CSE_E---1.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SWV913-1 : 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 : n005.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 05:27:43 PM UTC 2026

% Result   : Unsatisfiable 1.26s 1.65s
% Output   : CNFRefutation 1.32s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_522)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_singleton__conv2_0,axiom,
    c_Collect(c_fequal(X1,X2),X2) = hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),
    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,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),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,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2) = hAPP(hAPP(X1,X3),c_Finite__Set_Ofold1(X1,X4,X2))
    | hBOOL(c_in(X3,X4,X2))
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X4,X2)
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
    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_linorder_OMax__singleton_0,axiom,
    ( c_Finite__Set_Ofold1(X4,hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))),X5) = X6
    | ~ c_Orderings_Olinorder(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_OMax__singleton_0) ).

cnf(cls_fold1__singleton_0,axiom,
    c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X3,
    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,hAPP(hAPP(c_Set_Oinsert(X2),X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))) = hAPP(hAPP(X5,X3),X4)
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X6,X7,X8,X5,X9,X10,X11,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).

cnf(cls_complete__lattice_OSup__binary_0,axiom,
    ( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))) = hAPP(hAPP(X5,X3),X4)
    | ~ c_Complete__Lattice_Ocomplete__lattice(X6,X1,X7,X8,X9,X5,X10,X11,X2) ),
    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,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) = X3
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X4,X5,X6,X7,X8,X9,X10,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).

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

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

cnf(cls_complete__lattice_OSup__insert_0,axiom,
    ( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4)) = hAPP(hAPP(X5,X3),hAPP(X1,X4))
    | ~ c_Complete__Lattice_Ocomplete__lattice(X6,X1,X7,X8,X9,X5,X10,X11,X2) ),
    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_conseq_2,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X2,X4,X3,X5,X6)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_2) ).

cnf(cls_hoare__derivs_Ointros_I6_J_2,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X2,X4,X3,X5,X6)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).

cnf(cls_hoare__derivs_Ointros_I6_J_1,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X5,X6),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X2,X4,X3,X7,X5)))
    | ~ hBOOL(hAPP(hAPP(X7,X6),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X2,X4,X3)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X7,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).

cnf(cls_conseq_1,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X5,X6),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X2,X4,X3,X7,X5)))
    | ~ hBOOL(hAPP(hAPP(X7,X6),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X2,X4,X3)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X7,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_1) ).

cnf(cls_conseq12_2,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq12__1(X2,X5,X4,X6)),v_sko__Hoare__Mirabelle__Xconseq12__3(X2,X5,X4,X6)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_2) ).

cnf(cls_Comp_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OSemi(X4,X5),X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X7,X5,X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comp_0) ).

cnf(cls_conseq12_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq12__1(X2,X5,X4,X6)),v_sko__Hoare__Mirabelle__Xconseq12__2(X2,X5,X4,X6)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_0) ).

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

cnf(cls_conseq12_1,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X5,X6),v_sko__Hoare__Mirabelle__Xconseq12__3(X2,X7,X4,X5)))
    | ~ hBOOL(hAPP(hAPP(X7,X6),v_sko__Hoare__Mirabelle__Xconseq12__2(X2,X7,X4,X5)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X7,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_1) ).

cnf(cls_conseq2_1,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq2__1(X4,X5)),v_sko__Hoare__Mirabelle__Xconseq2__2(X4,X5)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq2_1) ).

cnf(cls_conseq1_1,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq1__1(X2,X5)),v_sko__Hoare__Mirabelle__Xconseq1__2(X2,X5)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq1_1) ).

cnf(cls_conseq1_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X2,X5)),v_sko__Hoare__Mirabelle__Xconseq1__2(X2,X5)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq1_0) ).

cnf(cls_conseq2_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq2__1(X4,X5)),v_sko__Hoare__Mirabelle__Xconseq2__2(X4,X5)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq2_0) ).

cnf(cls_escape_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xescape__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xescape__2(X1,X2,X4,X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_escape_0) ).

cnf(cls_conseq_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X2,X4,X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_0) ).

cnf(cls_hoare__derivs_Ointros_I6_J_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X2,X4,X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).

cnf(cls_image__image_0,axiom,
    hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X4,X5,X2),X6)) = hAPP(c_Set_Oimage(c_COMBB(X1,X4,X2,X3,X5),X5,X3),X6),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__image_0) ).

cnf(cls_inj__on__insert_1,axiom,
    ( ~ hBOOL(c_in(hAPP(X1,X2),hAPP(c_Set_Oimage(X1,X3,X4),c_HOL_Ominus__class_Ominus(X5,hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X4))
    | ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X3),X2),X5),X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).

cnf(cls_inj__on__Un_3,axiom,
    ( c_Fun_Oinj__on(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X3,X1)
    | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(c_Set_Oimage(X2,X3,X1),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X3,tc_bool)))),hAPP(c_Set_Oimage(X2,X3,X1),c_HOL_Ominus__class_Ominus(X5,X4,tc_fun(X3,tc_bool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ c_Fun_Oinj__on(X2,X5,X3,X1)
    | ~ c_Fun_Oinj__on(X2,X4,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).

cnf(cls_UN__simps_I3_J_1,axiom,
    ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X5),X5,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X5,tc_fun(X2,tc_bool)))
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__simps_I3_J_1) ).

cnf(cls_UN__extend__simps_I3_J_1,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,tc_fun(X1,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool),X5),X5,tc_fun(X1,tc_bool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_1) ).

cnf(cls_UN__simps_I5_J_0,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X5),X5,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X5,tc_fun(X2,tc_bool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__simps_I5_J_0) ).

cnf(cls_UN__extend__simps_I5_J_0,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,tc_fun(X1,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool),X5),X5,tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I5_J_0) ).

cnf(cls_Int__UN__distrib_0,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,tc_fun(X1,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool),X5),X5,tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__UN__distrib_0) ).

cnf(cls_inj__on__insert_2,axiom,
    ( c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2,X5)
    | hBOOL(c_in(hAPP(X1,X3),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))),X5))
    | ~ c_Fun_Oinj__on(X1,X4,X2,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).

cnf(cls_vimage__UN_0,axiom,
    hAPP(c_Set_Ovimage(X1,X2,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X5,X6,tc_fun(X3,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBB(c_Set_Ovimage(X1,X2,X3),X5,tc_fun(X3,tc_bool),tc_fun(X2,tc_bool),X6),X6,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__UN_0) ).

cnf(cls_image__UN_0,axiom,
    hAPP(c_Set_Oimage(X1,X2,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X5,X6,tc_fun(X2,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBB(c_Set_Oimage(X1,X2,X3),X5,tc_fun(X2,tc_bool),tc_fun(X3,tc_bool),X6),X6,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__UN_0) ).

cnf(cls_UN__insert__distrib_0,axiom,
    ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Set_Oinsert(X2),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X5),X5,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X5,tc_fun(X2,tc_bool)))
    | ~ hBOOL(c_in(X6,X1,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__insert__distrib_0) ).

