CSE_E---1.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SWV905-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n022.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 05:27:42 PM UTC 2026

% Result   : Unsatisfiable 1.06s 1.67s
% Output   : CNFRefutation 1.31s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_487)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_singleton__conv2_0,axiom,
    c_Collect(c_fequal(X1,X2),X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).

cnf(cls_Collect__def_0,axiom,
    c_Collect(X1,X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).

cnf(cls_ab__semigroup__mult_Ofold1__Un_0,axiom,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | c_Finite__Set_Ofold1(X4,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool)),X1) = hAPP(hAPP(X4,c_Finite__Set_Ofold1(X4,X2,X1)),c_Finite__Set_Ofold1(X4,X3,X1))
    | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | ~ c_Finite__Set_Ofinite(X2,X1)
    | ~ c_OrderedGroup_Oab__semigroup__mult(X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__Un_0) ).

cnf(cls_fold1__def_0,axiom,
    c_Finite__Set_Ofold1(X1,X2,X3) = c_The(c_Finite__Set_Ofold1Set(X1,X2,X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__def_0) ).

cnf(cls_Int__Collect_0,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Collect(X4,X3)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_0) ).

cnf(cls_Int__Collect_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),c_Collect(X1,X3)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_1) ).

cnf(cls_Int__Collect_2,axiom,
    ( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2))
    | ~ hBOOL(hAPP(X4,X1))
    | ~ hBOOL(c_in(X1,X3,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_2) ).

cnf(cls_ab__semigroup__mult_Ofold1__insert_0,axiom,
    ( c_Finite__Set_Ofold1(X1,c_Set_Oinsert(X2,X3,X4),X4) = hAPP(hAPP(X1,X2),c_Finite__Set_Ofold1(X1,X3,X4))
    | hBOOL(c_in(X2,X3,X4))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X4)
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__insert_0) ).

cnf(cls_below__fold1__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ hBOOL(c_in(X3,X4,X1))
    | ~ c_lessequals(X2,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X1),X4,X1),X1)
    | ~ c_Finite__Set_Ofinite(X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_below__fold1__iff_0) ).

cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(c_fequal(X1,X3),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

cnf(cls_fold1__singleton_0,axiom,
    c_Finite__Set_Ofold1(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).

cnf(cls_fold1__belowI_0,axiom,
    ( c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X1),X2,X1),X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ hBOOL(c_in(X3,X2,X1))
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__belowI_0) ).

cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
    hBOOL(hAPP(c_fequal(X1,X2),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

cnf(cls_the__sym__eq__trivial_0,axiom,
    c_The(c_fequal(X1,X2),X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the__sym__eq__trivial_0) ).

cnf(cls_CollectD_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,c_Collect(X1,X3),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectD_0) ).

cnf(cls_CollectI_0,axiom,
    ( hBOOL(c_in(X1,c_Collect(X2,X3),X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectI_0) ).

cnf(cls_empty__Collect__eq_0,axiom,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Collect(X2,X1)
    | ~ hBOOL(hAPP(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).

cnf(cls_Collect__empty__eq_0,axiom,
    ( c_Collect(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ hBOOL(hAPP(X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).

cnf(cls_complete__lattice_OInf__binary_0,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)) = hAPP(hAPP(X5,X2),X3)
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X6,X7,X8,X5,X9,X10,X11,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).

cnf(cls_complete__lattice_OSup__binary_0,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)) = hAPP(hAPP(X5,X2),X3)
    | ~ c_Complete__Lattice_Ocomplete__lattice(X6,X1,X7,X8,X9,X5,X10,X11,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).

cnf(cls_complete__lattice_OInf__lower_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,hAPP(X2,X3)),X4))
    | ~ hBOOL(c_in(X4,X3,X5))
    | ~ c_Complete__Lattice_Ocomplete__lattice(X2,X6,X1,X7,X8,X9,X10,X11,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).

cnf(cls_complete__lattice_OSup__upper_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),hAPP(X3,X4)))
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ c_Complete__Lattice_Ocomplete__lattice(X6,X3,X1,X7,X8,X9,X10,X11,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).

cnf(cls_complete__lattice_OInf__singleton_0,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X4,X5,X6,X7,X8,X9,X10,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).

cnf(cls_complete__lattice_OSup__singleton_0,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X4,X1,X5,X6,X7,X8,X9,X10,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).

cnf(cls_complete__lattice_OInf__insert_0,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,X3,X4)) = hAPP(hAPP(X5,X2),hAPP(X1,X3))
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X6,X7,X8,X5,X9,X10,X11,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).

cnf(cls_complete__lattice_OSup__insert_0,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,X3,X4)) = hAPP(hAPP(X5,X2),hAPP(X1,X3))
    | ~ c_Complete__Lattice_Ocomplete__lattice(X6,X1,X7,X8,X9,X5,X10,X11,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).

cnf(cls_complete__lattice_OInf__empty_0,axiom,
    ( hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X3
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X4,X5,X6,X7,X8,X9,X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).

cnf(cls_complete__lattice_OSup__empty_0,axiom,
    ( hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X3
    | ~ c_Complete__Lattice_Ocomplete__lattice(X4,X1,X5,X6,X7,X8,X3,X9,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).

cnf(cls_ab__semigroup__mult_Ofold__graph__permute__diff_0,axiom,
    ( c_Finite__Set_Ofold__graph(X1,X2,c_Set_Oinsert(X3,c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X5),X6,X5,X5)
    | hBOOL(c_in(X3,X4,X5))
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X6,X5,X5)
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__graph__permute__diff_0) ).

cnf(cls_Diff1__fold__graph_0,axiom,
    ( c_Finite__Set_Ofold__graph(X1,X2,X3,hAPP(hAPP(X1,X4),X5),X6,X7)
    | ~ hBOOL(c_in(X4,X3,X6))
    | ~ c_Finite__Set_Ofold__graph(X1,X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6),tc_fun(X6,tc_bool)),X5,X6,X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).

cnf(cls_ab__semigroup__mult_Ofold__graph__insert__swap_0,axiom,
    ( c_Finite__Set_Ofold__graph(X1,X2,c_Set_Oinsert(X3,X4,X5),hAPP(hAPP(X1,X2),X6),X5,X5)
    | hBOOL(c_in(X3,X4,X5))
    | ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X6,X5,X5)
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__graph__insert__swap_0) ).

cnf(cls_fold__graph_OinsertI_0,axiom,
    ( c_Finite__Set_Ofold__graph(X1,X2,c_Set_Oinsert(X3,X4,X5),hAPP(hAPP(X1,X3),X6),X5,X7)
    | hBOOL(c_in(X3,X4,X5))
    | ~ c_Finite__Set_Ofold__graph(X1,X2,X4,X6,X5,X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).

cnf(cls_fold1Set_Ointros_0,axiom,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,X3,X4),X4),X5))
    | hBOOL(c_in(X2,X3,X4))
    | ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X5,X4,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set_Ointros_0) ).

cnf(cls_empty__fold__graphE_0,axiom,
    ( X1 = X2
    | ~ c_Finite__Set_Ofold__graph(X3,X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X1,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).

cnf(cls_fold__graph__imp__finite_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofold__graph(X3,X4,X1,X5,X2,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph__imp__finite_0) ).

cnf(cls_fold__graph_OemptyI_0,axiom,
    c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2,X3,X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).

cnf(cls_BodyN_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X5),X1,tc_Hoare__Mirabelle_Otriple(X5)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Option_Othe(hAPP(c_Com_Obody,X3),tc_Com_Ocom),X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_BodyN_0) ).

cnf(cls_image__Int__subset_0,axiom,
    c_lessequals(c_Set_Oimage(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2,X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),c_Set_Oimage(X1,X3,X2,X5)),c_Set_Oimage(X1,X4,X2,X5)),tc_fun(X5,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).

cnf(cls_Un__Int__crazy_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4),tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X2),tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool)))),c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X1,tc_bool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).

cnf(cls_MGF__complete_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(c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,tc_Com_Ostate),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__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,tc_Com_Ostate),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_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(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) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGF__complete_0) ).

cnf(cls_weak__Body_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Option_Othe(hAPP(c_Com_Obody,X3),tc_Com_Ocom),X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_weak__Body_0) ).

cnf(cls_vimage__singleton__eq_0,axiom,
    ( hAPP(X1,X2) = X3
    | ~ hBOOL(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/sandbox2/benchmark/theBenchmark.p',cls_vimage__singleton__eq_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/sandbox2/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).

cnf(cls_map__add__le__mapI_0,axiom,
    ( c_Map_Omap__le(c_Map_Omap__add(X1,X2,X3,X4),X5,X3,X4)
    | ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4)
    | ~ c_Map_Omap__le(X2,X5,X3,X4)
    | ~ c_Map_Omap__le(X1,X5,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__le__mapI_0) ).

cnf(cls_vimage__Int_0,axiom,
    c_Set_Ovimage(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X5,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),c_Set_Ovimage(X1,X3,X5,X2)),c_Set_Ovimage(X1,X4,X5,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Int_0) ).

cnf(cls_vimage__singleton__eq_1,axiom,
    hBOOL(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/sandbox2/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).

cnf(cls_vimageD_0,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),X3,X4))
    | ~ hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageD_0) ).

cnf(cls_vimageE_0,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),X3,X4))
    | ~ hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageE_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/sandbox2/benchmark/theBenchmark.p',cls_vimage__insert_0) ).

cnf(cls_fold1Set__sing_0,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_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/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_0) ).

cnf(cls_map__le__iff__map__add__commute_0,axiom,
    ( c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4)
    | ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__iff__map__add__commute_0) ).

cnf(cls_UN__I_0,axiom,
    ( hBOOL(c_in(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X3,X4,tc_fun(X5,tc_bool)),X5))
    | ~ hBOOL(c_in(X1,hAPP(X3,X6),X5))
    | ~ hBOOL(c_in(X6,X2,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__I_0) ).

cnf(cls_UN__iff_2,axiom,
    ( hBOOL(c_in(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X3,X4,tc_fun(X5,tc_bool)),X5))
    | ~ hBOOL(c_in(X1,hAPP(X3,X6),X5))
    | ~ hBOOL(c_in(X6,X2,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__iff_2) ).

cnf(cls_UN__Un_0,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,X3,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X3,tc_fun(X5,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__Un_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/sandbox2/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).

cnf(cls_map__le__iff__map__add__commute_1,axiom,
    ( c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4)
    | c_Map_Omap__add(X1,X2,X3,X4) != c_Map_Omap__add(X2,X1,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__iff__map__add__commute_1) ).

cnf(cls_map__add__assoc_0,axiom,
    c_Map_Omap__add(X1,c_Map_Omap__add(X2,X3,X4,X5),X4,X5) = c_Map_Omap__add(c_Map_Omap__add(X1,X2,X4,X5),X3,X4,X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__assoc_0) ).

cnf(cls_MGT__BodyN_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(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(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X2)),X1,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Option_Othe(hAPP(c_Com_Obody,X2),tc_Com_Ocom)),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/sandbox2/benchmark/theBenchmark.p',cls_MGT__BodyN_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/sandbox2/benchmark/theBenchmark.p',cls_image__Un_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/sandbox2/benchmark/theBenchmark.p',cls_vimage__Un_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/sandbox2/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).

cnf(cls_SUP1__I_0,axiom,
    ( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X4,tc_bool)),X5))
    | ~ hBOOL(hAPP(hAPP(X2,X6),X5))
    | ~ hBOOL(c_in(X6,X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP1__I_0) ).

cnf(cls_SUP1__iff_2,axiom,
    ( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X4,tc_bool)),X5))
    | ~ hBOOL(hAPP(hAPP(X2,X6),X5))
    | ~ hBOOL(c_in(X6,X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).

cnf(cls_map__add__le__mapE_0,axiom,
    ( c_Map_Omap__le(X1,X2,X3,X4)
    | ~ c_Map_Omap__le(c_Map_Omap__add(X5,X1,X3,X4),X2,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__le__mapE_0) ).

cnf(cls_subset__insert__iff_3,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ hBOOL(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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

cnf(cls_diff__single__insert_0,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ hBOOL(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/sandbox2/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).

cnf(cls_vimageI_0,axiom,
    ( hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4))
    | ~ hBOOL(c_in(hAPP(X2,X1),X3,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageI_0) ).

cnf(cls_vimageI2_0,axiom,
    ( hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4))
    | ~ hBOOL(c_in(hAPP(X2,X1),X3,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageI2_0) ).

cnf(cls_vimage__eq_1,axiom,
    ( hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4))
    | ~ hBOOL(c_in(hAPP(X2,X1),X3,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__eq_1) ).

cnf(cls_Nitpick_OEx1__def_2,axiom,
    hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).

cnf(cls_imageI_0,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).

cnf(cls_image__eqI_0,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__eqI_0) ).

cnf(cls_image__iff_2,axiom,
    ( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
    | ~ hBOOL(c_in(X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__iff_2) ).

cnf(cls_rev__image__eqI_0,axiom,
    ( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
    | ~ hBOOL(c_in(X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

cnf(cls_map__add__comm_0,axiom,
    ( c_Map_Omap__add(X2,X4,X1,X3) = c_Map_Omap__add(X4,X2,X1,X3)
    | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Map_Odom(X2,X1,X3)),c_Map_Odom(X4,X1,X3)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__comm_0) ).

cnf(cls_UN__subset__iff_0,axiom,
    ( c_lessequals(hAPP(X1,X2),X3,tc_fun(X4,tc_bool))
    | ~ hBOOL(c_in(X2,X5,X6))
    | ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X1,X6,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).

cnf(cls_image__subset__iff_0,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),X3,X4))
    | ~ hBOOL(c_in(X2,X5,X6))
    | ~ c_lessequals(c_Set_Oimage(X1,X5,X6,X4),X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_vimage__mono_0) ).

cnf(cls_IntE_0,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_0) ).

cnf(cls_IntE_1,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_1) ).

cnf(cls_Int__assoc_0,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_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))
    | ~ hBOOL(c_in(X2,X1,X3))
    | ~ c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).

cnf(cls_distrib__sup__le_0,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).

cnf(cls_Un__Int__assoc__eq_0,axiom,
    ( c_lessequals(X4,X2,tc_fun(X1,tc_bool))
    | c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).

cnf(cls_finite__UN_0,axiom,
    ( c_Finite__Set_Ofinite(hAPP(X1,X2),X3)
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X1,X5,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UN_0) ).

cnf(cls_Int__Un__distrib2_0,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool))),X4) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4),tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).

cnf(cls_Diff__Int__distrib2_0,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4),tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

cnf(cls_UN__absorb_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X1,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X5,tc_bool))
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__absorb_0) ).

cnf(cls_fold1Set__sing_1,axiom,
    hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).

cnf(cls_IntI_0,axiom,
    ( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2))
    | ~ hBOOL(c_in(X1,X4,X2))
    | ~ hBOOL(c_in(X1,X3,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntI_0) ).

cnf(cls_Int__iff_2,axiom,
    ( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2))
    | ~ hBOOL(c_in(X1,X4,X2))
    | ~ hBOOL(c_in(X1,X3,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__iff_2) ).

cnf(cls_map__add__dom__app__simps_I1_J_0,axiom,
    ( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(X2,X5)
    | ~ hBOOL(c_in(X5,c_Map_Odom(X2,X3,X4),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I1_J_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/sandbox2/benchmark/theBenchmark.p',cls_map__le__trans_0) ).

cnf(cls_UN__insert_0,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X1,X2,X3),X4,X3,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__insert_0) ).

cnf(cls_Diff__Int2_0,axiom,
    c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3),tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int2_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)
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).

cnf(cls_inf1E_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X4),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_0) ).

cnf(cls_inf1E_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X1),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).

cnf(cls_Un__Int__distrib2_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X1,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).

cnf(cls_Un__Int__distrib_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).

cnf(cls_Int__Un__distrib_0,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).

cnf(cls_Diff__Int__distrib_0,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

cnf(cls_Nitpick_OEx1__def_3,axiom,
    ( X1 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
    | ~ hBOOL(hAPP(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).

