = c_Map_Odom(X2,X3,X4) ) ).

cnf(i_0_1311_062,axiom,
    ( X1 != X2
    | c_Map_Odom(X3,X1,X4) = c_Map_Odom(X3,X2,X4) ) ).

cnf(i_0_1312_063,axiom,
    ( X1 != X2
    | c_Map_Odom(X3,X4,X1) = c_Map_Odom(X3,X4,X2) ) ).

cnf(i_0_1313_064,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1314_065,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1315_066,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).

cnf(i_0_1316_067,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).

cnf(i_0_1317_068,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).

cnf(i_0_1318_069,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1319_070,axiom,
    ( X1 != X2
    | ~ c_Com_OWT(X1)
    | c_Com_OWT(X2) ) ).

cnf(i_0_1320_071,axiom,
    ( X1 != X2
    | ~ c_Map_Omap__le(X1,X3,X4,X5)
    | c_Map_Omap__le(X2,X3,X4,X5) ) ).

cnf(i_0_1321_072,axiom,
    ( X1 != X2
    | ~ c_Map_Omap__le(X3,X1,X4,X5)
    | c_Map_Omap__le(X3,X2,X4,X5) ) ).

cnf(i_0_1322_073,axiom,
    ( X1 != X2
    | ~ c_Map_Omap__le(X3,X4,X1,X5)
    | c_Map_Omap__le(X3,X4,X2,X5) ) ).

cnf(i_0_1323_074,axiom,
    ( X1 != X2
    | ~ c_Map_Omap__le(X3,X4,X5,X1)
    | c_Map_Omap__le(X3,X4,X5,X2) ) ).

cnf(i_0_1324_075,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_1325_076,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1326_077,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1327_078,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_1328_079,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oupper__semilattice(X1)
    | class_Lattices_Oupper__semilattice(X2) ) ).

cnf(i_0_1329_080,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | c_Finite__Set_Ofinite(X2,X3) ) ).

cnf(i_0_1330_081,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | c_Finite__Set_Ofinite(X3,X2) ) ).

cnf(i_0_1331_082,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | class_Lattices_Olower__semilattice(X2) ) ).

cnf(i_0_1332_083,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_1333_084,axiom,
    ( X1 != X2
    | ~ c_Natural_Oevalc(X1,X3,X4)
    | c_Natural_Oevalc(X2,X3,X4) ) ).

cnf(i_0_1334_085,axiom,
    ( X1 != X2
    | ~ c_Natural_Oevalc(X3,X1,X4)
    | c_Natural_Oevalc(X3,X2,X4) ) ).

cnf(i_0_1335_086,axiom,
    ( X1 != X2
    | ~ c_Natural_Oevalc(X3,X4,X1)
    | c_Natural_Oevalc(X3,X4,X2) ) ).

cnf(i_0_1336_087,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_1337_088,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1338_089,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oboolean__algebra(X1)
    | class_Lattices_Oboolean__algebra(X2) ) ).

cnf(i_0_1339_090,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_1340_091,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1341_092,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_1342_093,axiom,
    ( X1 != X2
    | ~ c_fequal(X1,X3,X4)
    | c_fequal(X2,X3,X4) ) ).

cnf(i_0_1343_094,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X1,X4)
    | c_fequal(X3,X2,X4) ) ).

cnf(i_0_1344_095,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X4,X1)
    | c_fequal(X3,X4,X2) ) ).

cnf(i_0_1345_096,axiom,
    ( X1 != X2
    | ~ c_in(X1,X3,X4)
    | c_in(X2,X3,X4) ) ).

cnf(i_0_1346_097,axiom,
    ( X1 != X2
    | ~ c_in(X3,X1,X4)
    | c_in(X3,X2,X4) ) ).

cnf(i_0_1347_098,axiom,
    ( X1 != X2
    | ~ c_in(X3,X4,X1)
    | c_in(X3,X4,X2) ) ).

cnf(i_0_1348_099,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite_Ofinite(X1)
    | class_Finite__Set_Ofinite_Ofinite(X2) ) ).

cnf(i_0_1349_100,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_1350_101,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_1351_102,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | class_OrderedGroup_Ogroup__add(X2) ) ).

cnf(i_0_1352_103,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_1353_104,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_1354_105,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_1355_106,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_1356_107,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_1357_108,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_1358_109,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_1359_110,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X1,X3,X4,X5,X6)
    | c_Fun_Obij__betw(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1360_111,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X1,X4,X5,X6)
    | c_Fun_Obij__betw(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1361_112,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X1,X5,X6)
    | c_Fun_Obij__betw(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1362_113,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X5,X1,X6)
    | c_Fun_Obij__betw(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1363_114,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X5,X6,X1)
    | c_Fun_Obij__betw(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1364_115,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij(X1,X3,X4)
    | c_Fun_Obij(X2,X3,X4) ) ).

cnf(i_0_1365_116,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij(X3,X1,X4)
    | c_Fun_Obij(X3,X2,X4) ) ).