cnf(cls_UN__simps_I1_J_1,axiom,
    ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Set_Oinsert(X2),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X5),X5,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X5,tc_fun(X2,tc_bool)))
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__simps_I1_J_1) ).

cnf(cls_UN__extend__simps_I1_J_1,axiom,
    ( hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,tc_fun(X1,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_COMBB(hAPP(c_Set_Oinsert(X1),X2),X4,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool),X5),X5,tc_fun(X1,tc_bool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_1) ).

cnf(cls_UN__extend__simps_I10_J_0,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(X2,X3,X4,tc_fun(X5,tc_bool),X6),X6,tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X3,X6,X4),X1),X2,X4,tc_fun(X5,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I10_J_0) ).

cnf(cls_UN__simps_I10_J_0,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X1,X2,X3),X4),X5,X3,tc_fun(X6,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBB(X5,X1,X3,tc_fun(X6,tc_bool),X2),X2,tc_fun(X6,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__simps_I10_J_0) ).

cnf(cls_UN__simps_I3_J_0,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),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_UN__simps_I3_J_0) ).

cnf(cls_UN__simps_I1_J_0,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_COMBB(hAPP(c_Set_Oinsert(X2),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),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_UN__simps_I1_J_0) ).

cnf(cls_inj__on__Un_2,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(c_Set_Oimage(X2,X3,X1),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X3,tc_bool)))),hAPP(c_Set_Oimage(X2,X3,X1),c_HOL_Ominus__class_Ominus(X5,X4,tc_fun(X3,tc_bool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ c_Fun_Oinj__on(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).

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

cnf(cls_fun__left__comm__idem_Ofun__left__comm__idem__apply_0,axiom,
    ( c_Finite__Set_Ofun__left__comm__idem(c_COMBB(X1,X2,X3,tc_fun(X4,X4),X5),X5,X4)
    | ~ c_Finite__Set_Ofun__left__comm__idem(X1,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm__idem_Ofun__left__comm__idem__apply_0) ).

cnf(cls_COMBB__def_0,axiom,
    hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).

cnf(cls_hoare__derivs_OSkip_0,axiom,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OSKIP,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).

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

cnf(cls_vimage__singleton__eq_0,axiom,
    ( hAPP(X1,X2) = X3
    | ~ hBOOL(c_in(X2,hAPP(c_Set_Ovimage(X1,X4,X5),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)))),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).

cnf(cls_order_OatLeastatMost__subset__iff_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X3),X4))
    | ~ c_lessequals(c_SetInterval_Oord_OatLeastAtMost(X1,X3,X4,X5),c_SetInterval_Oord_OatLeastAtMost(X1,X2,X6,X5),tc_fun(X5,tc_bool))
    | ~ c_Orderings_Oorder(X1,X7,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_OatLeastatMost__subset__iff_0) ).

cnf(cls_order_OatLeastatMost__subset__iff_1,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X4),X2))
    | ~ c_lessequals(c_SetInterval_Oord_OatLeastAtMost(X1,X4,X2,X5),c_SetInterval_Oord_OatLeastAtMost(X1,X6,X3,X5),tc_fun(X5,tc_bool))
    | ~ c_Orderings_Oorder(X1,X7,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_OatLeastatMost__subset__iff_1) ).

cnf(cls_vimage__insert_0,axiom,
    hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X3),X4),X5)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))),hAPP(c_Set_Ovimage(X1,X2,X3),X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__insert_0) ).

cnf(cls_inj__on__image__Int_0,axiom,
    ( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X4),X5)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5))
    | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
    | ~ c_lessequals(X4,X6,tc_fun(X2,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X6,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).

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

cnf(cls_vimage__singleton__eq_1,axiom,
    hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))),X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).

cnf(cls_ord_OatLeastAtMost__iff_1,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(c_in(X2,c_SetInterval_Oord_OatLeastAtMost(X1,X4,X3,X5),X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_1) ).

cnf(cls_ord_OatLeastAtMost__iff_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(c_in(X3,c_SetInterval_Oord_OatLeastAtMost(X1,X2,X4,X5),X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_0) ).

cnf(cls_image__diff__subset_0,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X1,X2,X3),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5),tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X2,tc_bool))),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).

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

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

cnf(cls_fold1Set__sing_0,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),X4),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_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_inj__on__image__set__diff_0,axiom,
    ( hAPP(c_Set_Oimage(X1,X2,X3),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X2,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X1,X2,X3),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
    | ~ c_lessequals(X4,X6,tc_fun(X2,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X6,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).

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

cnf(cls_Un__Int__distrib_0,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(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)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),
    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),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),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)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib_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_order_OatLeastatMost__subset__iff_3,axiom,
    ( c_lessequals(c_SetInterval_Oord_OatLeastAtMost(X1,X2,X3,X4),c_SetInterval_Oord_OatLeastAtMost(X1,X5,X6,X4),tc_fun(X4,tc_bool))
    | ~ hBOOL(hAPP(hAPP(X1,X3),X6))
    | ~ hBOOL(hAPP(hAPP(X1,X5),X2))
    | ~ c_Orderings_Oorder(X1,X7,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_OatLeastatMost__subset__iff_3) ).

cnf(cls_subset__insert__iff_3,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
    | ~ hBOOL(c_in(X3,X1,X2))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

cnf(cls_diff__single__insert_0,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
    | ~ hBOOL(c_in(X3,X1,X2))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).

cnf(cls_ord_OatLeastAtMost__iff_2,axiom,
    ( hBOOL(c_in(X1,c_SetInterval_Oord_OatLeastAtMost(X2,X3,X4,X5),X5))
    | ~ hBOOL(hAPP(hAPP(X2,X1),X4))
    | ~ hBOOL(hAPP(hAPP(X2,X3),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_2) ).

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

cnf(cls_subset__insert__iff_4,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).

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

cnf(cls_vimage__Un_0,axiom,
    hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Un_0) ).

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

cnf(cls_image__Un_0,axiom,
    hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X4),X5)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Un_0) ).

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

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_order_OatLeastatMost__subset__iff_2,axiom,
    ( c_lessequals(c_SetInterval_Oord_OatLeastAtMost(X1,X2,X3,X4),c_SetInterval_Oord_OatLeastAtMost(X1,X5,X6,X4),tc_fun(X4,tc_bool))
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_Orderings_Oorder(X1,X7,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_OatLeastatMost__subset__iff_2) ).

cnf(cls_inj__on__Un__image__eq__iff_0,axiom,
    ( X4 = X5
    | hAPP(c_Set_Oimage(X1,X2,X3),X4) != hAPP(c_Set_Oimage(X1,X2,X3),X5)
    | ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X4),X5),X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_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_UN__absorb_0,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(X2,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X2,X5,tc_fun(X1,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X2,X5,tc_fun(X1,tc_bool))
    | ~ hBOOL(c_in(X3,X4,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__absorb_0) ).

cnf(cls_Un__assoc_0,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

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_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_UN__insert_0,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,X1,tc_fun(X5,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),hAPP(X4,X2)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__insert_0) ).

cnf(cls_subset__insert__iff_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
    | ~ hBOOL(c_in(X3,X1,X2))
    | ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_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_vimageD_0,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),X3,X4))
    | ~ hBOOL(c_in(X2,hAPP(c_Set_Ovimage(X1,X5,X4),X3),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,hAPP(c_Set_Ovimage(X1,X5,X4),X3),X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageE_0) ).

cnf(cls_inj__on__Un_0,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X5),X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).

cnf(cls_inj__on__Un_1,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X5),X2),X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).