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/sandbox2/benchmark/theBenchmark.p',cls_finite__surj_0) ).

cnf(cls_map__le__def_0,axiom,
    ( hAPP(X1,X2) = hAPP(X3,X2)
    | ~ hBOOL(c_in(X2,c_Map_Odom(X1,X4,X5),X4))
    | ~ c_Map_Omap__le(X1,X3,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__def_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/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).

cnf(cls_MGF__lemma1_1,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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(c_Hoare__Mirabelle_OMGT(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/sandbox2/benchmark/theBenchmark.p',cls_MGF__lemma1_1) ).

cnf(cls_distrib__inf__le_0,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).

cnf(cls_Int__mono_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X5),tc_fun(X1,tc_bool))
    | ~ c_lessequals(X3,X5,tc_fun(X1,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__mono_0) ).

cnf(cls_UnE_0,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | hBOOL(c_in(X1,X4,X3))
    | ~ hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).

cnf(cls_map__add__SomeD_1,axiom,
    ( hAPP(X1,X5) = c_Option_Ooption_OSome(X6,X4)
    | hAPP(X2,X5) = c_Option_Ooption_OSome(X6,X4)
    | hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) != c_Option_Ooption_OSome(X6,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__SomeD_1) ).

cnf(cls_Int__insert__left_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4) = c_Set_Oinsert(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4),X1)
    | ~ hBOOL(c_in(X2,X4,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

cnf(cls_map__add__SomeD_0,axiom,
    ( hAPP(X2,X5) = c_Option_Ooption_ONone(X4)
    | hAPP(X2,X5) = c_Option_Ooption_OSome(X6,X4)
    | hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) != c_Option_Ooption_OSome(X6,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__SomeD_0) ).

cnf(cls_Int__left__commute_0,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

cnf(cls_map__add__dom__app__simps_I3_J_0,axiom,
    ( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(X1,X5)
    | hBOOL(c_in(X5,c_Map_Odom(X2,X3,X4),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I3_J_0) ).

cnf(cls_map__add__dom__app__simps_I2_J_0,axiom,
    ( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(X2,X5)
    | hBOOL(c_in(X5,c_Map_Odom(X1,X3,X4),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I2_J_0) ).

cnf(cls_singletonE_0,axiom,
    ( X1 = X2
    | ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).

cnf(cls_dom__map__add_0,axiom,
    c_Map_Odom(c_Map_Omap__add(X1,X2,X3,X4),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(X2,X3,X4),c_Map_Odom(X1,X3,X4),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__map__add_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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_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)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool))),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Un_0) ).

cnf(cls_DiffE_1,axiom,
    ( ~ hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).

cnf(cls_map__add__None_1,axiom,
    ( hAPP(X1,X5) = c_Option_Ooption_ONone(X4)
    | hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) != c_Option_Ooption_ONone(X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__None_1) ).

cnf(cls_map__add__None_0,axiom,
    ( hAPP(X2,X5) = c_Option_Ooption_ONone(X4)
    | hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) != c_Option_Ooption_ONone(X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__None_0) ).

cnf(cls_UN__upper_0,axiom,
    ( c_lessequals(hAPP(X1,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__upper_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
    | ~ hBOOL(c_in(X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

cnf(cls_insert__inter__insert_0,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),c_Set_Oinsert(X2,X4,X1)) = c_Set_Oinsert(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

cnf(cls_UN__extend__simps_I1_J_0,axiom,
    c_Set_Oinsert(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X4,tc_bool)),X4) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_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/sandbox2/benchmark/theBenchmark.p',cls_map__le__antisym_0) ).

cnf(cls_Un__Int__assoc__eq_1,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool)))
    | ~ c_lessequals(X4,X2,tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).

cnf(cls_triple_Oinject_0,axiom,
    ( X1 = X5
    | c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,X4) != c_Hoare__Mirabelle_Otriple_Otriple(X5,X6,X7,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).

cnf(cls_triple_Oinject_1,axiom,
    ( X2 = X6
    | c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,X4) != c_Hoare__Mirabelle_Otriple_Otriple(X5,X6,X7,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).

cnf(cls_triple_Oinject_2,axiom,
    ( X3 = X7
    | c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,X4) != c_Hoare__Mirabelle_Otriple_Otriple(X5,X6,X7,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).

cnf(cls_DiffE_0,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_0) ).

cnf(cls_Int__insert__right_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)) = c_Set_Oinsert(X3,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),X1)
    | ~ hBOOL(c_in(X3,X2,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_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/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).

cnf(cls_le__SUPI_0,axiom,
    ( c_lessequals(hAPP(X2,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X2,X5,X1),X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(c_in(X3,X4,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SUPI_0) ).

cnf(cls_Diff__Int_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int_0) ).

cnf(cls_map__le__map__add_0,axiom,
    c_Map_Omap__le(X1,c_Map_Omap__add(X2,X1,X3,X4),X3,X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__map__add_0) ).

cnf(cls_UN__extend__simps_I2_J_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = X4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).

cnf(cls_UN__extend__simps_I3_J_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).

cnf(cls_INT__extend__simps_I4_J_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).

cnf(cls_empty__fold1SetE_0,axiom,
    ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__fold1SetE_0) ).

cnf(cls_DiffI_0,axiom,
    ( hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4))
    | hBOOL(c_in(X1,X3,X4))
    | ~ hBOOL(c_in(X1,X2,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffI_0) ).

cnf(cls_Diff__iff_2,axiom,
    ( hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4))
    | hBOOL(c_in(X1,X3,X4))
    | ~ hBOOL(c_in(X1,X2,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

cnf(cls_inf1I_0,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
    | ~ hBOOL(hAPP(X3,X4))
    | ~ hBOOL(hAPP(X2,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).

cnf(cls_UNION__empty__conv_I2_J_0,axiom,
    ( hAPP(X2,X5) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | ~ hBOOL(c_in(X5,X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).

cnf(cls_UNION__empty__conv_I1_J_0,axiom,
    ( hAPP(X3,X5) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X3,X4,tc_fun(X1,tc_bool))
    | ~ hBOOL(c_in(X5,X2,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_map__le__implies__dom__le_0) ).

cnf(cls_Int__Diff_0,axiom,
    c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Diff_0) ).

cnf(cls_Int__subset__iff_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/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,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).

cnf(cls_MGF__lemma1_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)
    | hBOOL(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/sandbox2/benchmark/theBenchmark.p',cls_MGF__lemma1_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/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_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/sandbox2/benchmark/theBenchmark.p',cls_Diff__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/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

cnf(cls_insertE_0,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | X1 = X4
    | ~ hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).

cnf(cls_disjoint__iff__not__equal_0,axiom,
    ( ~ hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,X4,X3))
    | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).

cnf(cls_Int__insert__left_1,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)
    | hBOOL(c_in(X2,X4,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_0) ).

cnf(cls_Int__subset__iff_2,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).

cnf(cls_Int__greatest_0,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__greatest_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).

cnf(cls_Sup__binary_0,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__binary_0) ).

cnf(cls_conjecture_4,negated_conjecture,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_x)),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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).

cnf(cls_Inf__binary_0,axiom,
    ( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__binary_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_0) ).

cnf(cls_map__add__Some__iff_3,axiom,
    ( hAPP(c_Map_Omap__add(X1,X5,X6,X4),X2) = c_Option_Ooption_OSome(X3,X4)
    | hAPP(X1,X2) != c_Option_Ooption_OSome(X3,X4)
    | hAPP(X5,X2) != c_Option_Ooption_ONone(X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__Some__iff_3) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

cnf(cls_UnCI_1,axiom,
    ( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4))
    | ~ hBOOL(c_in(X1,X2,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).

cnf(cls_UnCI_0,axiom,
    ( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4))
    | ~ hBOOL(c_in(X1,X3,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).

cnf(cls_Int__left__absorb_0,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

cnf(cls_map__add__None_2,axiom,
    ( hAPP(c_Map_Omap__add(X1,X4,X5,X3),X2) = c_Option_Ooption_ONone(X3)
    | hAPP(X1,X2) != c_Option_Ooption_ONone(X3)
    | hAPP(X4,X2) != c_Option_Ooption_ONone(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__None_2) ).

cnf(cls_map__add__Some__iff_2,axiom,
    ( hAPP(c_Map_Omap__add(X5,X1,X6,X4),X2) = c_Option_Ooption_OSome(X3,X4)
    | hAPP(X1,X2) != c_Option_Ooption_OSome(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__Some__iff_2) ).

cnf(cls_map__add__find__right_0,axiom,
    ( hAPP(c_Map_Omap__add(X5,X1,X6,X4),X2) = c_Option_Ooption_OSome(X3,X4)
    | hAPP(X1,X2) != c_Option_Ooption_OSome(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__find__right_0) ).

cnf(cls_domIff_0,axiom,
    ( hAPP(X1,X2) != c_Option_Ooption_ONone(X3)
    | ~ hBOOL(c_in(X2,c_Map_Odom(X1,X4,X3),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domIff_0) ).

cnf(cls_sup__inf__distrib2_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).

cnf(cls_sup__inf__distrib1_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).

cnf(cls_singleton__iff_1,axiom,
    hBOOL(c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

cnf(cls_inf__sup__distrib2_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1)
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib2_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_finite__imageI_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)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2),tc_fun(X3,tc_bool)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__Int_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
    | hBOOL(c_in(X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

cnf(cls_Int__insert__right_1,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)
    | hBOOL(c_in(X3,X2,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

cnf(cls_dom__minus_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X4,X3),c_Set_Oinsert(X2,X5,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X4,X3),X5,tc_fun(X4,tc_bool))
    | hAPP(X1,X2) != c_Option_Ooption_ONone(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__minus_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)
    | hBOOL(c_in(X1,X4,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

cnf(cls_insertCI_0,axiom,
    ( hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4))
    | ~ hBOOL(c_in(X1,X3,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).

cnf(cls_insert__iff_2,axiom,
    ( hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4))
    | ~ hBOOL(c_in(X1,X3,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).

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))
    | ~ hBOOL(c_in(X1,X4,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).

cnf(cls_subset__insert_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | hBOOL(c_in(X4,X1,X3))
    | ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).

cnf(cls_subset__insert__iff_1,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | hBOOL(c_in(X4,X1,X3))
    | ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_double__diff_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/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).

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/sandbox2/benchmark/theBenchmark.p',cls_Un__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/sandbox2/benchmark/theBenchmark.p',cls_Un__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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

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))
    | ~ hBOOL(c_in(X1,X4,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

cnf(cls_inf__fun__eq_0,axiom,
    ( hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).

cnf(cls_inf__sup__distrib1_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),X1)
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).

cnf(cls_inf__sup__aci_I2_J_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

cnf(cls_inf__assoc_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

cnf(cls_subset__insert_1,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | hBOOL(c_in(X2,X1,X4))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/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))
    | hBOOL(c_in(X2,X1,X4))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

cnf(cls_insert__code_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | X3 = X2
    | ~ hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_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/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).

cnf(cls_set__mp_0,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,X4,X3))
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).

cnf(cls_subsetD_0,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,X4,X3))
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).

cnf(cls_set__rev__mp_0,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
    | ~ hBOOL(c_in(X1,X4,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

cnf(cls_subset__iff_0,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,X4,X3))
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).

cnf(cls_insert__subset_0,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).

cnf(cls_insert__ident_0,axiom,
    ( hBOOL(c_in(X1,X4,X3))
    | hBOOL(c_in(X1,X2,X3))
    | X2 = X4
    | c_Set_Oinsert(X1,X2,X3) != c_Set_Oinsert(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

cnf(cls_bex__empty_0,axiom,
    ( ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_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(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/sandbox2/benchmark/theBenchmark.p',cls_MGF_0) ).

cnf(cls_domI_0,axiom,
    ( hBOOL(c_in(X2,c_Map_Odom(X1,X5,X4),X5))
    | hAPP(X1,X2) != c_Option_Ooption_OSome(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domI_0) ).

cnf(cls_ball__empty_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_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/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).

cnf(cls_Int__lower1_0,axiom,
    c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X2,tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

cnf(cls_Int__lower2_0,axiom,
    c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X3,tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Diff__partition_0) ).

cnf(cls_Diff__triv_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool)) = X2
    | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__triv_0) ).

cnf(cls_domIff_1,axiom,
    ( hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3))
    | hAPP(X2,X1) = c_Option_Ooption_ONone(X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domIff_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/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_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/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_sup__least_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/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

cnf(cls_emptyE_0,axiom,
    ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).

cnf(cls_empty__iff_0,axiom,
    ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).

cnf(cls_ex__in__conv_0,axiom,
    ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

cnf(cls_le__infI_0,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI_0) ).

cnf(cls_le__inf__iff_2,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).

cnf(cls_inf__greatest_0,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__greatest_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/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

cnf(cls_ab__semigroup__mult_Omult__ac_I1_J_0,axiom,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4) = hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4))
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__ac_I1_J_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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_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/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_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/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_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/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_image__empty_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/sandbox2/benchmark/theBenchmark.p',cls_vimage__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/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).

cnf(cls_insertCI_1,axiom,
    hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).

cnf(cls_insertI1_0,axiom,
    hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).

cnf(cls_insert__iff_1,axiom,
    hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).

cnf(cls_Diff__disjoint_0,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__disjoint_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/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).

cnf(cls_finite__Int_0,axiom,
    ( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_0) ).

cnf(cls_finite__Int_1,axiom,
    ( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1)
    | ~ c_Finite__Set_Ofinite(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_1) ).

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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_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/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

cnf(cls_inf__sup__aci_I3_J_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

cnf(cls_inf__left__commute_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

cnf(cls_le__inf__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1) ),
    file('/export/starexec/sandbox2/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,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1) ),
    file('/export/starexec/sandbox2/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,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X3),X1) ),
    file('/export/starexec/sandbox2/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,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X3),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_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/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_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/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_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/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_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/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

cnf(cls_conjecture_3,negated_conjecture,
    hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

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/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).

cnf(cls_insert__code_2,axiom,
    ( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
    | ~ hBOOL(hAPP(X2,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).

cnf(cls_Int__commute_0,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Min__antimono_0) ).

cnf(cls_Min__le_0,axiom,
    ( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X1),X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(c_in(X3,X2,X1))
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    file('/export/starexec/sandbox2/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)
    | ~ hBOOL(c_in(X2,X3,X1))
    | ~ c_Finite__Set_Ofinite(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__ge_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_1) ).

cnf(cls_Int__empty__left_0,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

cnf(cls_sup__fun__eq_0,axiom,
    ( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(t_a,X1)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X2,v_x),hAPP(X3,v_x),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).

cnf(cls_fun__diff__def_0,axiom,
    ( hAPP(c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(t_a,X1)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X2,v_x),hAPP(X3,v_x),X1)
    | ~ class_HOL_Ominus(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).

cnf(cls_Int__absorb2_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = X2
    | ~ c_lessequals(X2,X3,tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).

cnf(cls_Int__absorb1_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = X3
    | ~ c_lessequals(X3,X2,tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

cnf(cls_Inf__lower_0,axiom,
    ( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,X1),X3,X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(c_in(X3,X2,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__lower_0) ).

cnf(cls_Sup__upper_0,axiom,
    ( c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(c_in(X2,X3,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__upper_0) ).

cnf(cls_ab__semigroup__mult_Ononempty__iff_2,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | ~ c_OrderedGroup_Oab__semigroup__mult(X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ononempty__iff_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_insert__dom_0) ).

cnf(cls_ab__semigroup__mult_Omult__left__commute_0,axiom,
    ( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X2),X4))
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__left__commute_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).

cnf(cls_le__infI1_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI1_0) ).

cnf(cls_le__infI2_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).

cnf(cls_map__le__refl_0,axiom,
    c_Map_Omap__le(X1,X1,X2,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__refl_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/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).

cnf(cls_insert__code_1,axiom,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).

cnf(cls_comm__monoid__add_Ononempty__iff_2,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_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/sandbox2/benchmark/theBenchmark.p',cls_Min__singleton_0) ).

cnf(cls_Sup__singleton_0,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).

cnf(cls_Inf__singleton_0,axiom,
    ( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).

cnf(cls_insert__absorb_0,axiom,
    ( c_Set_Oinsert(X1,X2,X3) = X2
    | ~ hBOOL(c_in(X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_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/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_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/sandbox2/benchmark/theBenchmark.p',cls_cut_0) ).

cnf(cls_contents__eq_0,axiom,
    c_Set_Ocontents(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_contents__eq_0) ).

cnf(cls_Nitpick_OThe__psimp_0,axiom,
    c_The(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OThe__psimp_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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

cnf(cls_Int__empty__right_0,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).

cnf(cls_Min__in_0,axiom,
    ( hBOOL(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/sandbox2/benchmark/theBenchmark.p',cls_Min__in_0) ).

cnf(cls_Max__in_0,axiom,
    ( hBOOL(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/sandbox2/benchmark/theBenchmark.p',cls_Max__in_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/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

cnf(cls_inf__sup__aci_I4_J_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

cnf(cls_inf__left__idem_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_finite__UnI_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).

cnf(cls_bot1E_0,axiom,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).

cnf(cls_Sup__insert_0,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__insert_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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).

cnf(cls_Inf__insert_0,axiom,
    ( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X2,X3,X1),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,X1))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__insert_0) ).

cnf(cls_mem__def_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_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/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_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/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff_0) ).

cnf(cls_WTs__elim__cases_I8_J_0,axiom,
    ( c_Com_OWT(c_Com_Ocom_OBODY(X1))
    | ~ c_Com_OWT(c_Com_Ocom_OCall(X2,X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I8_J_0) ).

cnf(cls_subset__insertI_0,axiom,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_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/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_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/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

cnf(cls_com_Osimps_I7_J_0,axiom,
    ( X1 = X4
    | c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OCall(X4,X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_0) ).