cnf(i_0_1366_117,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij(X3,X4,X1)
    | c_Fun_Obij(X3,X4,X2) ) ).

cnf(i_0_1367_118,axiom,
    ( X1 != X2
    | ~ class_HOL_Oord(X1)
    | class_HOL_Oord(X2) ) ).

cnf(i_0_1368_119,axiom,
    ( X1 != X2
    | ~ c_Fun_Osurj(X1,X3,X4)
    | c_Fun_Osurj(X2,X3,X4) ) ).

cnf(i_0_1369_120,axiom,
    ( X1 != X2
    | ~ c_Fun_Osurj(X3,X1,X4)
    | c_Fun_Osurj(X3,X2,X4) ) ).

cnf(i_0_1370_121,axiom,
    ( X1 != X2
    | ~ c_Fun_Osurj(X3,X4,X1)
    | c_Fun_Osurj(X3,X4,X2) ) ).

cnf(i_0_1371,plain,
    c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X1,X2,X3,X4),
    inference(equality_inference,[],[631]) ).

cnf(i_0_1372,plain,
    hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(c_Fun_Ocomp(X1,X2,X7,X4,X8),X6),
    inference(equality_inference,[],[637]) ).

cnf(i_0_1373,plain,
    hAPP(X1,hAPP(X2,X3)) = hAPP(X1,hAPP(X2,X3)),
    inference(equality_inference,[],[640]) ).

cnf(i_0_1374,plain,
    hAPP(c_Fun_Oid(X1),hAPP(X2,X3)) = hAPP(X2,X3),
    inference(equality_inference,[],[642]) ).

cnf(i_0_1375,plain,
    ( X1 = X1
    | ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5)
    | ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
    inference(equality_inference,[],[655]) ).

cnf(i_0_1376,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X3,tc_bool)),X3,X4) ),
    inference(equality_inference,[],[712]) ).

cnf(i_0_1377,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    inference(equality_inference,[],[717]) ).

cnf(i_0_1378,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[758]) ).

cnf(i_0_1379,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[759]) ).

cnf(i_0_1380,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[760]) ).

cnf(i_0_1381,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[761]) ).

cnf(i_0_1382,plain,
    ( ~ c_in(X1,X2,X3)
    | ~ c_in(X1,X2,X3)
    | X1 = X1
    | ~ c_Fun_Oinj__on(X4,X2,X3,X5) ),
    inference(equality_inference,[],[807]) ).

cnf(i_0_1383,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    inference(equality_inference,[],[825]) ).

cnf(i_0_1384,plain,
    X1 = X1,
    inference(equality_inference,[],[903]) ).

cnf(i_0_1385,plain,
    ( X1 = X1
    | c_in(X2,X1,X3)
    | c_in(X2,X1,X3) ),
    inference(equality_inference,[],[961]) ).

cnf(i_0_1386,plain,
    ( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))
    | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ),
    inference(equality_inference,[],[977]) ).

cnf(i_0_1387,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[1076]) ).

cnf(i_0_1388,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[1077]) ).

cnf(i_0_1389,plain,
    X1 = X1,
    inference(equality_inference,[],[1139]) ).

cnf(i_0_1390,plain,
    ( X1 = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(equality_inference,[],[1190]) ).

cnf(i_0_1391,plain,
    ( X1 = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(equality_inference,[],[1191]) ).

cnf(i_0_1392,plain,
    ( X1 = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(equality_inference,[],[1192]) ).

cnf(i_0_1393,plain,
    ( X1 = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(equality_inference,[],[1193]) ).

cnf(i_0_1394,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ogroup__add(X2) ),
    inference(equality_inference,[],[1194]) ).

cnf(i_0_1395,plain,
    ( X1 = X1
    | ~ class_Lattices_Oboolean__algebra(X2) ),
    inference(equality_inference,[],[1195]) ).

cnf(i_0_1396,plain,
    X1 = X1,
    inference(equality_inference,[],[1202]) ).

cnf(i_0_1397,plain,
    X1 = X1,
    inference(equality_inference,[],[1205]) ).

cnf(i_0_1398,plain,
    $false,
    inference(scs_inference,[],[i_0_626,i_0_1170,i_0_1148,i_0_746]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWV898-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33  % Computer : n028.cluster.edu
% 0.15/0.33  % Model    : x86_64 x86_64
% 0.15/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33  % Memory   : 8042.1875MB
% 0.15/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33  % CPULimit   : 300
% 0.15/0.33  % WCLimit    : 300
% 0.15/0.33  % DateTime   : Tue May  5 06:08:00 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 1.12/1.67  % Version  : CSE_E---1.7
% 1.12/1.67  % Problem  : theBenchmark.p
% 1.12/1.67  % SZS status Unsatisfiable for theBenchmark.p
% 1.12/1.67  % SZS output start CNFRefutation
% See solution above
% 1.18/1.74  % Total time : 1.327s
%------------------------------------------------------------------------------