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

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

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

cnf(cls_endo__inj__surj_0,axiom,
    ( hAPP(c_Set_Oimage(X1,X2,X2),X3) = X3
    | ~ c_Fun_Oinj__on(X1,X3,X2,X2)
    | ~ c_lessequals(hAPP(c_Set_Oimage(X1,X2,X2),X3),X3,tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_endo__inj__surj_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_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_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_sup1E_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X3,X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),X1),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_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__Diff_0,axiom,
    c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X1,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_0) ).

cnf(cls_Diff__Un_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(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_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool))),c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Un_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)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool))),c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int_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(hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2)
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).

cnf(cls_Un__mono_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(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_Un__mono_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_vimage__code_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X2,X4,X5),X1),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_0) ).

cnf(cls_conjecture_0,negated_conjecture,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_Int__insert__left_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4) = hAPP(hAPP(c_Set_Oinsert(X1),X2),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_0) ).

cnf(cls_Un__left__commute_0,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_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_UnCI_1,axiom,
    ( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2))
    | ~ hBOOL(c_in(X1,X3,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).

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

cnf(cls_hoare__derivs_Oinsert_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).

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

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

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

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

cnf(cls_vimage__Diff_0,axiom,
    hAPP(c_Set_Ovimage(X1,X2,X3),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X3,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(X1,X2,X3),X4),hAPP(c_Set_Ovimage(X1,X2,X3),X5),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Diff_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_singletonE_0,axiom,
    ( X1 = X2
    | ~ hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).

cnf(cls_Diff__insert2_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_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_imageI_0,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),hAPP(c_Set_Oimage(X1,X3,X4),X5),X4))
    | ~ hBOOL(c_in(X2,X5,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).

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

cnf(cls_image__iff_2,axiom,
    ( hBOOL(c_in(hAPP(X4,X1),hAPP(c_Set_Oimage(X4,X3,X5),X2),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),hAPP(c_Set_Oimage(X4,X3,X5),X2),X5))
    | ~ hBOOL(c_in(X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

cnf(cls_doubleton__eq__iff_0,axiom,
    ( X2 = X5
    | X2 = X4
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

cnf(cls_doubleton__eq__iff_1,axiom,
    ( X3 = X4
    | X2 = X4
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

cnf(cls_doubleton__eq__iff_2,axiom,
    ( X2 = X5
    | X3 = X5
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

cnf(cls_doubleton__eq__iff_3,axiom,
    ( X3 = X4
    | X3 = X5
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

cnf(cls_finite__imageD_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Fun_Oinj__on(X3,X1,X2,X4)
    | ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X3,X2,X4),X1),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__imageD_0) ).

cnf(cls_Diff__subset__conv_1,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

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

cnf(cls_inj__on__insert_0,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X3),X5),X2),X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).

cnf(cls_image__vimage__subset_0,axiom,
    c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),X4,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).

cnf(cls_insert__Diff_0,axiom,
    ( hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))) = X3
    | ~ hBOOL(c_in(X2,X3,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

cnf(cls_inj__on__diff_0,axiom,
    ( c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).

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

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

cnf(cls_inj__onD_0,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6)
    | ~ hBOOL(c_in(X3,X4,X5))
    | ~ hBOOL(c_in(X2,X4,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__onD_0) ).

cnf(cls_inj__on__def_0,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ hBOOL(c_in(X3,X4,X5))
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__def_0) ).

cnf(cls_inj__on__iff_0,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ hBOOL(c_in(X3,X4,X5))
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).

cnf(cls_inj__on__contraD_0,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ hBOOL(c_in(X3,X4,X5))
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).

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_finite__surj__inj_0,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X3)
    | ~ c_lessequals(X2,hAPP(c_Set_Oimage(X1,X3,X3),X2),tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__surj__inj_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_subset__inj__on_0,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X5,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).

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

cnf(cls_Un__Diff__Int_0,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).

cnf(cls_Diff__subset__conv_0,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_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_Un__insert__left_0,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_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_derivs__insertD_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_0) ).

cnf(cls_vimage__mono_0,axiom,
    ( c_lessequals(hAPP(c_Set_Ovimage(X1,X2,X3),X4),hAPP(c_Set_Ovimage(X1,X2,X3),X5),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__mono_0) ).

cnf(cls_image__mono_0,axiom,
    ( c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X4,X5,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__mono_0) ).

cnf(cls_subset__image__iff_2,axiom,
    ( c_lessequals(hAPP(c_Set_Oimage(X4,X3,X5),X1),hAPP(c_Set_Oimage(X4,X3,X5),X2),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_insert__Diff__single_0,axiom,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__single_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_sup1CI_1,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
    | ~ hBOOL(hAPP(X2,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).

cnf(cls_sup1CI_0,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
    | ~ hBOOL(hAPP(X3,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).

cnf(cls_Un__subset__iff_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),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(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1),X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

cnf(cls_Int__subset__iff_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,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_order_OatLeastatMost__empty__iff2_0,axiom,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord_OatLeastAtMost(X2,X3,X4,X1)
    | ~ c_Orderings_Oorder(X2,X5,X1)
    | ~ hBOOL(hAPP(hAPP(X2,X3),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_OatLeastatMost__empty__iff2_0) ).

cnf(cls_order_OatLeastatMost__empty__iff_0,axiom,
    ( c_SetInterval_Oord_OatLeastAtMost(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | ~ c_Orderings_Oorder(X1,X5,X4)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_OatLeastatMost__empty__iff_0) ).

cnf(cls_insert__image_0,axiom,
    ( hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X2,X4,X1),X5)) = hAPP(c_Set_Oimage(X2,X4,X1),X5)
    | ~ hBOOL(c_in(X3,X5,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).

cnf(cls_vimage__code_1,axiom,
    ( hBOOL(hAPP(hAPP(c_Set_Ovimage(X1,X2,X3),X4),X5))
    | ~ hBOOL(hAPP(X4,hAPP(X1,X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_1) ).

cnf(cls_finite__Diff__insert_1,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).

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_sup__inf__distrib2_0,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).

cnf(cls_inf__sup__distrib2_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib2_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_Diff__insert_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,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,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).

cnf(cls_insert__is__Un_0,axiom,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

cnf(cls_Un__least_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool))
    | ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).

cnf(cls_Un__subset__iff_2,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool))
    | ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

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_Int__insert__left_1,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),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__cancel2_0,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

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

cnf(cls_Inf__binary_0,axiom,
    ( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),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_Un__insert__right_0,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

cnf(cls_subset__singletonD_0,axiom,
    ( X1 = hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

cnf(cls_Un__left__absorb_0,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_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_image__insert_0,axiom,
    hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),X5)) = hAPP(hAPP(c_Set_Oinsert(X3),hAPP(X1,X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).

cnf(cls_finite__surj_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_lessequals(X1,hAPP(c_Set_Oimage(X3,X4,X2),X5),tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X5,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__surj_0) ).