cnf(cls_com_Osimps_I7_J_1,axiom,
    ( X2 = X5
    | c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OCall(X4,X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_1) ).

cnf(cls_com_Osimps_I7_J_2,axiom,
    ( X3 = X6
    | c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OCall(X4,X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_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/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_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/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_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/sandbox2/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).

cnf(cls_inf__sup__absorb_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) = X2
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

cnf(cls_sup__inf__absorb_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X1) = X2
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

cnf(cls_inf__sup__ord_I1_J_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

cnf(cls_inf__le1_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).

cnf(cls_inf__sup__ord_I2_J_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

cnf(cls_inf__le2_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_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/sandbox2/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_finite__subset_0) ).

cnf(cls_mem__def_1,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

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

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/sandbox2/benchmark/theBenchmark.p',cls_Un__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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

cnf(cls_le__iff__inf_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

cnf(cls_inf__absorb2_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X3
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

cnf(cls_le__iff__inf_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

cnf(cls_Int__absorb_0,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X2) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).

cnf(cls_hoare__sound_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__sound_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_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/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_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/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

cnf(cls_WT_OCall_0,axiom,
    ( c_Com_OWT(c_Com_Ocom_OCall(X1,X2,X3))
    | ~ c_Com_OWT(c_Com_Ocom_OBODY(X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OCall_0) ).

cnf(cls_linorder__linear_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_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/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).

cnf(cls_inf__sup__aci_I1_J_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

cnf(cls_inf__commute_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_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/sandbox2/benchmark/theBenchmark.p',cls_finite__dom__body_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/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

cnf(cls_ab__semigroup__mult_Omult__commute_0,axiom,
    ( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X3),X2)
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__commute_0) ).

cnf(cls_com_Osimps_I63_J_0,axiom,
    c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OBODY(X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I63_J_0) ).

cnf(cls_com_Osimps_I62_J_0,axiom,
    c_Com_Ocom_OBODY(X1) != c_Com_Ocom_OCall(X2,X3,X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I62_J_0) ).

cnf(cls_Un__absorb_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

cnf(cls_subset__refl_0,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).

cnf(cls_equalityE_0,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).

cnf(cls_Sup__empty_0,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__empty_0) ).

cnf(cls_inf__bot__left_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

cnf(cls_bot__fun__eq_0,axiom,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Orderings_Obot(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

cnf(cls_inf__bot__right_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__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/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__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/sandbox2/benchmark/theBenchmark.p',cls_bot__least_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).

cnf(cls_order__eq__refl_0,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Opreorder(X1) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

cnf(cls_inf__idem_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).

cnf(cls_option_Oinject_0,axiom,
    ( X1 = X3
    | c_Option_Ooption_OSome(X1,X2) != c_Option_Ooption_OSome(X3,X2) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).

cnf(cls_the_Osimps_0,axiom,
    c_Option_Othe(c_Option_Ooption_OSome(X1,X2),X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the_Osimps_0) ).

cnf(clsarity_fun__Orderings_Opreorder,axiom,
    ( class_Orderings_Opreorder(tc_fun(X1,X2))
    | ~ class_Orderings_Opreorder(X2) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

cnf(clsarity_fun__Lattices_Obounded__lattice,axiom,
    ( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
    | ~ class_Lattices_Obounded__lattice(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

cnf(clsarity_fun__Orderings_Oorder,axiom,
    ( class_Orderings_Oorder(tc_fun(X1,X2))
    | ~ class_Orderings_Oorder(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

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/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).

cnf(clsarity_fun__Lattices_Odistrib__lattice,axiom,
    ( class_Lattices_Odistrib__lattice(tc_fun(X1,X2))
    | ~ class_Lattices_Odistrib__lattice(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).

cnf(clsarity_fun__HOL_Oord,axiom,
    ( class_HOL_Oord(tc_fun(X1,X2))
    | ~ class_HOL_Oord(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

cnf(clsarity_fun__Lattices_Olattice,axiom,
    ( class_Lattices_Olattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

cnf(clsarity_fun__Lattices_Oupper__semilattice,axiom,
    ( class_Lattices_Oupper__semilattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

cnf(clsarity_fun__HOL_Ominus,axiom,
    ( class_HOL_Ominus(tc_fun(X1,X2))
    | ~ class_HOL_Ominus(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).

cnf(cls_not__None__eq_1,axiom,
    c_Option_Ooption_OSome(X1,X2) != c_Option_Ooption_ONone(X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__None__eq_1) ).

cnf(cls_option_Osimps_I3_J_0,axiom,
    c_Option_Ooption_OSome(X1,X2) != c_Option_Ooption_ONone(X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).

cnf(cls_not__Some__eq_1,axiom,
    c_Option_Ooption_ONone(X1) != c_Option_Ooption_OSome(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).

cnf(cls_option_Osimps_I2_J_0,axiom,
    c_Option_Ooption_ONone(X1) != c_Option_Ooption_OSome(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).

cnf(cls_WT_OBody_0,axiom,
    ( c_Com_OWT(c_Com_Ocom_OBODY(X1))
    | hAPP(c_Com_Obody,X1) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OBody_0) ).

cnf(cls_finite_0,axiom,
    ( c_Finite__Set_Ofinite(X2,X1)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_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/sandbox2/benchmark/theBenchmark.p',clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite) ).

cnf(cls_com_Osimps_I6_J_0,axiom,
    ( X1 = X2
    | c_Com_Ocom_OBODY(X1) != c_Com_Ocom_OBODY(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).

cnf(cls_state__not__singleton__def_1,axiom,
    ( c_Hoare__Mirabelle_Ostate__not__singleton
    | X1 = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_state__not__singleton__def_1) ).

cnf(cls_conjecture_2,negated_conjecture,
    c_Com_OWT(v_c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

cnf(clsarity_nat__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

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

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

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

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

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

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

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

cnf(clsarity_nat__Lattices_Odistrib__lattice,axiom,
    class_Lattices_Odistrib__lattice(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).

cnf(clsarity_bool__Lattices_Odistrib__lattice,axiom,
    class_Lattices_Odistrib__lattice(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).

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

cnf(clsarity_nat__HOL_Oord,axiom,
    class_HOL_Oord(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

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

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

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

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

cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom,
    class_Lattices_Oupper__semilattice(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

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

cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
    class_Lattices_Olower__semilattice(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).

cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

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

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

cnf(cls_conjecture_0,negated_conjecture,
    c_Hoare__Mirabelle_Ostate__not__singleton,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_conjecture_1,negated_conjecture,
    c_Com_OWT__bodies,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(i_0_486,axiom,
    c_Collect(c_fequal(X1,X2),X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    cls_singleton__conv2_0 ).

cnf(i_0_487,axiom,
    c_Collect(X1,X2) = X1,
    cls_Collect__def_0 ).

cnf(i_0_488,axiom,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | c_Finite__Set_Ofold1(X4,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool)),X1) = hAPP(hAPP(X4,c_Finite__Set_Ofold1(X4,X2,X1)),c_Finite__Set_Ofold1(X4,X3,X1))
    | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | ~ c_Finite__Set_Ofinite(X2,X1)
    | ~ c_OrderedGroup_Oab__semigroup__mult(X4,X1) ),
    cls_ab__semigroup__mult_Ofold1__Un_0 ).

cnf(i_0_489,axiom,
    c_Finite__Set_Ofold1(X1,X2,X3) = c_The(c_Finite__Set_Ofold1Set(X1,X2,X3),X3),
    cls_fold1__def_0 ).

cnf(i_0_490,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Collect(X4,X3)),X3)) ),
    cls_Int__Collect_0 ).

cnf(i_0_491,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),c_Collect(X1,X3)),X3)) ),
    cls_Int__Collect_1 ).

cnf(i_0_492,axiom,
    ( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Collect(X4,X2)),X2))
    | ~ hBOOL(hAPP(X4,X1))
    | ~ hBOOL(c_in(X1,X3,X2)) ),
    cls_Int__Collect_2 ).

cnf(i_0_493,axiom,
    ( c_Finite__Set_Ofold1(X1,c_Set_Oinsert(X2,X3,X4),X4) = hAPP(hAPP(X1,X2),c_Finite__Set_Ofold1(X1,X3,X4))
    | hBOOL(c_in(X2,X3,X4))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X4)
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4) ),
    cls_ab__semigroup__mult_Ofold1__insert_0 ).

cnf(i_0_494,axiom,
    ( c_lessequals(X2,X3,X1)
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ hBOOL(c_in(X3,X4,X1))
    | ~ c_lessequals(X2,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X1),X4,X1),X1)
    | ~ c_Finite__Set_Ofinite(X4,X1) ),
    cls_below__fold1__iff_0 ).

cnf(i_0_495,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(c_fequal(X1,X3),X2)) ),
    cls_ATP__Linkup_Ofequal__imp__equal_0 ).

cnf(i_0_496,plain,
    c_fequal(X1,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    inference(rw,[status(thm)],[i_0_486,c_0_487]) ).

cnf(i_0_497,axiom,
    c_Finite__Set_Ofold1(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X2,
    cls_fold1__singleton_0 ).

cnf(i_0_498,axiom,
    ( c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X1),X2,X1),X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ hBOOL(c_in(X3,X2,X1))
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    cls_fold1__belowI_0 ).

cnf(i_0_499,axiom,
    hBOOL(hAPP(c_fequal(X1,X2),X1)),
    cls_ATP__Linkup_Oequal__imp__fequal_0 ).

cnf(i_0_500,axiom,
    c_The(c_fequal(X1,X2),X2) = X1,
    cls_the__sym__eq__trivial_0 ).

cnf(i_0_501,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,c_Collect(X1,X3),X3)) ),
    cls_CollectD_0 ).

cnf(i_0_502,axiom,
    ( hBOOL(c_in(X1,c_Collect(X2,X3),X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    cls_CollectI_0 ).

cnf(i_0_503,axiom,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Collect(X2,X1)
    | ~ hBOOL(hAPP(X2,X3)) ),
    cls_empty__Collect__eq_0 ).

cnf(i_0_504,axiom,
    ( c_Collect(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ hBOOL(hAPP(X1,X3)) ),
    cls_Collect__empty__eq_0 ).

cnf(i_0_505,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)) = hAPP(hAPP(X5,X2),X3)
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X6,X7,X8,X5,X9,X10,X11,X4) ),
    cls_complete__lattice_OInf__binary_0,
    [final] ).

cnf(i_0_506,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)) = hAPP(hAPP(X5,X2),X3)
    | ~ c_Complete__Lattice_Ocomplete__lattice(X6,X1,X7,X8,X9,X5,X10,X11,X4) ),
    cls_complete__lattice_OSup__binary_0,
    [final] ).

cnf(i_0_507,axiom,
    ( hBOOL(hAPP(hAPP(X1,hAPP(X2,X3)),X4))
    | ~ hBOOL(c_in(X4,X3,X5))
    | ~ c_Complete__Lattice_Ocomplete__lattice(X2,X6,X1,X7,X8,X9,X10,X11,X5) ),
    cls_complete__lattice_OInf__lower_0,
    [final] ).

cnf(i_0_508,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),hAPP(X3,X4)))
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ c_Complete__Lattice_Ocomplete__lattice(X6,X3,X1,X7,X8,X9,X10,X11,X5) ),
    cls_complete__lattice_OSup__upper_0,
    [final] ).

cnf(i_0_509,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X4,X5,X6,X7,X8,X9,X10,X3) ),
    cls_complete__lattice_OInf__singleton_0,
    [final] ).

cnf(i_0_510,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X4,X1,X5,X6,X7,X8,X9,X10,X3) ),
    cls_complete__lattice_OSup__singleton_0,
    [final] ).

cnf(i_0_511,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,X3,X4)) = hAPP(hAPP(X5,X2),hAPP(X1,X3))
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X6,X7,X8,X5,X9,X10,X11,X4) ),
    cls_complete__lattice_OInf__insert_0,
    [final] ).

cnf(i_0_512,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,X3,X4)) = hAPP(hAPP(X5,X2),hAPP(X1,X3))
    | ~ c_Complete__Lattice_Ocomplete__lattice(X6,X1,X7,X8,X9,X5,X10,X11,X4) ),
    cls_complete__lattice_OSup__insert_0,
    [final] ).

cnf(i_0_513,axiom,
    ( hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X3
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X4,X5,X6,X7,X8,X9,X3,X2) ),
    cls_complete__lattice_OInf__empty_0,
    [final] ).

cnf(i_0_514,axiom,
    ( hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X3
    | ~ c_Complete__Lattice_Ocomplete__lattice(X4,X1,X5,X6,X7,X8,X3,X9,X2) ),
    cls_complete__lattice_OSup__empty_0,
    [final] ).

cnf(i_0_515,axiom,
    ( c_Finite__Set_Ofold__graph(X1,X2,c_Set_Oinsert(X3,c_HOL_Ominus__class_Ominus(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X5),X6,X5,X5)
    | hBOOL(c_in(X3,X4,X5))
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X6,X5,X5)
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
    cls_ab__semigroup__mult_Ofold__graph__permute__diff_0,
    [final] ).

cnf(i_0_516,axiom,
    ( c_Finite__Set_Ofold__graph(X1,X2,X3,hAPP(hAPP(X1,X4),X5),X6,X7)
    | ~ hBOOL(c_in(X4,X3,X6))
    | ~ c_Finite__Set_Ofold__graph(X1,X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6),tc_fun(X6,tc_bool)),X5,X6,X7) ),
    cls_Diff1__fold__graph_0,
    [final] ).

cnf(i_0_517,axiom,
    ( c_Finite__Set_Ofold__graph(X1,X2,c_Set_Oinsert(X3,X4,X5),hAPP(hAPP(X1,X2),X6),X5,X5)
    | hBOOL(c_in(X3,X4,X5))
    | ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X6,X5,X5)
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
    cls_ab__semigroup__mult_Ofold__graph__insert__swap_0,
    [final] ).

cnf(i_0_518,axiom,
    ( c_Finite__Set_Ofold__graph(X1,X2,c_Set_Oinsert(X3,X4,X5),hAPP(hAPP(X1,X3),X6),X5,X7)
    | hBOOL(c_in(X3,X4,X5))
    | ~ c_Finite__Set_Ofold__graph(X1,X2,X4,X6,X5,X7) ),
    cls_fold__graph_OinsertI_0,
    [final] ).

cnf(i_0_519,axiom,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,X3,X4),X4),X5))
    | hBOOL(c_in(X2,X3,X4))
    | ~ c_Finite__Set_Ofold__graph(X1,X2,X3,X5,X4,X4) ),
    cls_fold1Set_Ointros_0,
    [final] ).

cnf(i_0_520,axiom,
    ( X1 = X2
    | ~ c_Finite__Set_Ofold__graph(X3,X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X1,X4,X5) ),
    cls_empty__fold__graphE_0,
    [final] ).

cnf(i_0_521,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofold__graph(X3,X4,X1,X5,X2,X6) ),
    cls_fold__graph__imp__finite_0,
    [final] ).

cnf(i_0_522,axiom,
    c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2,X3,X4),
    cls_fold__graph_OemptyI_0,
    [final] ).

cnf(i_0_523,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X5),X1,tc_Hoare__Mirabelle_Otriple(X5)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Option_Othe(hAPP(c_Com_Obody,X3),tc_Com_Ocom),X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5) ),
    cls_BodyN_0,
    [final] ).

cnf(i_0_524,axiom,
    c_lessequals(c_Set_Oimage(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2,X5),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),c_Set_Oimage(X1,X3,X2,X5)),c_Set_Oimage(X1,X4,X2,X5)),tc_fun(X5,tc_bool)),
    cls_image__Int__subset_0,
    [final] ).

cnf(i_0_525,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4),tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X2),tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool)))),c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X1,tc_bool))),
    cls_Un__Int__crazy_0,
    [final] ).

cnf(i_0_526,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(c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,tc_Com_Ostate),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__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,tc_Com_Ostate),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_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(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) ),
    cls_MGF__complete_0,
    [final] ).

cnf(i_0_527,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Option_Othe(hAPP(c_Com_Obody,X3),tc_Com_Ocom),X4,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_bool)),tc_Hoare__Mirabelle_Otriple(X5)),X5) ),
    cls_weak__Body_0,
    [final] ).

cnf(i_0_528,axiom,
    ( hAPP(X1,X2) = X3
    | ~ hBOOL(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_529,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_530,axiom,
    ( c_Map_Omap__le(c_Map_Omap__add(X1,X2,X3,X4),X5,X3,X4)
    | ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4)
    | ~ c_Map_Omap__le(X2,X5,X3,X4)
    | ~ c_Map_Omap__le(X1,X5,X3,X4) ),
    cls_map__add__le__mapI_0,
    [final] ).

cnf(i_0_531,axiom,
    c_Set_Ovimage(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X5,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),c_Set_Ovimage(X1,X3,X5,X2)),c_Set_Ovimage(X1,X4,X5,X2)),
    cls_vimage__Int_0,
    [final] ).