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

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

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

cnf(cls_doubleton__eq__iff_4,axiom,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

cnf(cls_Int__insert__right_1,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = 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_Diff__insert__absorb_0,axiom,
    ( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)) = X3
    | hBOOL(c_in(X2,X3,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

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

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

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

cnf(cls_order_OatLeastatMost__empty_0,axiom,
    ( c_SetInterval_Oord_OatLeastAtMost(X1,X2,X3,X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | ~ hBOOL(hAPP(hAPP(X5,X3),X2))
    | ~ c_Orderings_Oorder(X1,X5,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_OatLeastatMost__empty_0) ).

cnf(cls_finite__Un_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),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(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_1) ).

cnf(cls_insert__subset_2,axiom,
    ( c_lessequals(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,tc_fun(X1,tc_bool))
    | ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool))
    | ~ hBOOL(c_in(X2,X4,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).

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_subset__insert_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | hBOOL(c_in(X4,X1,X3))
    | ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),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,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

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_order_OatLeastatMost__empty__iff2_1,axiom,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord_OatLeastAtMost(X2,X3,X4,X1)
    | hBOOL(hAPP(hAPP(X2,X3),X4))
    | ~ c_Orderings_Oorder(X2,X5,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_OatLeastatMost__empty__iff2_1) ).

cnf(cls_order_OatLeastatMost__empty__iff_1,axiom,
    ( c_SetInterval_Oord_OatLeastAtMost(X1,X2,X3,X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_Orderings_Oorder(X1,X5,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_OatLeastatMost__empty__iff_1) ).

cnf(cls_Un__Diff__cancel_0,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).

cnf(cls_order_OatLeastAtMost__singleton_0,axiom,
    ( c_SetInterval_Oord_OatLeastAtMost(X1,X2,X2,X3) = hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))
    | ~ c_Orderings_Oorder(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_OatLeastAtMost__singleton_0) ).

cnf(cls_insert__Diff1_0,axiom,
    ( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))
    | ~ hBOOL(c_in(X2,X4,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

cnf(cls_sup__fun__eq_0,axiom,
    ( hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__fun__eq_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_single__Diff__lessThan_0,axiom,
    ( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_SetInterval_Oord__class_OlessThan(X2,X1),tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__Diff__lessThan_0) ).

cnf(cls_Diff__partition_0,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = X3
    | ~ c_lessequals(X2,X3,tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__partition_0) ).

cnf(cls_sup__assoc_0,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

cnf(cls_inf__sup__aci_I6_J_0,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_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_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_subset__insert_1,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
    | hBOOL(c_in(X3,X1,X2))
    | ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).

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

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_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_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__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_insert__mono_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),tc_fun(X1,tc_bool))
    | ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).

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

cnf(cls_insert__subset_0,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),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(X2,X4,X1))
    | hBOOL(c_in(X2,X3,X1))
    | X3 = X4
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_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_derivs__insertD_1,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X4),X2),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).

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_comm__monoid__add_Ononempty__iff_1,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1(X1,X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2(X1,X2),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_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_Un__upper1_0,axiom,
    c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

cnf(cls_Un__upper2_0,axiom,
    c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

cnf(cls_insert__subset_1,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).

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_order_Oantisym__conv_0,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(X3,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ c_Orderings_Oorder(X3,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Oantisym__conv_0) ).

cnf(cls_order_Oantisym_0,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ hBOOL(hAPP(hAPP(X3,X1),X2))
    | ~ c_Orderings_Oorder(X3,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Oantisym_0) ).

cnf(cls_order_Oeq__iff_2,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ hBOOL(hAPP(hAPP(X3,X1),X2))
    | ~ c_Orderings_Oorder(X3,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Oeq__iff_2) ).

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_finite__UnI_0,axiom,
    ( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1)
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UnI_0) ).

cnf(cls_finite__Un_2,axiom,
    ( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1)
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_2) ).

cnf(cls_linorder_Oantisym__conv2_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
    | ~ c_Orderings_Olinorder(X1,X3,X4)
    | ~ hBOOL(hAPP(hAPP(X3,X2),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv2_1) ).

cnf(cls_linorder_Onot__le_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X4,X3),X2))
    | ~ c_Orderings_Olinorder(X1,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__le_1) ).

cnf(cls_linorder_Onot__less__iff__gr__or__eq_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ c_Orderings_Olinorder(X4,X1,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__less__iff__gr__or__eq_1) ).

cnf(cls_linorder_OleD_0,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X4,X3),X2))
    | ~ c_Orderings_Olinorder(X4,X1,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_OleD_0) ).

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__sup__iff_2,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),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_sup__least_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),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__supI_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),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_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_ivl__disj__int_I4_J_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__int_I4_J_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_singleton__inject_0,axiom,
    ( X2 = X3
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

cnf(cls_Un__empty_2,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),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_Un__empty_2) ).

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_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_sup__left__commute_0,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

cnf(cls_inf__sup__aci_I7_J_0,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_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_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_insertCI_1,axiom,
    hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X1),X3),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).

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

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

cnf(cls_le__supE_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4),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(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4),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(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X2),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(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X2),X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

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_insert__commute_0,axiom,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_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_subset__Un__eq_1,axiom,
    ( c_lessequals(X2,X3,tc_fun(X1,tc_bool))
    | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

cnf(cls_subset__insertI2_0,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

cnf(cls_linorder_Oantisym__conv2_0,axiom,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(X3,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X4,X1),X2))
    | ~ c_Orderings_Olinorder(X4,X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv2_0) ).

cnf(cls_order_Ole__less_0,axiom,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(X3,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X4,X1),X2))
    | ~ c_Orderings_Oorder(X4,X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Ole__less_0) ).

cnf(cls_linorder_Oantisym__conv1_0,axiom,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(X4,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X3,X1),X2))
    | ~ c_Orderings_Olinorder(X3,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv1_0) ).

cnf(cls_order_Oless__le_2,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | X2 = X3
    | ~ hBOOL(hAPP(hAPP(X4,X2),X3))
    | ~ c_Orderings_Oorder(X4,X1,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Oless__le_2) ).

cnf(cls_order_Ole__neq__trans_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | X2 = X3
    | ~ hBOOL(hAPP(hAPP(X4,X2),X3))
    | ~ c_Orderings_Oorder(X4,X1,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Ole__neq__trans_0) ).

cnf(cls_order_Oneq__le__trans_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | X2 = X3
    | ~ hBOOL(hAPP(hAPP(X4,X2),X3))
    | ~ c_Orderings_Oorder(X4,X1,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Oneq__le__trans_0) ).