cnf(i_0_532,axiom,
    hBOOL(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_533,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),X3,X4))
    | ~ hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)) ),
    cls_vimageD_0,
    [final] ).

cnf(i_0_534,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),X3,X4))
    | ~ hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)) ),
    cls_vimageE_0,
    [final] ).

cnf(i_0_535,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_536,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4),X2)) ),
    cls_fold1Set__sing_0,
    [final] ).

cnf(i_0_537,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_538,axiom,
    ( c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4)
    | ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4) ),
    cls_map__le__iff__map__add__commute_0,
    [final] ).

cnf(i_0_539,axiom,
    ( hBOOL(c_in(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X3,X4,tc_fun(X5,tc_bool)),X5))
    | ~ hBOOL(c_in(X1,hAPP(X3,X6),X5))
    | ~ hBOOL(c_in(X6,X2,X4)) ),
    cls_UN__I_0,
    [final] ).

cnf(i_0_540,axiom,
    ( hBOOL(c_in(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X3,X4,tc_fun(X5,tc_bool)),X5))
    | ~ hBOOL(c_in(X1,hAPP(X3,X6),X5))
    | ~ hBOOL(c_in(X6,X2,X4)) ),
    cls_UN__iff_2,
    [final] ).

cnf(i_0_541,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | c_The(c_Finite__Set_Ofold1Set(X4,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool)),X1),X1) = hAPP(hAPP(X4,c_The(c_Finite__Set_Ofold1Set(X4,X2,X1),X1)),c_The(c_Finite__Set_Ofold1Set(X4,X3,X1),X1))
    | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | ~ c_Finite__Set_Ofinite(X2,X1)
    | ~ c_OrderedGroup_Oab__semigroup__mult(X4,X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_488,c_0_489]),c_0_489]),c_0_489]),
    [final] ).

cnf(i_0_542,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,X3,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X3,tc_fun(X5,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
    cls_UN__Un_0,
    [final] ).

cnf(i_0_543,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_544,axiom,
    ( c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4)
    | c_Map_Omap__add(X1,X2,X3,X4) != c_Map_Omap__add(X2,X1,X3,X4) ),
    cls_map__le__iff__map__add__commute_1,
    [final] ).

cnf(i_0_545,axiom,
    c_Map_Omap__add(X1,c_Map_Omap__add(X2,X3,X4,X5),X4,X5) = c_Map_Omap__add(c_Map_Omap__add(X1,X2,X4,X5),X3,X4,X5),
    cls_map__add__assoc_0,
    [final] ).

cnf(i_0_546,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(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(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X2)),X1,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Option_Othe(hAPP(c_Com_Obody,X2),tc_Com_Ocom)),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_547,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_548,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_549,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_550,axiom,
    ( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X4,tc_bool)),X5))
    | ~ hBOOL(hAPP(hAPP(X2,X6),X5))
    | ~ hBOOL(c_in(X6,X1,X3)) ),
    cls_SUP1__I_0,
    [final] ).

cnf(i_0_551,axiom,
    ( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X4,tc_bool)),X5))
    | ~ hBOOL(hAPP(hAPP(X2,X6),X5))
    | ~ hBOOL(c_in(X6,X1,X3)) ),
    cls_SUP1__iff_2,
    [final] ).

cnf(i_0_552,axiom,
    ( c_Map_Omap__le(X1,X2,X3,X4)
    | ~ c_Map_Omap__le(c_Map_Omap__add(X5,X1,X3,X4),X2,X3,X4) ),
    cls_map__add__le__mapE_0,
    [final] ).

cnf(i_0_553,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ hBOOL(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_554,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ hBOOL(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_555,axiom,
    ( hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4))
    | ~ hBOOL(c_in(hAPP(X2,X1),X3,X5)) ),
    cls_vimageI_0,
    [final] ).

cnf(i_0_556,axiom,
    ( hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4))
    | ~ hBOOL(c_in(hAPP(X2,X1),X3,X5)) ),
    cls_vimageI2_0,
    [final] ).

cnf(i_0_557,axiom,
    ( hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4))
    | ~ hBOOL(c_in(hAPP(X2,X1),X3,X5)) ),
    cls_vimage__eq_1,
    [final] ).

cnf(i_0_558,axiom,
    hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2))),
    cls_Nitpick_OEx1__def_2,
    [final] ).

cnf(i_0_559,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_560,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    cls_imageI_0,
    [final] ).

cnf(i_0_561,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    cls_image__eqI_0,
    [final] ).

cnf(i_0_562,axiom,
    ( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
    | ~ hBOOL(c_in(X1,X2,X3)) ),
    cls_image__iff_2,
    [final] ).

cnf(i_0_563,axiom,
    ( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
    | ~ hBOOL(c_in(X1,X2,X3)) ),
    cls_rev__image__eqI_0,
    [final] ).

cnf(i_0_564,axiom,
    ( c_Map_Omap__add(X2,X4,X1,X3) = c_Map_Omap__add(X4,X2,X1,X3)
    | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Map_Odom(X2,X1,X3)),c_Map_Odom(X4,X1,X3)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
    cls_map__add__comm_0,
    [final] ).

cnf(i_0_565,axiom,
    ( c_lessequals(hAPP(X1,X2),X3,tc_fun(X4,tc_bool))
    | ~ hBOOL(c_in(X2,X5,X6))
    | ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X1,X6,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    cls_UN__subset__iff_0,
    [final] ).

cnf(i_0_566,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),X3,X4))
    | ~ hBOOL(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_567,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_568,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_569,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_570,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3)) ),
    cls_IntE_0,
    [final] ).

cnf(i_0_571,plain,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3)) ),
    inference(rw,[status(thm)],[i_0_490,c_0_487]),
    [final] ).

cnf(i_0_572,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2),X3)) ),
    cls_IntE_1,
    [final] ).

cnf(i_0_573,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_574,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
    cls_Int__assoc_0,
    [final] ).

cnf(i_0_575,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))
    | ~ hBOOL(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_576,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_distrib__sup__le_0,
    [final] ).

cnf(i_0_577,axiom,
    ( c_lessequals(X4,X2,tc_fun(X1,tc_bool))
    | c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))) ),
    cls_Un__Int__assoc__eq_0,
    [final] ).

cnf(i_0_578,axiom,
    ( c_Finite__Set_Ofinite(hAPP(X1,X2),X3)
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X1,X5,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X4,X5) ),
    cls_finite__UN_0,
    [final] ).

cnf(i_0_579,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X1),X3)) ),
    inference(rw,[status(thm)],[i_0_491,c_0_487]),
    [final] ).

cnf(i_0_580,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool))),X4) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4),tc_fun(X1,tc_bool)),
    cls_Int__Un__distrib2_0,
    [final] ).

cnf(i_0_581,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4),tc_fun(X1,tc_bool)),
    cls_Diff__Int__distrib2_0,
    [final] ).

cnf(i_0_582,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X1,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X5,tc_bool))
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    cls_UN__absorb_0,
    [final] ).

cnf(i_0_583,axiom,
    hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X2)),
    cls_fold1Set__sing_1,
    [final] ).

cnf(i_0_584,axiom,
    ( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2))
    | ~ hBOOL(c_in(X1,X4,X2))
    | ~ hBOOL(c_in(X1,X3,X2)) ),
    cls_IntI_0,
    [final] ).

cnf(i_0_585,axiom,
    ( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2))
    | ~ hBOOL(c_in(X1,X4,X2))
    | ~ hBOOL(c_in(X1,X3,X2)) ),
    cls_Int__iff_2,
    [final] ).

cnf(i_0_586,axiom,
    ( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(X2,X5)
    | ~ hBOOL(c_in(X5,c_Map_Odom(X2,X3,X4),X3)) ),
    cls_map__add__dom__app__simps_I1_J_0,
    [final] ).

cnf(i_0_587,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_588,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X1,X2,X3),X4,X3,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
    cls_UN__insert_0,
    [final] ).

cnf(i_0_589,axiom,
    c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3),tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)),
    cls_Diff__Int2_0,
    [final] ).

cnf(i_0_590,axiom,
    ( c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) = c_Set_Oimage(X1,X3,X4,X5)
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    cls_insert__image_0,
    [final] ).

cnf(i_0_591,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X4),X2)) ),
    cls_inf1E_0,
    [final] ).

cnf(i_0_592,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X1),X2)) ),
    cls_inf1E_1,
    [final] ).

cnf(i_0_593,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X1,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))),
    cls_Un__Int__distrib2_0,
    [final] ).

cnf(i_0_594,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X2,tc_bool))),
    cls_Un__Int__distrib_0,
    [final] ).

cnf(i_0_595,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),tc_fun(X1,tc_bool)),
    cls_Int__Un__distrib_0,
    [final] ).

cnf(i_0_596,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),tc_fun(X1,tc_bool)),
    cls_Diff__Int__distrib_0,
    [final] ).

cnf(i_0_597,axiom,
    ( X1 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
    | ~ hBOOL(hAPP(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X1)) ),
    cls_Nitpick_OEx1__def_3,
    [final] ).

cnf(i_0_598,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_599,axiom,
    ( hAPP(X1,X2) = hAPP(X3,X2)
    | ~ hBOOL(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_600,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_601,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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(c_Hoare__Mirabelle_OMGT(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_602,plain,
    ( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2))
    | ~ hBOOL(hAPP(X4,X1))
    | ~ hBOOL(c_in(X1,X3,X2)) ),
    inference(rw,[status(thm)],[i_0_492,c_0_487]),
    [final] ).

cnf(i_0_603,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_distrib__inf__le_0,
    [final] ).

cnf(i_0_604,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X5),tc_fun(X1,tc_bool))
    | ~ c_lessequals(X3,X5,tc_fun(X1,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X1,tc_bool)) ),
    cls_Int__mono_0,
    [final] ).

cnf(i_0_605,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | hBOOL(c_in(X1,X4,X3))
    | ~ hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3)) ),
    cls_UnE_0,
    [final] ).

cnf(i_0_606,axiom,
    ( hAPP(X1,X5) = c_Option_Ooption_OSome(X6,X4)
    | hAPP(X2,X5) = c_Option_Ooption_OSome(X6,X4)
    | hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) != c_Option_Ooption_OSome(X6,X4) ),
    cls_map__add__SomeD_1,
    [final] ).

cnf(i_0_607,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4) = c_Set_Oinsert(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4),X1)
    | ~ hBOOL(c_in(X2,X4,X1)) ),
    cls_Int__insert__left_0,
    [final] ).

cnf(i_0_608,axiom,
    ( hAPP(X2,X5) = c_Option_Ooption_ONone(X4)
    | hAPP(X2,X5) = c_Option_Ooption_OSome(X6,X4)
    | hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) != c_Option_Ooption_OSome(X6,X4) ),
    cls_map__add__SomeD_0,
    [final] ).

cnf(i_0_609,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),
    cls_Int__left__commute_0,
    [final] ).

cnf(i_0_610,axiom,
    ( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(X1,X5)
    | hBOOL(c_in(X5,c_Map_Odom(X2,X3,X4),X3)) ),
    cls_map__add__dom__app__simps_I3_J_0,
    [final] ).

cnf(i_0_611,axiom,
    ( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(X2,X5)
    | hBOOL(c_in(X5,c_Map_Odom(X1,X3,X4),X3)) ),
    cls_map__add__dom__app__simps_I2_J_0,
    [final] ).

cnf(i_0_612,axiom,
    ( X1 = X2
    | ~ hBOOL(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_613,axiom,
    c_Map_Odom(c_Map_Omap__add(X1,X2,X3,X4),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(X2,X3,X4),c_Map_Odom(X1,X3,X4),tc_fun(X3,tc_bool)),
    cls_dom__map__add_0,
    [final] ).

cnf(i_0_614,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_615,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_616,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_617,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_618,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_619,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)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool))),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool))),
    cls_Diff__Un_0,
    [final] ).

cnf(i_0_620,axiom,
    ( ~ hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3)) ),
    cls_DiffE_1,
    [final] ).

cnf(i_0_621,axiom,
    ( hAPP(X1,X5) = c_Option_Ooption_ONone(X4)
    | hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) != c_Option_Ooption_ONone(X4) ),
    cls_map__add__None_1,
    [final] ).

cnf(i_0_622,axiom,
    ( hAPP(X2,X5) = c_Option_Ooption_ONone(X4)
    | hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) != c_Option_Ooption_ONone(X4) ),
    cls_map__add__None_0,
    [final] ).

cnf(i_0_623,axiom,
    ( c_lessequals(hAPP(X1,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    cls_UN__upper_0,
    [final] ).

cnf(i_0_624,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
    | ~ hBOOL(c_in(X1,X2,X3)) ),
    cls_insert__Diff_0,
    [final] ).

cnf(i_0_625,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),c_Set_Oinsert(X2,X4,X1)) = c_Set_Oinsert(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4),X1),
    cls_insert__inter__insert_0,
    [final] ).

cnf(i_0_626,axiom,
    c_Set_Oinsert(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X4,tc_bool)),X4) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
    cls_UN__extend__simps_I1_J_0,
    [final] ).

cnf(i_0_627,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | c_The(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,X3,X4),X4),X4) = hAPP(hAPP(X1,X2),c_The(c_Finite__Set_Ofold1Set(X1,X3,X4),X4))
    | hBOOL(c_in(X2,X3,X4))
    | ~ c_Finite__Set_Ofinite(X3,X4)
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_493,c_0_489]),c_0_489]),
    [final] ).

cnf(i_0_628,plain,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_Finite__Set_Ofinite(X4,X1)
    | ~ hBOOL(c_in(X3,X4,X1))
    | ~ c_lessequals(X2,c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X1),X4,X1),X1),X1) ),
    inference(rw,[status(thm)],[i_0_494,c_0_489]),
    [final] ).

cnf(i_0_629,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_630,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool)))
    | ~ c_lessequals(X4,X2,tc_fun(X1,tc_bool)) ),
    cls_Un__Int__assoc__eq_1,
    [final] ).

cnf(i_0_631,axiom,
    ( X1 = X5
    | c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,X4) != c_Hoare__Mirabelle_Otriple_Otriple(X5,X6,X7,X4) ),
    cls_triple_Oinject_0,
    [final] ).

cnf(i_0_632,axiom,
    ( X2 = X6
    | c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,X4) != c_Hoare__Mirabelle_Otriple_Otriple(X5,X6,X7,X4) ),
    cls_triple_Oinject_1,
    [final] ).

cnf(i_0_633,axiom,
    ( X3 = X7
    | c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,X4) != c_Hoare__Mirabelle_Otriple_Otriple(X5,X6,X7,X4) ),
    cls_triple_Oinject_2,
    [final] ).

cnf(i_0_634,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_635,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)) ),
    cls_DiffE_0,
    [final] ).

cnf(i_0_636,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)) = c_Set_Oinsert(X3,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),X1)
    | ~ hBOOL(c_in(X3,X2,X1)) ),
    cls_Int__insert__right_0,
    [final] ).

cnf(i_0_637,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_638,axiom,
    ( c_lessequals(hAPP(X2,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X2,X5,X1),X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(c_in(X3,X4,X5)) ),
    cls_le__SUPI_0,
    [final] ).

cnf(i_0_639,axiom,
    c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    cls_Diff__Int_0,
    [final] ).

cnf(i_0_640,axiom,
    c_Map_Omap__le(X1,c_Map_Omap__add(X2,X1,X3,X4),X3,X4),
    cls_map__le__map__add_0,
    [final] ).

cnf(i_0_641,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = X4,
    cls_UN__extend__simps_I2_J_0,
    [final] ).

cnf(i_0_642,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X1,
    cls_UN__extend__simps_I3_J_0,
    [final] ).

cnf(i_0_643,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X1,
    cls_INT__extend__simps_I4_J_0,
    [final] ).

cnf(i_0_644,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2)) ),
    inference(rw,[status(thm)],[i_0_495,c_0_496]),
    [final] ).

cnf(i_0_645,axiom,
    ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3)),
    cls_empty__fold1SetE_0,
    [final] ).

cnf(i_0_646,axiom,
    ( hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4))
    | hBOOL(c_in(X1,X3,X4))
    | ~ hBOOL(c_in(X1,X2,X4)) ),
    cls_DiffI_0,
    [final] ).

cnf(i_0_647,axiom,
    ( hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4))
    | hBOOL(c_in(X1,X3,X4))
    | ~ hBOOL(c_in(X1,X2,X4)) ),
    cls_Diff__iff_2,
    [final] ).

cnf(i_0_648,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
    | ~ hBOOL(hAPP(X3,X4))
    | ~ hBOOL(hAPP(X2,X4)) ),
    cls_inf1I_0,
    [final] ).

cnf(i_0_649,axiom,
    ( hAPP(X2,X5) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2,X3,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | ~ hBOOL(c_in(X5,X1,X3)) ),
    cls_UNION__empty__conv_I2_J_0,
    [final] ).

cnf(i_0_650,axiom,
    ( hAPP(X3,X5) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X3,X4,tc_fun(X1,tc_bool))
    | ~ hBOOL(c_in(X5,X2,X4)) ),
    cls_UNION__empty__conv_I1_J_0,
    [final] ).

cnf(i_0_651,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_652,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_653,axiom,
    c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))),
    cls_Int__Diff_0,
    [final] ).

cnf(i_0_654,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool)) ),
    cls_Int__subset__iff_0,
    [final] ).

cnf(i_0_655,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2),tc_fun(X3,tc_bool)) ),
    cls_Int__subset__iff_1,
    [final] ).

cnf(i_0_656,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_657,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(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)
    | hBOOL(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_658,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_659,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_660,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_661,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | X1 = X4
    | ~ hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)) ),
    cls_insertE_0,
    [final] ).

cnf(i_0_662,axiom,
    ( ~ hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,X4,X3))
    | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_disjoint__iff__not__equal_0,
    [final] ).

cnf(i_0_663,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)
    | hBOOL(c_in(X2,X4,X1)) ),
    cls_Int__insert__left_1,
    [final] ).

cnf(i_0_664,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_665,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
    cls_Int__subset__iff_2,
    [final] ).

cnf(i_0_666,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
    cls_Int__greatest_0,
    [final] ).

cnf(i_0_667,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_668,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_669,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_Sup__binary_0,
    [final] ).

cnf(i_0_670,negated_conjecture,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_x)),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_conjecture_4,
    [final] ).

cnf(i_0_671,axiom,
    ( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_Inf__binary_0,
    [final] ).

cnf(i_0_672,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_673,axiom,
    ( hAPP(c_Map_Omap__add(X1,X5,X6,X4),X2) = c_Option_Ooption_OSome(X3,X4)
    | hAPP(X1,X2) != c_Option_Ooption_OSome(X3,X4)
    | hAPP(X5,X2) != c_Option_Ooption_ONone(X4) ),
    cls_map__add__Some__iff_3,
    [final] ).

cnf(i_0_674,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_675,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_676,axiom,
    ( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4))
    | ~ hBOOL(c_in(X1,X2,X4)) ),
    cls_UnCI_1,
    [final] ).

cnf(i_0_677,axiom,
    ( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4))
    | ~ hBOOL(c_in(X1,X3,X4)) ),
    cls_UnCI_0,
    [final] ).

cnf(i_0_678,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_679,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_680,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),
    cls_Int__left__absorb_0,
    [final] ).

cnf(i_0_681,axiom,
    ( hAPP(c_Map_Omap__add(X1,X4,X5,X3),X2) = c_Option_Ooption_ONone(X3)
    | hAPP(X1,X2) != c_Option_Ooption_ONone(X3)
    | hAPP(X4,X2) != c_Option_Ooption_ONone(X3) ),
    cls_map__add__None_2,
    [final] ).

cnf(i_0_682,axiom,
    ( hAPP(c_Map_Omap__add(X5,X1,X6,X4),X2) = c_Option_Ooption_OSome(X3,X4)
    | hAPP(X1,X2) != c_Option_Ooption_OSome(X3,X4) ),
    cls_map__add__Some__iff_2,
    [final] ).

cnf(i_0_683,axiom,
    ( hAPP(c_Map_Omap__add(X5,X1,X6,X4),X2) = c_Option_Ooption_OSome(X3,X4)
    | hAPP(X1,X2) != c_Option_Ooption_OSome(X3,X4) ),
    cls_map__add__find__right_0,
    [final] ).

cnf(i_0_684,plain,
    c_The(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = X2,
    inference(rw,[status(thm)],[i_0_497,c_0_489]),
    [final] ).

cnf(i_0_685,axiom,
    ( hAPP(X1,X2) != c_Option_Ooption_ONone(X3)
    | ~ hBOOL(c_in(X2,c_Map_Odom(X1,X4,X3),X4)) ),
    cls_domIff_0,
    [final] ).

cnf(i_0_686,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1)),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    cls_sup__inf__distrib2_0,
    [final] ).

cnf(i_0_687,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    cls_sup__inf__distrib1_0,
    [final] ).

cnf(i_0_688,axiom,
    hBOOL(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_689,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1)
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    cls_inf__sup__distrib2_0,
    [final] ).

cnf(i_0_690,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_691,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_692,plain,
    ( c_lessequals(c_The(c_Finite__Set_Ofold1Set(c_Lattices_Olower__semilattice__class_Oinf(X1),X2,X1),X1),X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_Finite__Set_Ofinite(X2,X1)
    | ~ hBOOL(c_in(X3,X2,X1)) ),
    inference(rw,[status(thm)],[i_0_498,c_0_489]),
    [final] ).

cnf(i_0_693,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2),tc_fun(X3,tc_bool)) = X1,
    cls_Un__Diff__Int_0,
    [final] ).

cnf(i_0_694,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
    | hBOOL(c_in(X1,X2,X3)) ),
    cls_Diff__insert__absorb_0,
    [final] ).

cnf(i_0_695,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)
    | hBOOL(c_in(X3,X2,X1)) ),
    cls_Int__insert__right_1,
    [final] ).

cnf(i_0_696,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X4,X3),c_Set_Oinsert(X2,X5,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X4,X3),X5,tc_fun(X4,tc_bool))
    | hAPP(X1,X2) != c_Option_Ooption_ONone(X3) ),
    cls_dom__minus_0,
    [final] ).

cnf(i_0_697,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)
    | hBOOL(c_in(X1,X4,X3)) ),
    cls_insert__Diff__if_1,
    [final] ).

cnf(i_0_698,axiom,
    ( hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4))
    | ~ hBOOL(c_in(X1,X3,X4)) ),
    cls_insertCI_0,
    [final] ).

cnf(i_0_699,axiom,
    ( hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4))
    | ~ hBOOL(c_in(X1,X3,X4)) ),
    cls_insert__iff_2,
    [final] ).

cnf(i_0_700,axiom,
    ( c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
    | ~ hBOOL(c_in(X1,X4,X3)) ),
    cls_insert__subset_2,
    [final] ).

cnf(i_0_701,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | hBOOL(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_702,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | hBOOL(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_703,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_704,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_705,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_706,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_707,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_708,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_709,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_710,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_711,plain,
    hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X1)),
    inference(rw,[status(thm)],[i_0_499,c_0_496]),
    [final] ).

cnf(i_0_712,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_713,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_714,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))
    | ~ hBOOL(c_in(X1,X4,X3)) ),
    cls_insert__Diff1_0,
    [final] ).

cnf(i_0_715,axiom,
    ( hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__fun__eq_0,
    [final] ).

cnf(i_0_716,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4),X1)
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    cls_inf__sup__distrib1_0,
    [final] ).

cnf(i_0_717,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I2_J_0,
    [final] ).

cnf(i_0_718,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__assoc_0,
    [final] ).

cnf(i_0_719,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | hBOOL(c_in(X2,X1,X4))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    cls_subset__insert_1,
    [final] ).

cnf(i_0_720,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | hBOOL(c_in(X2,X1,X4))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    cls_subset__insert__iff_2,
    [final] ).

cnf(i_0_721,axiom,
    ( hBOOL(hAPP(X1,X2))
    | X3 = X2
    | ~ hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
    cls_insert__code_0,
    [final] ).

cnf(i_0_722,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_723,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,X4,X3))
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    cls_set__mp_0,
    [final] ).

cnf(i_0_724,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,X4,X3))
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    cls_subsetD_0,
    [final] ).

cnf(i_0_725,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
    | ~ hBOOL(c_in(X1,X4,X3)) ),
    cls_set__rev__mp_0,
    [final] ).

cnf(i_0_726,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,X4,X3))
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    cls_subset__iff_0,
    [final] ).

cnf(i_0_727,axiom,
    ( hBOOL(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_728,axiom,
    ( hBOOL(c_in(X1,X4,X3))
    | hBOOL(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_729,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_730,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_731,axiom,
    ( ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
    cls_bex__empty_0,
    [final] ).

cnf(i_0_732,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_733,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_734,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(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_735,axiom,
    ( hBOOL(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_736,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
    cls_ball__empty_0,
    [final] ).

cnf(i_0_737,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_738,axiom,
    c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X2,tc_fun(X1,tc_bool)),
    cls_Int__lower1_0,
    [final] ).

cnf(i_0_739,axiom,
    c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X3,tc_fun(X1,tc_bool)),
    cls_Int__lower2_0,
    [final] ).

cnf(i_0_740,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_741,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_742,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool)) = X2
    | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
    cls_Diff__triv_0,
    [final] ).

cnf(i_0_743,axiom,
    ( hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3))
    | hAPP(X2,X1) = c_Option_Ooption_ONone(X4) ),
    cls_domIff_1,
    [final] ).

cnf(i_0_744,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_745,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_746,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_747,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_748,axiom,
    ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
    cls_emptyE_0,
    [final] ).

cnf(i_0_749,axiom,
    ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
    cls_empty__iff_0,
    [final] ).

cnf(i_0_750,axiom,
    ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
    cls_ex__in__conv_0,
    [final] ).

cnf(i_0_751,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__infI_0,
    [final] ).

cnf(i_0_752,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),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_753,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_inf__greatest_0,
    [final] ).

cnf(i_0_754,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_755,axiom,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4) = hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4))
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
    cls_ab__semigroup__mult_Omult__ac_I1_J_0,
    [final] ).

cnf(i_0_756,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_757,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_758,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_759,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_760,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_761,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_762,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_763,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_764,axiom,
    hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
    cls_insertCI_1,
    [final] ).

cnf(i_0_765,axiom,
    hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
    cls_insertI1_0,
    [final] ).

cnf(i_0_766,axiom,
    hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
    cls_insert__iff_1,
    [final] ).

cnf(i_0_767,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_Diff__disjoint_0,
    [final] ).

cnf(i_0_768,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_769,axiom,
    ( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    cls_finite__Int_0,
    [final] ).

cnf(i_0_770,axiom,
    ( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1)
    | ~ c_Finite__Set_Ofinite(X3,X1) ),
    cls_finite__Int_1,
    [final] ).

cnf(i_0_771,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_772,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_773,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_774,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_775,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_776,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_777,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_778,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I3_J_0,
    [final] ).

cnf(i_0_779,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__left__commute_0,
    [final] ).

cnf(i_0_780,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1) ),
    cls_le__inf__iff_0,
    [final] ).

cnf(i_0_781,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1) ),
    cls_le__infE_0,
    [final] ).

cnf(i_0_782,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X3),X1) ),
    cls_le__inf__iff_1,
    [final] ).

cnf(i_0_783,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X3),X1) ),
    cls_le__infE_1,
    [final] ).

cnf(i_0_784,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_785,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_786,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_787,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_788,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_789,negated_conjecture,
    hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)),
    cls_conjecture_3,
    [final] ).

cnf(i_0_790,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_791,axiom,
    ( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
    | ~ hBOOL(hAPP(X2,X4)) ),
    cls_insert__code_2,
    [final] ).

cnf(i_0_792,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X2),
    cls_Int__commute_0,
    [final] ).

cnf(i_0_793,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_794,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_795,axiom,
    ( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X1),X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(c_in(X3,X2,X1))
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    cls_Min__le_0,
    [final] ).

cnf(i_0_796,axiom,
    ( c_lessequals(X2,c_Finite__Set_Olinorder__class_OMax(X3,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(c_in(X2,X3,X1))
    | ~ c_Finite__Set_Ofinite(X3,X1) ),
    cls_Max__ge_0,
    [final] ).

cnf(i_0_797,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_798,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_799,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_Int__empty__left_0,
    [final] ).

cnf(i_0_800,axiom,
    ( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(t_a,X1)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X2,v_x),hAPP(X3,v_x),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_sup__fun__eq_0,
    [final] ).

cnf(i_0_801,axiom,
    ( hAPP(c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(t_a,X1)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X2,v_x),hAPP(X3,v_x),X1)
    | ~ class_HOL_Ominus(X1) ),
    cls_fun__diff__def_0,
    [final] ).

cnf(i_0_802,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = X2
    | ~ c_lessequals(X2,X3,tc_fun(X1,tc_bool)) ),
    cls_Int__absorb2_0,
    [final] ).

cnf(i_0_803,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = X3
    | ~ c_lessequals(X3,X2,tc_fun(X1,tc_bool)) ),
    cls_Int__absorb1_0,
    [final] ).

cnf(i_0_804,axiom,
    ( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,X1),X3,X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(c_in(X3,X2,X1)) ),
    cls_Inf__lower_0,
    [final] ).

cnf(i_0_805,axiom,
    ( c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(c_in(X2,X3,X1)) ),
    cls_Sup__upper_0,
    [final] ).

cnf(i_0_806,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | ~ c_OrderedGroup_Oab__semigroup__mult(X4,X5) ),
    cls_ab__semigroup__mult_Ononempty__iff_2,
    [final] ).

cnf(i_0_807,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_808,axiom,
    ( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X2),X4))
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
    cls_ab__semigroup__mult_Omult__left__commute_0,
    [final] ).

cnf(i_0_809,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_810,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_811,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_le__infI1_0,
    [final] ).

cnf(i_0_812,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    cls_le__infI2_0,
    [final] ).

cnf(i_0_813,axiom,
    c_Map_Omap__le(X1,X1,X2,X3),
    cls_map__le__refl_0,
    [final] ).

cnf(i_0_814,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_815,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_816,axiom,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    cls_insert__code_1,
    [final] ).

cnf(i_0_817,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_818,axiom,
    ( hBOOL(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_819,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_820,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_821,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_822,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_Sup__singleton_0,
    [final] ).

cnf(i_0_823,axiom,
    ( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_Inf__singleton_0,
    [final] ).

cnf(i_0_824,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_825,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_826,axiom,
    ( c_Set_Oinsert(X1,X2,X3) = X2
    | ~ hBOOL(c_in(X1,X2,X3)) ),
    cls_insert__absorb_0,
    [final] ).

cnf(i_0_827,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_828,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_829,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_830,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_831,axiom,
    c_Set_Ocontents(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1,
    cls_contents__eq_0,
    [final] ).

cnf(i_0_832,axiom,
    c_The(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1,
    cls_Nitpick_OThe__psimp_0,
    [final] ).

cnf(i_0_833,plain,
    c_The(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1,
    inference(rw,[status(thm)],[i_0_500,c_0_496]),
    [final] ).

cnf(i_0_834,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_835,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_836,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_Int__empty__right_0,
    [final] ).

cnf(i_0_837,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_838,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_839,axiom,
    ( hBOOL(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_840,axiom,
    ( hBOOL(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_841,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_842,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I4_J_0,
    [final] ).

cnf(i_0_843,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__left__idem_0,
    [final] ).

cnf(i_0_844,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_845,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_846,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_847,axiom,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    cls_bot1E_0,
    [final] ).

cnf(i_0_848,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_Sup__insert_0,
    [final] ).

cnf(i_0_849,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_850,axiom,
    ( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X2,X3,X1),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,X1))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_Inf__insert_0,
    [final] ).

cnf(i_0_851,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,X1,X3)) ),
    cls_mem__def_0,
    [final] ).

cnf(i_0_852,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,X1,X3)) ),
    inference(rw,[status(thm)],[i_0_501,c_0_487]),
    [final] ).

cnf(i_0_853,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_854,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_855,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_856,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_857,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_858,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_859,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_860,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_861,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_862,axiom,
    ( c_Com_OWT(c_Com_Ocom_OBODY(X1))
    | ~ c_Com_OWT(c_Com_Ocom_OCall(X2,X1,X3)) ),
    cls_WTs__elim__cases_I8_J_0,
    [final] ).

cnf(i_0_863,axiom,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    cls_subset__insertI_0,
    [final] ).

cnf(i_0_864,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_865,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_866,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_867,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_868,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_869,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_870,axiom,
    ( X1 = X4
    | c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OCall(X4,X5,X6) ),
    cls_com_Osimps_I7_J_0,
    [final] ).

cnf(i_0_871,axiom,
    ( X2 = X5
    | c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OCall(X4,X5,X6) ),
    cls_com_Osimps_I7_J_1,
    [final] ).

cnf(i_0_872,axiom,
    ( X3 = X6
    | c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OCall(X4,X5,X6) ),
    cls_com_Osimps_I7_J_2,
    [final] ).

cnf(i_0_873,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_874,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_875,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_876,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_877,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_878,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) = X2
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__absorb_0,
    [final] ).

cnf(i_0_879,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X1) = X2
    | ~ class_Lattices_Olattice(X1) ),
    cls_sup__inf__absorb_0,
    [final] ).

cnf(i_0_880,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__ord_I1_J_0,
    [final] ).

cnf(i_0_881,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X2,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__le1_0,
    [final] ).

cnf(i_0_882,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__ord_I2_J_0,
    [final] ).

cnf(i_0_883,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__le2_0,
    [final] ).

cnf(i_0_884,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_885,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_886,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    cls_mem__def_1,
    [final] ).