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_inj__on__empty_0,axiom,
    c_Fun_Oinj__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).

cnf(cls_order_Ole__less_1,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X4,X2),X3))
    | ~ c_Orderings_Oorder(X1,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Ole__less_1) ).

cnf(cls_Un__empty_0,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(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_Un__empty_0) ).

cnf(cls_Un__empty_1,axiom,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(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_Un__empty_1) ).

cnf(cls_Un__commute_0,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).

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_insert__code_2,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4))
    | ~ hBOOL(hAPP(X3,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).

cnf(cls_weaken_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_lessequals(X2,X4,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_weaken_0) ).

cnf(cls_thin_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_lessequals(X4,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_thin_0) ).

cnf(cls_finite__imageI_0,axiom,
    ( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X1,X2,X3),X4),X3)
    | ~ c_Finite__Set_Ofinite(X4,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__imageI_0) ).

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_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_Un__absorb2_0,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = X2
    | ~ c_lessequals(X3,X2,tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

cnf(cls_Un__absorb1_0,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = X3
    | ~ c_lessequals(X2,X3,tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_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_lessThan__subset__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OlessThan(X2,X1),c_SetInterval_Oord__class_OlessThan(X3,X1),tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__subset__iff_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_image__is__empty_0,axiom,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | hAPP(c_Set_Oimage(X1,X2,X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

cnf(cls_empty__is__image_0,axiom,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(c_Set_Oimage(X2,X3,X1),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

cnf(cls_ab__semigroup__mult_Ononempty__iff_2,axiom,
    ( hBOOL(c_in(X2,X3,X1))
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,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_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_linorder_Oantisym__conv3_0,axiom,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(X3,X1),X2))
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ c_Orderings_Olinorder(X4,X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv3_0) ).

cnf(cls_linorder_Onot__less__iff__gr__or__eq_0,axiom,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | hBOOL(hAPP(hAPP(X3,X1),X2))
    | ~ c_Orderings_Olinorder(X4,X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__less__iff__gr__or__eq_0) ).

cnf(cls_linorder_Oless__linear_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | X3 = X2
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ c_Orderings_Olinorder(X4,X1,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oless__linear_0) ).

cnf(cls_linorder_OneqE_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | X3 = X2
    | ~ c_Orderings_Olinorder(X4,X1,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_OneqE_0) ).

cnf(cls_linorder_Olinear_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ c_Orderings_Olinorder(X1,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Olinear_0) ).

cnf(cls_linorder_Oantisym__conv1_1,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X2))
    | hBOOL(hAPP(hAPP(X3,X2),X2))
    | ~ c_Orderings_Olinorder(X3,X1,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv1_1) ).

cnf(cls_linorder_OleI_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(X4,X3),X2))
    | ~ c_Orderings_Olinorder(X1,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_OleI_0) ).

cnf(cls_linorder_Onot__leE_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(X4,X3),X2))
    | ~ c_Orderings_Olinorder(X4,X1,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__leE_0) ).

cnf(cls_linorder_Onot__le_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(X4,X3),X2))
    | ~ c_Orderings_Olinorder(X4,X1,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__le_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_le__supI1_0,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4),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,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4),X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).

cnf(cls_Un__empty__left_0,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_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_fun__left__comm__idem_Ofun__left__idem_0,axiom,
    ( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X2),X3)) = hAPP(hAPP(X1,X2),X3)
    | ~ c_Finite__Set_Ofun__left__comm__idem(X1,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm__idem_Ofun__left__idem_0) ).

cnf(cls_le__funD_0,axiom,
    ( c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1)
    | ~ class_HOL_Oord(X1)
    | ~ c_lessequals(X2,X4,tc_fun(X5,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).

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

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

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_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_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_Min__singleton_0,axiom,
    ( c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),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(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),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(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),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(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__singleton_0) ).

cnf(cls_insert__absorb_0,axiom,
    ( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3
    | ~ hBOOL(c_in(X2,X3,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_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_lessThan__subset__iff_1,axiom,
    ( c_lessequals(c_SetInterval_Oord__class_OlessThan(X2,X1),c_SetInterval_Oord__class_OlessThan(X3,X1),tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__subset__iff_1) ).

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_contents__eq_0,axiom,
    c_Set_Ocontents(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_contents__eq_0) ).

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

cnf(cls_linorder_Onot__less__iff__gr__or__eq_2,axiom,
    ( ~ c_Orderings_Olinorder(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X2,X4),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__less__iff__gr__or__eq_2) ).

cnf(cls_linorder_Oneq__iff_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
    | ~ c_Orderings_Olinorder(X3,X1,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oneq__iff_1) ).

cnf(cls_order_Oless__le_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
    | ~ c_Orderings_Oorder(X3,X1,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Oless__le_1) ).

cnf(cls_sup__left__idem_0,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

cnf(cls_inf__sup__aci_I8_J_0,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_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_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_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_insert__absorb2_0,axiom,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_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_Sup__insert_0,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,X1))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__insert_0) ).

cnf(cls_Inf__insert_0,axiom,
    ( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),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_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_vimage__empty_0,axiom,
    hAPP(c_Set_Ovimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__empty_0) ).

cnf(cls_image__empty_0,axiom,
    hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__empty_0) ).

cnf(cls_empty__is__image_1,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Set_Oimage(X2,X3,X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).

cnf(cls_finite__insert_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_0) ).

cnf(cls_Un__empty__right_0,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

cnf(cls_asm_0,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_lessequals(X2,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_asm_0) ).

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_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_subset__insertI_0,axiom,
    c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

cnf(cls_order_Oeq__iff_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X4),X4))
    | ~ c_Orderings_Oorder(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order_Oeq__iff_0) ).

cnf(cls_atLeastAtMost__singleton_0,axiom,
    ( c_SetInterval_Oord__class_OatLeastAtMost(X2,X2,X1) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_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_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__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_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_sup__ge1_0,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

cnf(cls_inf__sup__ord_I3_J_0,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

cnf(cls_sup__ge2_0,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2),X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

cnf(cls_inf__sup__ord_I4_J_0,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

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

cnf(cls_inf__sup__absorb_0,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_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_comm__monoid__add_Ononempty__iff_0,axiom,
    ( X1 = hAPP(hAPP(c_Set_Oinsert(X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1(X1,X2)),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2(X1,X2))
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_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_sup__absorb1_0,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = 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,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = 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__sup_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

cnf(cls_le__iff__inf_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | 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_Un__absorb_0,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X2) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

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_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_finite__insert_1,axiom,
    ( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1)
    | ~ c_Finite__Set_Ofinite(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_1) ).

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_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_insert__not__empty_0,axiom,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

cnf(cls_empty__not__insert_0,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_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_sup__commute_0,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).

cnf(cls_inf__sup__aci_I5_J_0,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_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_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_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_sup__eq__bot__eq1_0,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != 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)
    | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != c_Orderings_Obot__class_Obot(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

cnf(cls_fun__left__comm__idem__insert_0,axiom,
    c_Finite__Set_Ofun__left__comm__idem(c_Set_Oinsert(X1),X1,tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm__idem__insert_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_sup__bot__left_0,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_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_fun__left__comm__idem__sup_0,axiom,
    ( c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(X1),X1,X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm__idem__sup_0) ).

cnf(cls_fun__left__comm__idem__inf_0,axiom,
    ( c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(X1),X1,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm__idem__inf_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_sup__bot__right_0,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_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_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_sup__idem_0,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_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_lessThan__eq__iff_0,axiom,
    ( X2 = X3
    | ~ class_Orderings_Olinorder(X1)
    | c_SetInterval_Oord__class_OlessThan(X2,X1) != c_SetInterval_Oord__class_OlessThan(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__eq__iff_0) ).

cnf(cls_com_Osimps_I3_J_0,axiom,
    ( X1 = X3
    | c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSemi(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).

cnf(cls_com_Osimps_I3_J_1,axiom,
    ( X2 = X4
    | c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSemi(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).

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(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__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__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(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__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__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_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__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__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(cls_com_Osimps_I13_J_0,axiom,
    c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).

cnf(cls_com_Osimps_I12_J_0,axiom,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_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_bool__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

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

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__Lattices_Olower__semilattice,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__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_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_bool__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

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(i_0_521,axiom,
    c_Collect(c_fequal(X1,X2),X2) = hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),
    cls_singleton__conv2_0 ).

cnf(i_0_522,axiom,
    c_Collect(X1,X2) = X1,
    cls_Collect__def_0 ).

cnf(i_0_523,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,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),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_524,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_525,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_526,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_527,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_528,axiom,
    ( c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2) = hAPP(hAPP(X1,X3),c_Finite__Set_Ofold1(X1,X4,X2))
    | hBOOL(c_in(X3,X4,X2))
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X4,X2)
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
    cls_ab__semigroup__mult_Ofold1__insert_0 ).

cnf(i_0_529,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_530,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(c_fequal(X1,X3),X2)) ),
    cls_ATP__Linkup_Ofequal__imp__equal_0 ).

cnf(i_0_531,plain,
    c_fequal(X1,X2) = hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),
    inference(rw,[status(thm)],[i_0_521,c_0_522]) ).

cnf(i_0_532,axiom,
    ( c_Finite__Set_Ofold1(X4,hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))),X5) = X6
    | ~ c_Orderings_Olinorder(X1,X2,X3) ),
    cls_linorder_OMax__singleton_0 ).

cnf(i_0_533,axiom,
    c_Finite__Set_Ofold1(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X3,
    cls_fold1__singleton_0 ).

cnf(i_0_534,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_535,axiom,
    hBOOL(hAPP(c_fequal(X1,X2),X1)),
    cls_ATP__Linkup_Oequal__imp__fequal_0 ).

cnf(i_0_536,axiom,
    c_The(c_fequal(X1,X2),X2) = X1,
    cls_the__sym__eq__trivial_0 ).

cnf(i_0_537,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,c_Collect(X1,X3),X3)) ),
    cls_CollectD_0 ).

cnf(i_0_538,axiom,
    ( hBOOL(c_in(X1,c_Collect(X2,X3),X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    cls_CollectI_0 ).

cnf(i_0_539,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_540,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_541,axiom,
    ( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))) = hAPP(hAPP(X5,X3),X4)
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X6,X7,X8,X5,X9,X10,X11,X2) ),
    cls_complete__lattice_OInf__binary_0,
    [final] ).

cnf(i_0_542,axiom,
    ( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))) = hAPP(hAPP(X5,X3),X4)
    | ~ c_Complete__Lattice_Ocomplete__lattice(X6,X1,X7,X8,X9,X5,X10,X11,X2) ),
    cls_complete__lattice_OSup__binary_0,
    [final] ).

cnf(i_0_543,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_544,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_545,axiom,
    ( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) = X3
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X4,X5,X6,X7,X8,X9,X10,X2) ),
    cls_complete__lattice_OInf__singleton_0,
    [final] ).

cnf(i_0_546,axiom,
    ( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) = X3
    | ~ c_Complete__Lattice_Ocomplete__lattice(X4,X1,X5,X6,X7,X8,X9,X10,X2) ),
    cls_complete__lattice_OSup__singleton_0,
    [final] ).

cnf(i_0_547,axiom,
    ( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4)) = hAPP(hAPP(X5,X3),hAPP(X1,X4))
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X6,X7,X8,X5,X9,X10,X11,X2) ),
    cls_complete__lattice_OInf__insert_0,
    [final] ).

cnf(i_0_548,axiom,
    ( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4)) = hAPP(hAPP(X5,X3),hAPP(X1,X4))
    | ~ c_Complete__Lattice_Ocomplete__lattice(X6,X1,X7,X8,X9,X5,X10,X11,X2) ),
    cls_complete__lattice_OSup__insert_0,
    [final] ).

cnf(i_0_549,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_550,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_551,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X2,X4,X3,X5,X6)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    cls_conseq_2,
    [final] ).

cnf(i_0_552,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X2,X4,X3,X5,X6)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    cls_hoare__derivs_Ointros_I6_J_2,
    [final] ).

cnf(i_0_553,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X5,X6),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X2,X4,X3,X7,X5)))
    | ~ hBOOL(hAPP(hAPP(X7,X6),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X2,X4,X3)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X7,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    cls_hoare__derivs_Ointros_I6_J_1,
    [final] ).

cnf(i_0_554,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X5,X6),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X2,X4,X3,X7,X5)))
    | ~ hBOOL(hAPP(hAPP(X7,X6),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X2,X4,X3)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X7,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    cls_conseq_1,
    [final] ).

cnf(i_0_555,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq12__1(X2,X5,X4,X6)),v_sko__Hoare__Mirabelle__Xconseq12__3(X2,X5,X4,X6)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    cls_conseq12_2,
    [final] ).

cnf(i_0_556,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OSemi(X4,X5),X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X7,X5,X6,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
    cls_Comp_0,
    [final] ).

cnf(i_0_557,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq12__1(X2,X5,X4,X6)),v_sko__Hoare__Mirabelle__Xconseq12__2(X2,X5,X4,X6)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    cls_conseq12_0,
    [final] ).

cnf(i_0_558,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),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))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X2)) = 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)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X2)),
    cls_Un__Int__crazy_0,
    [final] ).

cnf(i_0_559,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X5,X6),v_sko__Hoare__Mirabelle__Xconseq12__3(X2,X7,X4,X5)))
    | ~ hBOOL(hAPP(hAPP(X7,X6),v_sko__Hoare__Mirabelle__Xconseq12__2(X2,X7,X4,X5)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X7,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    cls_conseq12_1,
    [final] ).

cnf(i_0_560,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq2__1(X4,X5)),v_sko__Hoare__Mirabelle__Xconseq2__2(X4,X5)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    cls_conseq2_1,
    [final] ).

cnf(i_0_561,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq1__1(X2,X5)),v_sko__Hoare__Mirabelle__Xconseq1__2(X2,X5)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    cls_conseq1_1,
    [final] ).

cnf(i_0_562,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X2,X5)),v_sko__Hoare__Mirabelle__Xconseq1__2(X2,X5)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    cls_conseq1_0,
    [final] ).