cnf(i_0_887,plain,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    inference(rw,[status(thm)],[i_0_502,c_0_487]),
    [final] ).

cnf(i_0_888,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_889,axiom,
    hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),
    cls_bot__empty__eq_0,
    [final] ).

cnf(i_0_890,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_891,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_892,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_893,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_894,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__iff__inf_0,
    [final] ).

cnf(i_0_895,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X3
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_inf__absorb2_0,
    [final] ).

cnf(i_0_896,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != X2 ),
    cls_le__iff__inf_1,
    [final] ).

cnf(i_0_897,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X2) = X2,
    cls_Int__absorb_0,
    [final] ).

cnf(i_0_898,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_899,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_900,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_901,axiom,
    ( c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3) ),
    cls_hoare__sound_0,
    [final] ).

cnf(i_0_902,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_903,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_904,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_905,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_906,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_907,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_908,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_909,axiom,
    ( c_Com_OWT(c_Com_Ocom_OCall(X1,X2,X3))
    | ~ c_Com_OWT(c_Com_Ocom_OBODY(X2)) ),
    cls_WT_OCall_0,
    [final] ).

cnf(i_0_910,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__linear_0,
    [final] ).

cnf(i_0_911,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_912,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_913,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I1_J_0,
    [final] ).

cnf(i_0_914,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__commute_0,
    [final] ).

cnf(i_0_915,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_916,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_917,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_918,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_919,axiom,
    ( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X3),X2)
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4) ),
    cls_ab__semigroup__mult_Omult__commute_0,
    [final] ).

cnf(i_0_920,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X2
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(rw,[status(thm)],[i_0_503,c_0_487]),
    [final] ).

cnf(i_0_921,plain,
    ( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(rw,[status(thm)],[i_0_504,c_0_487]),
    [final] ).

cnf(i_0_922,axiom,
    c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OBODY(X4),
    cls_com_Osimps_I63_J_0,
    [final] ).

cnf(i_0_923,axiom,
    c_Com_Ocom_OBODY(X1) != c_Com_Ocom_OCall(X2,X3,X4),
    cls_com_Osimps_I62_J_0,
    [final] ).

cnf(i_0_924,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
    cls_Un__absorb_0,
    [final] ).

cnf(i_0_925,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    cls_subset__refl_0,
    [final] ).

cnf(i_0_926,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    cls_equalityE_0,
    [final] ).

cnf(i_0_927,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_Sup__empty_0,
    [final] ).

cnf(i_0_928,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_inf__bot__left_0,
    [final] ).

cnf(i_0_929,axiom,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Orderings_Obot(X1) ),
    cls_bot__fun__eq_0,
    [final] ).

cnf(i_0_930,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_inf__bot__right_0,
    [final] ).

cnf(i_0_931,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_932,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_933,axiom,
    ( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
    | ~ class_Orderings_Obot(X1) ),
    cls_bot__least_0,
    [final] ).

cnf(i_0_934,axiom,
    c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
    cls_finite_OemptyI_0,
    [final] ).

cnf(i_0_935,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X2,X1) = X2
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__idem_0,
    [final] ).

cnf(i_0_936,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Opreorder(X1) ),
    cls_order__eq__refl_0,
    [final] ).

cnf(i_0_937,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_order__eq__iff_0,
    [final] ).

cnf(i_0_938,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__idem_0,
    [final] ).

cnf(i_0_939,axiom,
    ( X1 = X3
    | c_Option_Ooption_OSome(X1,X2) != c_Option_Ooption_OSome(X3,X2) ),
    cls_option_Oinject_0,
    [final] ).

cnf(i_0_940,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_941,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_942,axiom,
    c_Option_Othe(c_Option_Ooption_OSome(X1,X2),X2) = X1,
    cls_the_Osimps_0,
    [final] ).

cnf(i_0_943,axiom,
    ( class_Orderings_Opreorder(tc_fun(X1,X2))
    | ~ class_Orderings_Opreorder(X2) ),
    clsarity_fun__Orderings_Opreorder,
    [final] ).

cnf(i_0_944,axiom,
    ( class_Orderings_Obot(tc_fun(X1,X2))
    | ~ class_Orderings_Obot(X2) ),
    clsarity_fun__Orderings_Obot,
    [final] ).

cnf(i_0_945,axiom,
    ( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
    | ~ class_Lattices_Obounded__lattice(X2) ),
    clsarity_fun__Lattices_Obounded__lattice,
    [final] ).

cnf(i_0_946,axiom,
    ( class_Orderings_Oorder(tc_fun(X1,X2))
    | ~ class_Orderings_Oorder(X2) ),
    clsarity_fun__Orderings_Oorder,
    [final] ).

cnf(i_0_947,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_948,axiom,
    ( class_Lattices_Odistrib__lattice(tc_fun(X1,X2))
    | ~ class_Lattices_Odistrib__lattice(X2) ),
    clsarity_fun__Lattices_Odistrib__lattice,
    [final] ).

cnf(i_0_949,axiom,
    ( class_HOL_Oord(tc_fun(X1,X2))
    | ~ class_HOL_Oord(X2) ),
    clsarity_fun__HOL_Oord,
    [final] ).

cnf(i_0_950,axiom,
    ( class_Lattices_Olattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Olattice,
    [final] ).

cnf(i_0_951,axiom,
    ( class_Lattices_Oupper__semilattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Oupper__semilattice,
    [final] ).

cnf(i_0_952,axiom,
    ( class_Lattices_Olower__semilattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_953,axiom,
    ( class_HOL_Ominus(tc_fun(X1,X2))
    | ~ class_HOL_Ominus(X2) ),
    clsarity_fun__HOL_Ominus,
    [final] ).

cnf(i_0_954,axiom,
    c_Option_Ooption_OSome(X1,X2) != c_Option_Ooption_ONone(X2),
    cls_not__None__eq_1,
    [final] ).

cnf(i_0_955,axiom,
    c_Option_Ooption_OSome(X1,X2) != c_Option_Ooption_ONone(X2),
    cls_option_Osimps_I3_J_0,
    [final] ).

cnf(i_0_956,axiom,
    c_Option_Ooption_ONone(X1) != c_Option_Ooption_OSome(X2,X1),
    cls_not__Some__eq_1,
    [final] ).

cnf(i_0_957,axiom,
    c_Option_Ooption_ONone(X1) != c_Option_Ooption_OSome(X2,X1),
    cls_option_Osimps_I2_J_0,
    [final] ).

cnf(i_0_958,axiom,
    ( c_Com_OWT(c_Com_Ocom_OBODY(X1))
    | hAPP(c_Com_Obody,X1) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
    cls_WT_OBody_0,
    [final] ).

cnf(i_0_959,axiom,
    ( c_Finite__Set_Ofinite(X2,X1)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    cls_finite_0,
    [final] ).

cnf(i_0_960,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_961,axiom,
    ( X1 = X2
    | c_Com_Ocom_OBODY(X1) != c_Com_Ocom_OBODY(X2) ),
    cls_com_Osimps_I6_J_0,
    [final] ).

cnf(i_0_962,axiom,
    ( c_Hoare__Mirabelle_Ostate__not__singleton
    | X1 = X2 ),
    cls_state__not__singleton__def_1,
    [final] ).

cnf(i_0_963,negated_conjecture,
    c_Com_OWT(v_c),
    cls_conjecture_2,
    [final] ).

cnf(i_0_964,axiom,
    class_Orderings_Opreorder(tc_nat),
    clsarity_nat__Orderings_Opreorder,
    [final] ).

cnf(i_0_965,axiom,
    class_Orderings_Opreorder(tc_bool),
    clsarity_bool__Orderings_Opreorder,
    [final] ).

cnf(i_0_966,axiom,
    class_Orderings_Obot(tc_nat),
    clsarity_nat__Orderings_Obot,
    [final] ).

cnf(i_0_967,axiom,
    class_Orderings_Obot(tc_bool),
    clsarity_bool__Orderings_Obot,
    [final] ).

cnf(i_0_968,axiom,
    class_Lattices_Obounded__lattice(tc_bool),
    clsarity_bool__Lattices_Obounded__lattice,
    [final] ).

cnf(i_0_969,axiom,
    class_Orderings_Oorder(tc_nat),
    clsarity_nat__Orderings_Oorder,
    [final] ).

cnf(i_0_970,axiom,
    class_Orderings_Oorder(tc_bool),
    clsarity_bool__Orderings_Oorder,
    [final] ).

cnf(i_0_971,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_bool),
    clsarity_bool__Complete__Lattice_Ocomplete__lattice,
    [final] ).

cnf(i_0_972,axiom,
    class_Lattices_Odistrib__lattice(tc_nat),
    clsarity_nat__Lattices_Odistrib__lattice,
    [final] ).

cnf(i_0_973,axiom,
    class_Lattices_Odistrib__lattice(tc_bool),
    clsarity_bool__Lattices_Odistrib__lattice,
    [final] ).

cnf(i_0_974,axiom,
    class_Orderings_Olinorder(tc_nat),
    clsarity_nat__Orderings_Olinorder,
    [final] ).

cnf(i_0_975,axiom,
    class_HOL_Oord(tc_nat),
    clsarity_nat__HOL_Oord,
    [final] ).

cnf(i_0_976,axiom,
    class_HOL_Oord(tc_bool),
    clsarity_bool__HOL_Oord,
    [final] ).

cnf(i_0_977,axiom,
    class_Finite__Set_Ofinite_Ofinite(tc_bool),
    clsarity_bool__Finite__Set_Ofinite_Ofinite,
    [final] ).

cnf(i_0_978,axiom,
    class_Lattices_Olattice(tc_nat),
    clsarity_nat__Lattices_Olattice,
    [final] ).

cnf(i_0_979,axiom,
    class_Lattices_Olattice(tc_bool),
    clsarity_bool__Lattices_Olattice,
    [final] ).

cnf(i_0_980,axiom,
    class_Lattices_Oupper__semilattice(tc_nat),
    clsarity_nat__Lattices_Oupper__semilattice,
    [final] ).

cnf(i_0_981,axiom,
    class_Lattices_Oupper__semilattice(tc_bool),
    clsarity_bool__Lattices_Oupper__semilattice,
    [final] ).

cnf(i_0_982,axiom,
    class_Lattices_Olower__semilattice(tc_nat),
    clsarity_nat__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_983,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    clsarity_bool__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_984,axiom,
    class_HOL_Ominus(tc_nat),
    clsarity_nat__HOL_Ominus,
    [final] ).

cnf(i_0_985,axiom,
    class_HOL_Ominus(tc_bool),
    clsarity_bool__HOL_Ominus,
    [final] ).

cnf(i_0_986,negated_conjecture,
    c_Hoare__Mirabelle_Ostate__not__singleton,
    cls_conjecture_0,
    [final] ).

cnf(i_0_987,negated_conjecture,
    c_Com_OWT__bodies,
    cls_conjecture_1,
    [final] ).

cnf(i_0_988,axiom,
    X1 = X1 ).

cnf(i_0_989,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_990,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_991,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_992,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_993,axiom,
    ( X1 != X2
    | c_Option_Othe(X1,X3) = c_Option_Othe(X2,X3) ) ).

cnf(i_0_994,axiom,
    ( X1 != X2
    | c_Option_Othe(X3,X1) = c_Option_Othe(X3,X2) ) ).

cnf(i_0_995,axiom,
    ( X1 != X2
    | c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).

cnf(i_0_996,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).

cnf(i_0_997,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).

cnf(i_0_998,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).

cnf(i_0_999,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4) ) ).

cnf(i_0_1000,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X4) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) ) ).

cnf(i_0_1001,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2) ) ).

cnf(i_0_1002,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X1,X3,X4,X5) = c_Set_Ovimage(X2,X3,X4,X5) ) ).

cnf(i_0_1003,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X1,X4,X5) = c_Set_Ovimage(X3,X2,X4,X5) ) ).

cnf(i_0_1004,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X1,X5) = c_Set_Ovimage(X3,X4,X2,X5) ) ).

cnf(i_0_1005,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X5,X1) = c_Set_Ovimage(X3,X4,X5,X2) ) ).

cnf(i_0_1006,axiom,
    ( X1 != X2
    | c_Map_Omap__add(X1,X3,X4,X5) = c_Map_Omap__add(X2,X3,X4,X5) ) ).

cnf(i_0_1007,axiom,
    ( X1 != X2
    | c_Map_Omap__add(X3,X1,X4,X5) = c_Map_Omap__add(X3,X2,X4,X5) ) ).

cnf(i_0_1008,axiom,
    ( X1 != X2
    | c_Map_Omap__add(X3,X4,X1,X5) = c_Map_Omap__add(X3,X4,X2,X5) ) ).

cnf(i_0_1009,axiom,
    ( X1 != X2
    | c_Map_Omap__add(X3,X4,X5,X1) = c_Map_Omap__add(X3,X4,X5,X2) ) ).

cnf(i_0_1010,axiom,
    ( X1 != X2
    | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X4,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X3,X4,X5) ) ).

cnf(i_0_1011,axiom,
    ( X1 != X2
    | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X2,X4,X5) ) ).

cnf(i_0_1012,axiom,
    ( X1 != X2
    | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X2,X5) ) ).

cnf(i_0_1013,axiom,
    ( X1 != X2
    | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,X1) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,X2) ) ).

cnf(i_0_1014,axiom,
    ( X1 != X2
    | c_The(X1,X3) = c_The(X2,X3) ) ).

cnf(i_0_1015,axiom,
    ( X1 != X2
    | c_The(X3,X1) = c_The(X3,X2) ) ).

cnf(i_0_1016,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).

cnf(i_0_1017,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).

cnf(i_0_1018,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).

cnf(i_0_1019,axiom,
    ( X1 != X2
    | c_Nitpick_Osko__Nitpick__XEx1__def__1__3(X1,X3) = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(X2,X3) ) ).

cnf(i_0_1020,axiom,
    ( X1 != X2
    | c_Nitpick_Osko__Nitpick__XEx1__def__1__3(X3,X1) = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(X3,X2) ) ).

cnf(i_0_1021,axiom,
    ( X1 != X2
    | c_Map_Odom(X1,X3,X4) = c_Map_Odom(X2,X3,X4) ) ).

cnf(i_0_1022,axiom,
    ( X1 != X2
    | c_Map_Odom(X3,X1,X4) = c_Map_Odom(X3,X2,X4) ) ).

cnf(i_0_1023,axiom,
    ( X1 != X2
    | c_Map_Odom(X3,X4,X1) = c_Map_Odom(X3,X4,X2) ) ).

cnf(i_0_1024,axiom,
    ( X1 != X2
    | c_Option_Ooption_OSome(X1,X3) = c_Option_Ooption_OSome(X2,X3) ) ).

cnf(i_0_1025,axiom,
    ( X1 != X2
    | c_Option_Ooption_OSome(X3,X1) = c_Option_Ooption_OSome(X3,X2) ) ).

cnf(i_0_1026,axiom,
    ( X1 != X2
    | c_Option_Ooption_ONone(X1) = c_Option_Ooption_ONone(X2) ) ).

cnf(i_0_1027,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).

cnf(i_0_1028,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).

cnf(i_0_1029,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).

cnf(i_0_1030,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).

cnf(i_0_1031,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).

cnf(i_0_1032,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).

cnf(i_0_1033,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).

cnf(i_0_1034,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X1,X3) = c_Finite__Set_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_1035,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X3,X1) = c_Finite__Set_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_1036,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X1,X3) = c_Finite__Set_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_1037,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X3,X1) = c_Finite__Set_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_1038,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_1039,axiom,
    ( X1 != X2
    | c_Set_Ocontents(X1,X3) = c_Set_Ocontents(X2,X3) ) ).

cnf(i_0_1040,axiom,
    ( X1 != X2
    | c_Set_Ocontents(X3,X1) = c_Set_Ocontents(X3,X2) ) ).

cnf(i_0_1041,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCall(X1,X3,X4) = c_Com_Ocom_OCall(X2,X3,X4) ) ).

cnf(i_0_1042,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCall(X3,X1,X4) = c_Com_Ocom_OCall(X3,X2,X4) ) ).

cnf(i_0_1043,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCall(X3,X4,X1) = c_Com_Ocom_OCall(X3,X4,X2) ) ).

cnf(i_0_1044,axiom,
    ( X1 != X2
    | c_in(X1,X3,X4) = c_in(X2,X3,X4) ) ).

cnf(i_0_1045,axiom,
    ( X1 != X2
    | c_in(X3,X1,X4) = c_in(X3,X2,X4) ) ).

cnf(i_0_1046,axiom,
    ( X1 != X2
    | c_in(X3,X4,X1) = c_in(X3,X4,X2) ) ).

cnf(i_0_1047,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_1048,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_1049,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_1050,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple(X1,X3,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X5) ) ).

cnf(i_0_1051,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple(X3,X1,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple(X3,X2,X4,X5) ) ).