cnf(i_0_563,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq2__1(X4,X5)),v_sko__Hoare__Mirabelle__Xconseq2__2(X4,X5)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
    cls_conseq2_0,
    [final] ).

cnf(i_0_564,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xescape__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xescape__2(X1,X2,X4,X3))) ),
    cls_escape_0,
    [final] ).

cnf(i_0_565,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X2,X4,X3))) ),
    cls_conseq_0,
    [final] ).

cnf(i_0_566,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
    | hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X2,X4,X3))) ),
    cls_hoare__derivs_Ointros_I6_J_0,
    [final] ).

cnf(i_0_567,axiom,
    hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X4,X5,X2),X6)) = hAPP(c_Set_Oimage(c_COMBB(X1,X4,X2,X3,X5),X5,X3),X6),
    cls_image__image_0,
    [final] ).

cnf(i_0_568,axiom,
    ( ~ hBOOL(c_in(hAPP(X1,X2),hAPP(c_Set_Oimage(X1,X3,X4),c_HOL_Ominus__class_Ominus(X5,hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X4))
    | ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X3),X2),X5),X3,X4) ),
    cls_inj__on__insert_1,
    [final] ).

cnf(i_0_569,axiom,
    ( c_Fun_Oinj__on(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X3,X1)
    | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(c_Set_Oimage(X2,X3,X1),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X3,tc_bool)))),hAPP(c_Set_Oimage(X2,X3,X1),c_HOL_Ominus__class_Ominus(X5,X4,tc_fun(X3,tc_bool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ c_Fun_Oinj__on(X2,X5,X3,X1)
    | ~ c_Fun_Oinj__on(X2,X4,X3,X1) ),
    cls_inj__on__Un_3,
    [final] ).

cnf(i_0_570,axiom,
    ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X5),X5,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X5,tc_fun(X2,tc_bool)))
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
    cls_UN__simps_I3_J_1,
    [final] ).

cnf(i_0_571,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,tc_fun(X1,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool),X5),X5,tc_fun(X1,tc_bool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
    cls_UN__extend__simps_I3_J_1,
    [final] ).

cnf(i_0_572,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X5),X5,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X5,tc_fun(X2,tc_bool))),
    cls_UN__simps_I5_J_0,
    [final] ).

cnf(i_0_573,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,tc_fun(X1,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool),X5),X5,tc_fun(X1,tc_bool)),
    cls_UN__extend__simps_I5_J_0,
    [final] ).

cnf(i_0_574,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,tc_fun(X1,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool),X5),X5,tc_fun(X1,tc_bool)),
    cls_Int__UN__distrib_0,
    [final] ).

cnf(i_0_575,axiom,
    ( c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2,X5)
    | hBOOL(c_in(hAPP(X1,X3),hAPP(c_Set_Oimage(X1,X2,X5),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))),X5))
    | ~ c_Fun_Oinj__on(X1,X4,X2,X5) ),
    cls_inj__on__insert_2,
    [final] ).

cnf(i_0_576,axiom,
    hAPP(c_Set_Ovimage(X1,X2,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X5,X6,tc_fun(X3,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBB(c_Set_Ovimage(X1,X2,X3),X5,tc_fun(X3,tc_bool),tc_fun(X2,tc_bool),X6),X6,tc_fun(X2,tc_bool)),
    cls_vimage__UN_0,
    [final] ).

cnf(i_0_577,axiom,
    hAPP(c_Set_Oimage(X1,X2,X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X5,X6,tc_fun(X2,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBB(c_Set_Oimage(X1,X2,X3),X5,tc_fun(X2,tc_bool),tc_fun(X3,tc_bool),X6),X6,tc_fun(X3,tc_bool)),
    cls_image__UN_0,
    [final] ).

cnf(i_0_578,axiom,
    ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Set_Oinsert(X2),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X5),X5,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X5,tc_fun(X2,tc_bool)))
    | ~ hBOOL(c_in(X6,X1,X5)) ),
    cls_UN__insert__distrib_0,
    [final] ).

cnf(i_0_579,axiom,
    ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(hAPP(c_Set_Oinsert(X2),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X5),X5,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X5,tc_fun(X2,tc_bool)))
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
    cls_UN__simps_I1_J_1,
    [final] ).

cnf(i_0_580,axiom,
    ( hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X5,tc_fun(X1,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,c_COMBB(hAPP(c_Set_Oinsert(X1),X2),X4,tc_fun(X1,tc_bool),tc_fun(X1,tc_bool),X5),X5,tc_fun(X1,tc_bool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
    cls_UN__extend__simps_I1_J_1,
    [final] ).

cnf(i_0_581,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,c_COMBB(X2,X3,X4,tc_fun(X5,tc_bool),X6),X6,tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X3,X6,X4),X1),X2,X4,tc_fun(X5,tc_bool)),
    cls_UN__extend__simps_I10_J_0,
    [final] ).

cnf(i_0_582,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(X1,X2,X3),X4),X5,X3,tc_fun(X6,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,c_COMBB(X5,X1,X3,tc_fun(X6,tc_bool),X2),X2,tc_fun(X6,tc_bool)),
    cls_UN__simps_I10_J_0,
    [final] ).

cnf(i_0_583,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X1),X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_UN__simps_I3_J_0,
    [final] ).

cnf(i_0_584,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_COMBB(hAPP(c_Set_Oinsert(X2),X3),X4,tc_fun(X2,tc_bool),tc_fun(X2,tc_bool),X1),X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_UN__simps_I1_J_0,
    [final] ).

cnf(i_0_585,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(c_Set_Oimage(X2,X3,X1),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X3,tc_bool)))),hAPP(c_Set_Oimage(X2,X3,X1),c_HOL_Ominus__class_Ominus(X5,X4,tc_fun(X3,tc_bool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ c_Fun_Oinj__on(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X3,X1) ),
    cls_inj__on__Un_2,
    [final] ).

cnf(i_0_586,axiom,
    c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X4),X5)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),tc_fun(X3,tc_bool)),
    cls_image__Int__subset_0,
    [final] ).

cnf(i_0_587,axiom,
    ( c_Finite__Set_Ofun__left__comm__idem(c_COMBB(X1,X2,X3,tc_fun(X4,X4),X5),X5,X4)
    | ~ c_Finite__Set_Ofun__left__comm__idem(X1,X3,X4) ),
    cls_fun__left__comm__idem_Ofun__left__comm__idem__apply_0,
    [final] ).

cnf(i_0_588,axiom,
    hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
    cls_COMBB__def_0,
    [final] ).

cnf(i_0_589,axiom,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OSKIP,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2),
    cls_hoare__derivs_OSkip_0,
    [final] ).

cnf(i_0_590,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,X1,tc_fun(X5,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X1,tc_fun(X5,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool))),
    cls_UN__Un_0,
    [final] ).

cnf(i_0_591,axiom,
    ( hAPP(X1,X2) = X3
    | ~ hBOOL(c_in(X2,hAPP(c_Set_Ovimage(X1,X4,X5),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)))),X4)) ),
    cls_vimage__singleton__eq_0,
    [final] ).