cnf(i_0_1052,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X1,X5) = c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X2,X5) ) ).

cnf(i_0_1053,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,X1) = c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,X2) ) ).

cnf(i_0_1054,axiom,
    ( X1 != X2
    | c_Com_Ocom_OBODY(X1) = c_Com_Ocom_OBODY(X2) ) ).

cnf(i_0_1055,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X3,X4,X5,X6,X7,X8,X9,X10)
    | c_Complete__Lattice_Ocomplete__lattice(X2,X3,X4,X5,X6,X7,X8,X9,X10) ) ).

cnf(i_0_1056,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X3,X1,X4,X5,X6,X7,X8,X9,X10)
    | c_Complete__Lattice_Ocomplete__lattice(X3,X2,X4,X5,X6,X7,X8,X9,X10) ) ).

cnf(i_0_1057,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X3,X4,X1,X5,X6,X7,X8,X9,X10)
    | c_Complete__Lattice_Ocomplete__lattice(X3,X4,X2,X5,X6,X7,X8,X9,X10) ) ).

cnf(i_0_1058,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X1,X6,X7,X8,X9,X10)
    | c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X2,X6,X7,X8,X9,X10) ) ).

cnf(i_0_1059,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X1,X7,X8,X9,X10)
    | c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X2,X7,X8,X9,X10) ) ).

cnf(i_0_1060,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X7,X1,X8,X9,X10)
    | c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X7,X2,X8,X9,X10) ) ).

cnf(i_0_1061,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X7,X8,X1,X9,X10)
    | c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X7,X8,X2,X9,X10) ) ).

cnf(i_0_1062,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X7,X8,X9,X1,X10)
    | c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X7,X8,X9,X2,X10) ) ).

cnf(i_0_1063,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X7,X8,X9,X10,X1)
    | c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X7,X8,X9,X10,X2) ) ).

cnf(i_0_1064,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_1065,axiom,
    ( X1 != X2
    | ~ c_Com_OWT(X1)
    | c_Com_OWT(X2) ) ).

cnf(i_0_1066,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | class_Lattices_Olower__semilattice(X2) ) ).

cnf(i_0_1067,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_1068,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1069,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_1070,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oupper__semilattice(X1)
    | class_Lattices_Oupper__semilattice(X2) ) ).

cnf(i_0_1071,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_1072,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1073,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1074,axiom,
    ( X1 != X2
    | ~ class_HOL_Ominus(X1)
    | class_HOL_Ominus(X2) ) ).

cnf(i_0_1075,axiom,
    ( X1 != X2
    | ~ class_HOL_Oord(X1)
    | class_HOL_Oord(X2) ) ).

cnf(i_0_1076,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1077,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1078,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_1079,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_1080,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite_Ofinite(X1)
    | class_Finite__Set_Ofinite_Ofinite(X2) ) ).

cnf(i_0_1081,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X6,X7)
    | c_Finite__Set_Ofold__graph(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_1082,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofold__graph(X3,X1,X4,X5,X6,X7)
    | c_Finite__Set_Ofold__graph(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_1083,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofold__graph(X3,X4,X1,X5,X6,X7)
    | c_Finite__Set_Ofold__graph(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_1084,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofold__graph(X3,X4,X5,X1,X6,X7)
    | c_Finite__Set_Ofold__graph(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_1085,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X1,X7)
    | c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_1086,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X7,X1)
    | c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_1087,axiom,
    ( X1 != X2
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X3)
    | c_OrderedGroup_Oab__semigroup__mult(X2,X3) ) ).

cnf(i_0_1088,axiom,
    ( X1 != X2
    | ~ c_OrderedGroup_Oab__semigroup__mult(X3,X1)
    | c_OrderedGroup_Oab__semigroup__mult(X3,X2) ) ).

cnf(i_0_1089,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | c_Finite__Set_Ofinite(X2,X3) ) ).

cnf(i_0_1090,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | c_Finite__Set_Ofinite(X3,X2) ) ).

cnf(i_0_1091,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).

cnf(i_0_1092,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).

cnf(i_0_1093,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).

cnf(i_0_1094,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_1095,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_1096,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_1097,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__valids(X2,X3,X4) ) ).

cnf(i_0_1098,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__valids(X3,X2,X4) ) ).

cnf(i_0_1099,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X2) ) ).

cnf(i_0_1100,axiom,
    ( X1 != X2
    | ~ c_Map_Omap__le(X1,X3,X4,X5)
    | c_Map_Omap__le(X2,X3,X4,X5) ) ).

cnf(i_0_1101,axiom,
    ( X1 != X2
    | ~ c_Map_Omap__le(X3,X1,X4,X5)
    | c_Map_Omap__le(X3,X2,X4,X5) ) ).

cnf(i_0_1102,axiom,
    ( X1 != X2
    | ~ c_Map_Omap__le(X3,X4,X1,X5)
    | c_Map_Omap__le(X3,X4,X2,X5) ) ).

cnf(i_0_1103,axiom,
    ( X1 != X2
    | ~ c_Map_Omap__le(X3,X4,X5,X1)
    | c_Map_Omap__le(X3,X4,X5,X2) ) ).

cnf(i_0_988_001,axiom,
    X1 = X1 ).

cnf(i_0_989_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_990_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_991_004,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_992_005,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_993_006,axiom,
    ( X1 != X2
    | c_Option_Othe(X1,X3) = c_Option_Othe(X2,X3) ) ).

cnf(i_0_994_007,axiom,
    ( X1 != X2
    | c_Option_Othe(X3,X1) = c_Option_Othe(X3,X2) ) ).

cnf(i_0_995_008,axiom,
    ( X1 != X2
    | c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).

cnf(i_0_996_009,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).

cnf(i_0_997_010,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).

cnf(i_0_998_011,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).

cnf(i_0_999_012,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4) ) ).

cnf(i_0_1000_013,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X4) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) ) ).

cnf(i_0_1001_014,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2) ) ).

cnf(i_0_1002_015,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X1,X3,X4,X5) = c_Set_Ovimage(X2,X3,X4,X5) ) ).

cnf(i_0_1003_016,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X1,X4,X5) = c_Set_Ovimage(X3,X2,X4,X5) ) ).

cnf(i_0_1004_017,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X1,X5) = c_Set_Ovimage(X3,X4,X2,X5) ) ).

cnf(i_0_1005_018,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X5,X1) = c_Set_Ovimage(X3,X4,X5,X2) ) ).

cnf(i_0_1006_019,axiom,
    ( X1 != X2
    | c_Map_Omap__add(X1,X3,X4,X5) = c_Map_Omap__add(X2,X3,X4,X5) ) ).

cnf(i_0_1007_020,axiom,
    ( X1 != X2
    | c_Map_Omap__add(X3,X1,X4,X5) = c_Map_Omap__add(X3,X2,X4,X5) ) ).

cnf(i_0_1008_021,axiom,
    ( X1 != X2
    | c_Map_Omap__add(X3,X4,X1,X5) = c_Map_Omap__add(X3,X4,X2,X5) ) ).

cnf(i_0_1009_022,axiom,
    ( X1 != X2
    | c_Map_Omap__add(X3,X4,X5,X1) = c_Map_Omap__add(X3,X4,X5,X2) ) ).

cnf(i_0_1010_023,axiom,
    ( X1 != X2
    | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X3,X4,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X3,X4,X5) ) ).

cnf(i_0_1011_024,axiom,
    ( X1 != X2
    | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X2,X4,X5) ) ).

cnf(i_0_1012_025,axiom,
    ( X1 != X2
    | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X2,X5) ) ).

cnf(i_0_1013_026,axiom,
    ( X1 != X2
    | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,X1) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,X2) ) ).

cnf(i_0_1014_027,axiom,
    ( X1 != X2
    | c_The(X1,X3) = c_The(X2,X3) ) ).

cnf(i_0_1015_028,axiom,
    ( X1 != X2
    | c_The(X3,X1) = c_The(X3,X2) ) ).

cnf(i_0_1016_029,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).

cnf(i_0_1017_030,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).

cnf(i_0_1018_031,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).

cnf(i_0_1019_032,axiom,
    ( X1 != X2
    | c_Nitpick_Osko__Nitpick__XEx1__def__1__3(X1,X3) = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(X2,X3) ) ).

cnf(i_0_1020_033,axiom,
    ( X1 != X2
    | c_Nitpick_Osko__Nitpick__XEx1__def__1__3(X3,X1) = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(X3,X2) ) ).

cnf(i_0_1021_034,axiom,
    ( X1 != X2
    | c_Map_Odom(X1,X3,X4) = c_Map_Odom(X2,X3,X4) ) ).

cnf(i_0_1022_035,axiom,
    ( X1 != X2
    | c_Map_Odom(X3,X1,X4) = c_Map_Odom(X3,X2,X4) ) ).

cnf(i_0_1023_036,axiom,
    ( X1 != X2
    | c_Map_Odom(X3,X4,X1) = c_Map_Odom(X3,X4,X2) ) ).

cnf(i_0_1024_037,axiom,
    ( X1 != X2
    | c_Option_Ooption_OSome(X1,X3) = c_Option_Ooption_OSome(X2,X3) ) ).

cnf(i_0_1025_038,axiom,
    ( X1 != X2
    | c_Option_Ooption_OSome(X3,X1) = c_Option_Ooption_OSome(X3,X2) ) ).

cnf(i_0_1026_039,axiom,
    ( X1 != X2
    | c_Option_Ooption_ONone(X1) = c_Option_Ooption_ONone(X2) ) ).

cnf(i_0_1027_040,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).

cnf(i_0_1028_041,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).

cnf(i_0_1029_042,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).

cnf(i_0_1030_043,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).

cnf(i_0_1031_044,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).

cnf(i_0_1032_045,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).

cnf(i_0_1033_046,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).

cnf(i_0_1034_047,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X1,X3) = c_Finite__Set_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_1035_048,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X3,X1) = c_Finite__Set_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_1036_049,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X1,X3) = c_Finite__Set_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_1037_050,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X3,X1) = c_Finite__Set_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_1038_051,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_1039_052,axiom,
    ( X1 != X2
    | c_Set_Ocontents(X1,X3) = c_Set_Ocontents(X2,X3) ) ).

cnf(i_0_1040_053,axiom,
    ( X1 != X2
    | c_Set_Ocontents(X3,X1) = c_Set_Ocontents(X3,X2) ) ).

cnf(i_0_1041_054,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCall(X1,X3,X4) = c_Com_Ocom_OCall(X2,X3,X4) ) ).

cnf(i_0_1042_055,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCall(X3,X1,X4) = c_Com_Ocom_OCall(X3,X2,X4) ) ).

cnf(i_0_1043_056,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCall(X3,X4,X1) = c_Com_Ocom_OCall(X3,X4,X2) ) ).

cnf(i_0_1044_057,axiom,
    ( X1 != X2
    | c_in(X1,X3,X4) = c_in(X2,X3,X4) ) ).

cnf(i_0_1045_058,axiom,
    ( X1 != X2
    | c_in(X3,X1,X4) = c_in(X3,X2,X4) ) ).

cnf(i_0_1046_059,axiom,
    ( X1 != X2
    | c_in(X3,X4,X1) = c_in(X3,X4,X2) ) ).

cnf(i_0_1047_060,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_1048_061,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_1049_062,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_1050_063,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple(X1,X3,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X5) ) ).

cnf(i_0_1051_064,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple(X3,X1,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple(X3,X2,X4,X5) ) ).

cnf(i_0_1052_065,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X1,X5) = c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X2,X5) ) ).

cnf(i_0_1053_066,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,X1) = c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,X2) ) ).

cnf(i_0_1054_067,axiom,
    ( X1 != X2
    | c_Com_Ocom_OBODY(X1) = c_Com_Ocom_OBODY(X2) ) ).

cnf(i_0_1055_068,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X3,X4,X5,X6,X7,X8,X9,X10)
    | c_Complete__Lattice_Ocomplete__lattice(X2,X3,X4,X5,X6,X7,X8,X9,X10) ) ).

cnf(i_0_1056_069,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X3,X1,X4,X5,X6,X7,X8,X9,X10)
    | c_Complete__Lattice_Ocomplete__lattice(X3,X2,X4,X5,X6,X7,X8,X9,X10) ) ).

cnf(i_0_1057_070,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X3,X4,X1,X5,X6,X7,X8,X9,X10)
    | c_Complete__Lattice_Ocomplete__lattice(X3,X4,X2,X5,X6,X7,X8,X9,X10) ) ).

cnf(i_0_1058_071,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X1,X6,X7,X8,X9,X10)
    | c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X2,X6,X7,X8,X9,X10) ) ).

cnf(i_0_1059_072,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X1,X7,X8,X9,X10)
    | c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X2,X7,X8,X9,X10) ) ).

cnf(i_0_1060_073,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X7,X1,X8,X9,X10)
    | c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X7,X2,X8,X9,X10) ) ).

cnf(i_0_1061_074,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X7,X8,X1,X9,X10)
    | c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X7,X8,X2,X9,X10) ) ).

cnf(i_0_1062_075,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X7,X8,X9,X1,X10)
    | c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X7,X8,X9,X2,X10) ) ).

cnf(i_0_1063_076,axiom,
    ( X1 != X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X7,X8,X9,X10,X1)
    | c_Complete__Lattice_Ocomplete__lattice(X3,X4,X5,X6,X7,X8,X9,X10,X2) ) ).

cnf(i_0_1064_077,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_1065_078,axiom,
    ( X1 != X2
    | ~ c_Com_OWT(X1)
    | c_Com_OWT(X2) ) ).

cnf(i_0_1066_079,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | class_Lattices_Olower__semilattice(X2) ) ).

cnf(i_0_1067_080,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_1068_081,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1069_082,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_1070_083,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oupper__semilattice(X1)
    | class_Lattices_Oupper__semilattice(X2) ) ).

cnf(i_0_1071_084,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_1072_085,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1073_086,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1074_087,axiom,
    ( X1 != X2
    | ~ class_HOL_Ominus(X1)
    | class_HOL_Ominus(X2) ) ).

cnf(i_0_1075_088,axiom,
    ( X1 != X2
    | ~ class_HOL_Oord(X1)
    | class_HOL_Oord(X2) ) ).

cnf(i_0_1076_089,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1077_090,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1078_091,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_1079_092,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_1080_093,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite_Ofinite(X1)
    | class_Finite__Set_Ofinite_Ofinite(X2) ) ).

cnf(i_0_1081_094,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X6,X7)
    | c_Finite__Set_Ofold__graph(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_1082_095,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofold__graph(X3,X1,X4,X5,X6,X7)
    | c_Finite__Set_Ofold__graph(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_1083_096,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofold__graph(X3,X4,X1,X5,X6,X7)
    | c_Finite__Set_Ofold__graph(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_1084_097,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofold__graph(X3,X4,X5,X1,X6,X7)
    | c_Finite__Set_Ofold__graph(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_1085_098,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X1,X7)
    | c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_1086_099,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X7,X1)
    | c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_1087_100,axiom,
    ( X1 != X2
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X3)
    | c_OrderedGroup_Oab__semigroup__mult(X2,X3) ) ).

cnf(i_0_1088_101,axiom,
    ( X1 != X2
    | ~ c_OrderedGroup_Oab__semigroup__mult(X3,X1)
    | c_OrderedGroup_Oab__semigroup__mult(X3,X2) ) ).

cnf(i_0_1089_102,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | c_Finite__Set_Ofinite(X2,X3) ) ).

cnf(i_0_1090_103,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | c_Finite__Set_Ofinite(X3,X2) ) ).

cnf(i_0_1091_104,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).

cnf(i_0_1092_105,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).

cnf(i_0_1093_106,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).

cnf(i_0_1094_107,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_1095_108,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_1096_109,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_1097_110,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__valids(X2,X3,X4) ) ).

cnf(i_0_1098_111,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__valids(X3,X2,X4) ) ).

cnf(i_0_1099_112,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X2) ) ).

cnf(i_0_1100_113,axiom,
    ( X1 != X2
    | ~ c_Map_Omap__le(X1,X3,X4,X5)
    | c_Map_Omap__le(X2,X3,X4,X5) ) ).

cnf(i_0_1101_114,axiom,
    ( X1 != X2
    | ~ c_Map_Omap__le(X3,X1,X4,X5)
    | c_Map_Omap__le(X3,X2,X4,X5) ) ).

cnf(i_0_1102_115,axiom,
    ( X1 != X2
    | ~ c_Map_Omap__le(X3,X4,X1,X5)
    | c_Map_Omap__le(X3,X4,X2,X5) ) ).

cnf(i_0_1103_116,axiom,
    ( X1 != X2
    | ~ c_Map_Omap__le(X3,X4,X5,X1)
    | c_Map_Omap__le(X3,X4,X5,X2) ) ).

cnf(i_0_1104,plain,
    c_Map_Omap__le(X1,c_Map_Omap__add(X1,X1,X2,X3),X2,X3),
    inference(equality_inference,[],[544]) ).

cnf(i_0_1105,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[614]) ).

cnf(i_0_1106,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[615]) ).

cnf(i_0_1107,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[616]) ).

cnf(i_0_1108,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[617]) ).

cnf(i_0_1109,plain,
    X1 = X1,
    inference(equality_inference,[],[631]) ).

cnf(i_0_1110,plain,
    X1 = X1,
    inference(equality_inference,[],[632]) ).

cnf(i_0_1111,plain,
    X1 = X1,
    inference(equality_inference,[],[633]) ).

cnf(i_0_1112,plain,
    ( X1 = X1
    | hBOOL(c_in(X2,X1,X3))
    | hBOOL(c_in(X2,X1,X3)) ),
    inference(equality_inference,[],[728]) ).

cnf(i_0_1113,plain,
    X1 = X1,
    inference(equality_inference,[],[754]) ).

cnf(i_0_1114,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[868]) ).

cnf(i_0_1115,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[869]) ).

cnf(i_0_1116,plain,
    X1 = X1,
    inference(equality_inference,[],[870]) ).

cnf(i_0_1117,plain,
    X1 = X1,
    inference(equality_inference,[],[871]) ).

cnf(i_0_1118,plain,
    X1 = X1,
    inference(equality_inference,[],[872]) ).

cnf(i_0_1119,plain,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    inference(equality_inference,[],[920]) ).

cnf(i_0_1120,plain,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    inference(equality_inference,[],[921]) ).

cnf(i_0_1121,plain,
    X1 = X1,
    inference(equality_inference,[],[939]) ).

cnf(i_0_1122,plain,
    X1 = X1,
    inference(equality_inference,[],[961]) ).

cnf(i_0_1123,plain,
    ( ~ c_Com_OWT(X1)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(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(X2,c_Set_Oinsert(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) ),
    inference(scs_inference,[],[i_0_986,i_0_601]) ).

cnf(i_0_1124,plain,
    ( ~ c_Com_OWT(X1)
    | c_Hoare__Mirabelle_Ohoare__derivs(X2,c_Set_Oinsert(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)
    | hBOOL(c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(X2),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)) ),
    inference(scs_inference,[],[i_0_986,i_0_657]) ).

cnf(i_0_1125,plain,
    ( ~ c_Com_OWT(X1)
    | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(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) ),
    inference(scs_inference,[],[i_0_987,i_0_986,i_0_734]) ).

cnf(i_0_1126,plain,
    ( c_Com_OWT(X1)
    | hAPP(c_Com_Obody,X2) != c_Option_Ooption_OSome(X1,tc_Com_Ocom) ),
    inference(scs_inference,[],[i_0_987,i_0_940]) ).

cnf(i_0_1127,plain,
    hAPP(c_Map_Omap__add(X1,c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),v_x) = hAPP(c_Com_Obody,v_x),
    inference(scs_inference,[],[i_0_789,i_0_586]) ).

cnf(i_0_1128,plain,
    ( ~ hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3))
    | hAPP(c_Map_Omap__add(X5,X2,X3,X4),X1) = hAPP(X2,X1) ),
    inference(rename_variables,[],[i_0_586]) ).

cnf(i_0_1129,plain,
    c_Set_Oinsert(hAPP(X1,v_x),c_Set_Oimage(X1,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,X2),X2) = c_Set_Oimage(X1,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,X2),
    inference(scs_inference,[],[i_0_789,i_0_586,i_0_590]) ).

cnf(i_0_1130,plain,
    ( ~ hBOOL(c_in(X1,X2,X3))
    | c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5) ),
    inference(rename_variables,[],[i_0_590]) ).

cnf(i_0_1131,plain,
    c_lessequals(hAPP(X1,v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),X1,tc_Com_Opname,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    inference(scs_inference,[],[i_0_789,i_0_586,i_0_590,i_0_623]) ).

cnf(i_0_1132,plain,
    ( ~ hBOOL(c_in(X1,X2,X3))
    | c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
    inference(rename_variables,[],[i_0_623]) ).

cnf(i_0_1133,plain,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_x)),X1,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_586,i_0_590,i_0_623,i_0_672]) ).

cnf(i_0_1134,plain,
    ( 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) ),
    inference(rename_variables,[],[i_0_672]) ).

cnf(i_0_1135,plain,
    hAPP(c_Com_Obody,v_x) != c_Option_Ooption_ONone(tc_Com_Ocom),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685]) ).

cnf(i_0_1136,plain,
    ( ~ hBOOL(c_in(X1,c_Map_Odom(X2,X3,X4),X3))
    | hAPP(X2,X1) != c_Option_Ooption_ONone(X4) ),
    inference(rename_variables,[],[i_0_685]) ).

cnf(i_0_1137,plain,
    c_Set_Oinsert(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname) = c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826]) ).

cnf(i_0_1138,plain,
    ( ~ hBOOL(c_in(X1,X2,X3))
    | c_Set_Oinsert(X1,X2,X3) = X2 ),
    inference(rename_variables,[],[i_0_826]) ).

cnf(i_0_1139,plain,
    ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852]) ).

cnf(i_0_1140,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,X1,X3)) ),
    inference(rename_variables,[],[i_0_852]) ).

cnf(i_0_1141,plain,
    ~ c_Com_OWT(c_Com_Ocom_OBODY(v_x)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125]) ).

cnf(i_0_1142,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(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) ),
    inference(rename_variables,[],[i_0_1125]) ).

cnf(i_0_1143,plain,
    ~ hBOOL(hAPP(c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),X5)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537]) ).

cnf(i_0_1144,plain,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    inference(rename_variables,[],[i_0_847]) ).

cnf(i_0_1145,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
    inference(rename_variables,[],[i_0_537]) ).

cnf(i_0_1146,plain,
    hBOOL(c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(hAPP(X2,X1),X3,X4),X5,X4),X5)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_766,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557]) ).

cnf(i_0_1147,plain,
    hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
    inference(rename_variables,[],[i_0_766]) ).

cnf(i_0_1148,plain,
    ( ~ hBOOL(c_in(hAPP(X1,X2),X3,X4))
    | hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)) ),
    inference(rename_variables,[],[i_0_557]) ).

cnf(i_0_1149,plain,
    c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,c_Set_Oinsert(X5,X2,X3),X3,X4),tc_fun(X4,tc_bool)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_766,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568]) ).

cnf(i_0_1150,plain,
    ( ~ 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)) ),
    inference(rename_variables,[],[i_0_568]) ).

cnf(i_0_1151,plain,
    c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),c_Set_Ovimage(X1,c_Set_Oinsert(X5,X2,X4),X3,X4),tc_fun(X3,tc_bool)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_766,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569]) ).

cnf(i_0_1152,plain,
    ( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_lessequals(c_Set_Ovimage(X4,X1,X5,X3),c_Set_Ovimage(X4,X2,X5,X3),tc_fun(X5,tc_bool)) ),
    inference(rename_variables,[],[i_0_569]) ).

cnf(i_0_1153,plain,
    hBOOL(hAPP(c_Set_Ovimage(X1,c_Set_Oinsert(hAPP(X1,X2),X3,X4),X5,X6),X2)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_766,i_0_816,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573]) ).

cnf(i_0_1154,plain,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    inference(rename_variables,[],[i_0_816]) ).

cnf(i_0_1155,plain,
    ( ~ hBOOL(hAPP(X1,hAPP(X2,X3)))
    | hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
    inference(rename_variables,[],[i_0_573]) ).

cnf(i_0_1156,plain,
    X1 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_766,i_0_816,i_0_1154,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573,i_0_597]) ).

cnf(i_0_1157,plain,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    inference(rename_variables,[],[i_0_816]) ).

cnf(i_0_1158,plain,
    ( ~ hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3))
    | X3 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
    inference(rename_variables,[],[i_0_597]) ).

cnf(i_0_1159,plain,
    c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_827,i_0_766,i_0_816,i_0_1154,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573,i_0_597,i_0_654]) ).

cnf(i_0_1160,plain,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_827]) ).

cnf(i_0_1161,plain,
    ( ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool))
    | c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
    inference(rename_variables,[],[i_0_654]) ).

cnf(i_0_1162,plain,
    c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_827,i_0_1160,i_0_766,i_0_816,i_0_1154,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573,i_0_597,i_0_654,i_0_655]) ).

cnf(i_0_1163,plain,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_827]) ).

cnf(i_0_1164,plain,
    ( ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool))
    | c_lessequals(X1,X4,tc_fun(X2,tc_bool)) ),
    inference(rename_variables,[],[i_0_655]) ).

cnf(i_0_1165,plain,
    c_lessequals(X1,c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_827,i_0_1160,i_0_766,i_0_816,i_0_1154,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573,i_0_597,i_0_654,i_0_655,i_0_712]) ).

cnf(i_0_1166,plain,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_863]) ).

cnf(i_0_1167,plain,
    ( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    inference(rename_variables,[],[i_0_712]) ).

cnf(i_0_1168,plain,
    c_lessequals(X1,c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_1166,i_0_827,i_0_1160,i_0_766,i_0_816,i_0_1154,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573,i_0_597,i_0_654,i_0_655,i_0_712,i_0_713]) ).

cnf(i_0_1169,plain,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_863]) ).

cnf(i_0_1170,plain,
    ( ~ 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)) ),
    inference(rename_variables,[],[i_0_713]) ).

cnf(i_0_1171,plain,
    ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_1166,i_0_827,i_0_1160,i_0_766,i_0_816,i_0_1154,i_0_750,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573,i_0_597,i_0_654,i_0_655,i_0_712,i_0_713,i_0_727]) ).

cnf(i_0_1172,plain,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
    inference(rename_variables,[],[i_0_727]) ).

cnf(i_0_1173,plain,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1,
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_1166,i_0_827,i_0_1160,i_0_767,i_0_766,i_0_816,i_0_1154,i_0_750,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573,i_0_597,i_0_654,i_0_655,i_0_712,i_0_713,i_0_727,i_0_742]) ).

cnf(i_0_1174,plain,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool)) = X2 ),
    inference(rename_variables,[],[i_0_742]) ).

cnf(i_0_1175,plain,
    c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_1166,i_0_827,i_0_1160,i_0_641,i_0_767,i_0_766,i_0_816,i_0_1154,i_0_750,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573,i_0_597,i_0_654,i_0_655,i_0_712,i_0_713,i_0_727,i_0_742,i_0_854]) ).

cnf(i_0_1176,plain,
    ( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2
    | c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    inference(rename_variables,[],[i_0_854]) ).

cnf(i_0_1177,plain,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_1166,i_0_827,i_0_1160,i_0_641,i_0_767,i_0_766,i_0_816,i_0_1154,i_0_750,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573,i_0_597,i_0_654,i_0_655,i_0_712,i_0_713,i_0_727,i_0_742,i_0_854,i_0_859]) ).

cnf(i_0_1178,plain,
    c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = X4,
    inference(rename_variables,[],[i_0_641]) ).

cnf(i_0_1179,plain,
    ( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    inference(rename_variables,[],[i_0_859]) ).

cnf(i_0_1180,plain,
    ~ c_Com_OWT(c_Com_Ocom_OCall(X1,v_x,X2)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_1166,i_0_827,i_0_1160,i_0_641,i_0_767,i_0_766,i_0_816,i_0_1154,i_0_750,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573,i_0_597,i_0_654,i_0_655,i_0_712,i_0_713,i_0_727,i_0_742,i_0_854,i_0_859,i_0_862]) ).

cnf(i_0_1181,plain,
    ( c_Com_OWT(c_Com_Ocom_OBODY(X1))
    | ~ c_Com_OWT(c_Com_Ocom_OCall(X2,X1,X3)) ),
    inference(rename_variables,[],[i_0_862]) ).

cnf(i_0_1182,plain,
    hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X4)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_1166,i_0_827,i_0_1160,i_0_641,i_0_767,i_0_766,i_0_816,i_0_1154,i_0_1157,i_0_750,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573,i_0_597,i_0_654,i_0_655,i_0_712,i_0_713,i_0_727,i_0_742,i_0_854,i_0_859,i_0_862,i_0_887]) ).

cnf(i_0_1183,plain,
    ( ~ hBOOL(hAPP(X1,X2))
    | hBOOL(c_in(X2,X1,X3)) ),
    inference(rename_variables,[],[i_0_887]) ).

cnf(i_0_1184,plain,
    c_Hoare__Mirabelle_Ohoare__valids(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_1166,i_0_827,i_0_1160,i_0_641,i_0_902,i_0_767,i_0_766,i_0_816,i_0_1154,i_0_1157,i_0_750,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573,i_0_597,i_0_654,i_0_655,i_0_712,i_0_713,i_0_727,i_0_742,i_0_854,i_0_859,i_0_862,i_0_887,i_0_901]) ).

cnf(i_0_1185,plain,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3) ),
    inference(rename_variables,[],[i_0_901]) ).

cnf(i_0_1186,plain,
    ~ hBOOL(hAPP(c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3),X4)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_1166,i_0_827,i_0_1160,i_0_641,i_0_902,i_0_767,i_0_763,i_0_766,i_0_816,i_0_1154,i_0_1157,i_0_750,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573,i_0_597,i_0_654,i_0_655,i_0_712,i_0_713,i_0_727,i_0_742,i_0_854,i_0_859,i_0_862,i_0_887,i_0_901,i_0_920]) ).

cnf(i_0_1187,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X2
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(rename_variables,[],[i_0_920]) ).

cnf(i_0_1188,plain,
    ~ hBOOL(hAPP(c_Option_Othe(c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),X2),X3)),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_1166,i_0_827,i_0_1160,i_0_942,i_0_641,i_0_902,i_0_767,i_0_763,i_0_766,i_0_816,i_0_1154,i_0_1157,i_0_750,i_0_847,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573,i_0_597,i_0_654,i_0_655,i_0_712,i_0_713,i_0_727,i_0_742,i_0_854,i_0_859,i_0_862,i_0_887,i_0_901,i_0_920,i_0_921]) ).

cnf(i_0_1189,plain,
    c_Option_Othe(c_Option_Ooption_OSome(X1,X2),X2) = X1,
    inference(rename_variables,[],[i_0_942]) ).

cnf(i_0_1190,plain,
    ( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(rename_variables,[],[i_0_921]) ).

cnf(i_0_1191,plain,
    c_lessequals(X1,X1,tc_nat),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_1166,i_0_827,i_0_1160,i_0_942,i_0_641,i_0_902,i_0_767,i_0_763,i_0_766,i_0_816,i_0_1154,i_0_1157,i_0_750,i_0_847,i_0_964,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573,i_0_597,i_0_654,i_0_655,i_0_712,i_0_713,i_0_727,i_0_742,i_0_854,i_0_859,i_0_862,i_0_887,i_0_901,i_0_920,i_0_921,i_0_936]) ).

cnf(i_0_1192,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | c_lessequals(X2,X2,X1) ),
    inference(rename_variables,[],[i_0_936]) ).

cnf(i_0_1193,plain,
    c_lessequals(X1,X1,tc_bool),
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_1166,i_0_827,i_0_1160,i_0_942,i_0_641,i_0_902,i_0_767,i_0_763,i_0_766,i_0_816,i_0_1154,i_0_1157,i_0_750,i_0_847,i_0_964,i_0_970,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573,i_0_597,i_0_654,i_0_655,i_0_712,i_0_713,i_0_727,i_0_742,i_0_854,i_0_859,i_0_862,i_0_887,i_0_901,i_0_920,i_0_921,i_0_936,i_0_937]) ).

cnf(i_0_1194,plain,
    ( ~ class_Orderings_Oorder(X1)
    | c_lessequals(X2,X2,X1) ),
    inference(rename_variables,[],[i_0_937]) ).

cnf(i_0_1195,plain,
    $false,
    inference(scs_inference,[],[i_0_670,i_0_789,i_0_863,i_0_1166,i_0_827,i_0_1160,i_0_942,i_0_641,i_0_902,i_0_767,i_0_763,i_0_766,i_0_816,i_0_1154,i_0_1157,i_0_750,i_0_847,i_0_964,i_0_970,i_0_586,i_0_590,i_0_623,i_0_672,i_0_685,i_0_826,i_0_852,i_0_1125,i_0_537,i_0_557,i_0_568,i_0_569,i_0_573,i_0_597,i_0_654,i_0_655,i_0_712,i_0_713,i_0_727,i_0_742,i_0_854,i_0_859,i_0_862,i_0_887,i_0_901,i_0_920,i_0_921,i_0_936,i_0_937,i_0_958]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWV905-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33  % Computer : n022.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 06:08:36 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 1.06/1.67  % Version  : CSE_E---1.7
% 1.06/1.67  % Problem  : theBenchmark.p
% 1.06/1.67  % SZS status Unsatisfiable for theBenchmark.p
% 1.06/1.67  % SZS output start CNFRefutation
% See solution above
% 1.31/1.98  % Total time : 1.325s
%------------------------------------------------------------------------------