cnf(i_0_592,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X3),X4))
    | ~ c_lessequals(c_SetInterval_Oord_OatLeastAtMost(X1,X3,X4,X5),c_SetInterval_Oord_OatLeastAtMost(X1,X2,X6,X5),tc_fun(X5,tc_bool))
    | ~ c_Orderings_Oorder(X1,X7,X5) ),
    cls_order_OatLeastatMost__subset__iff_0,
    [final] ).

cnf(i_0_593,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X4),X2))
    | ~ c_lessequals(c_SetInterval_Oord_OatLeastAtMost(X1,X4,X2,X5),c_SetInterval_Oord_OatLeastAtMost(X1,X6,X3,X5),tc_fun(X5,tc_bool))
    | ~ c_Orderings_Oorder(X1,X7,X5) ),
    cls_order_OatLeastatMost__subset__iff_1,
    [final] ).

cnf(i_0_594,axiom,
    hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X3),X4),X5)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))),hAPP(c_Set_Ovimage(X1,X2,X3),X5)),
    cls_vimage__insert_0,
    [final] ).

cnf(i_0_595,axiom,
    ( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X4),X5)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5))
    | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
    | ~ c_lessequals(X4,X6,tc_fun(X2,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X6,X2,X3) ),
    cls_inj__on__image__Int_0,
    [final] ).

cnf(i_0_596,axiom,
    ( c_lessequals(X4,X2,tc_fun(X1,tc_bool))
    | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(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_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) ),
    cls_Un__Int__assoc__eq_0,
    [final] ).

cnf(i_0_597,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,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),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_523,c_0_524]),c_0_524]),c_0_524]),
    [final] ).

cnf(i_0_598,axiom,
    hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))),X3)),
    cls_vimage__singleton__eq_1,
    [final] ).

cnf(i_0_599,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(c_in(X2,c_SetInterval_Oord_OatLeastAtMost(X1,X4,X3,X5),X5)) ),
    cls_ord_OatLeastAtMost__iff_1,
    [final] ).

cnf(i_0_600,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(c_in(X3,c_SetInterval_Oord_OatLeastAtMost(X1,X2,X4,X5),X5)) ),
    cls_ord_OatLeastAtMost__iff_0,
    [final] ).

cnf(i_0_601,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X1,X2,X3),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5),tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X2,tc_bool))),tc_fun(X3,tc_bool)),
    cls_image__diff__subset_0,
    [final] ).

cnf(i_0_602,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(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)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
    cls_Un__Int__distrib2_0,
    [final] ).

cnf(i_0_603,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),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)),
    cls_Int__Un__distrib2_0,
    [final] ).

cnf(i_0_604,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),X4),X2)) ),
    cls_fold1Set__sing_0,
    [final] ).

cnf(i_0_605,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_606,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_607,axiom,
    ( hAPP(c_Set_Oimage(X1,X2,X3),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X2,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(X1,X2,X3),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X5,X6,tc_fun(X2,tc_bool))
    | ~ c_lessequals(X4,X6,tc_fun(X2,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X6,X2,X3) ),
    cls_inj__on__image__set__diff_0,
    [final] ).

cnf(i_0_608,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X1,tc_bool))),X4) = X4,
    cls_UN__extend__simps_I2_J_0,
    [final] ).

cnf(i_0_609,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(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)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),
    cls_Un__Int__distrib_0,
    [final] ).

cnf(i_0_610,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),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)),
    cls_Int__Un__distrib_0,
    [final] ).

cnf(i_0_611,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_612,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_613,axiom,
    ( c_lessequals(c_SetInterval_Oord_OatLeastAtMost(X1,X2,X3,X4),c_SetInterval_Oord_OatLeastAtMost(X1,X5,X6,X4),tc_fun(X4,tc_bool))
    | ~ hBOOL(hAPP(hAPP(X1,X3),X6))
    | ~ hBOOL(hAPP(hAPP(X1,X5),X2))
    | ~ c_Orderings_Oorder(X1,X7,X4) ),
    cls_order_OatLeastatMost__subset__iff_3,
    [final] ).

cnf(i_0_614,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
    | ~ hBOOL(c_in(X3,X1,X2))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
    cls_subset__insert__iff_3,
    [final] ).

cnf(i_0_615,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
    | ~ hBOOL(c_in(X3,X1,X2))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
    cls_diff__single__insert_0,
    [final] ).

cnf(i_0_616,axiom,
    ( hBOOL(c_in(X1,c_SetInterval_Oord_OatLeastAtMost(X2,X3,X4,X5),X5))
    | ~ hBOOL(hAPP(hAPP(X2,X1),X4))
    | ~ hBOOL(hAPP(hAPP(X2,X3),X1)) ),
    cls_ord_OatLeastAtMost__iff_2,
    [final] ).

cnf(i_0_617,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1))),
    cls_Nitpick_OEx1__def_2,
    [final] ).

cnf(i_0_618,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
    cls_subset__insert__iff_4,
    [final] ).

cnf(i_0_619,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | hBOOL(c_in(X1,X4,X3))
    | ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2),X3)) ),
    cls_UnE_0,
    [final] ).

cnf(i_0_620,axiom,
    hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5)),
    cls_vimage__Un_0,
    [final] ).

cnf(i_0_621,axiom,
    hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X5)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5)),
    cls_vimage__Int_0,
    [final] ).

cnf(i_0_622,axiom,
    hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X4),X5)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),
    cls_image__Un_0,
    [final] ).

cnf(i_0_623,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(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_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))
    | ~ c_lessequals(X4,X2,tc_fun(X1,tc_bool)) ),
    cls_Un__Int__assoc__eq_1,
    [final] ).

cnf(i_0_624,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_625,axiom,
    ( c_lessequals(c_SetInterval_Oord_OatLeastAtMost(X1,X2,X3,X4),c_SetInterval_Oord_OatLeastAtMost(X1,X5,X6,X4),tc_fun(X4,tc_bool))
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_Orderings_Oorder(X1,X7,X4) ),
    cls_order_OatLeastatMost__subset__iff_2,
    [final] ).

cnf(i_0_626,axiom,
    ( X4 = X5
    | hAPP(c_Set_Oimage(X1,X2,X3),X4) != hAPP(c_Set_Oimage(X1,X2,X3),X5)
    | ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X4),X5),X2,X3) ),
    cls_inj__on__Un__image__eq__iff_0,
    [final] ).

cnf(i_0_627,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_525,c_0_522]),
    [final] ).

cnf(i_0_628,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_629,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_630,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(X2,X3)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X2,X5,tc_fun(X1,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X2,X5,tc_fun(X1,tc_bool))
    | ~ hBOOL(c_in(X3,X4,X5)) ),
    cls_UN__absorb_0,
    [final] ).

cnf(i_0_631,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
    cls_Un__assoc_0,
    [final] ).

cnf(i_0_632,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_633,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_634,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,X1,tc_fun(X5,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),hAPP(X4,X2)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X4,X1,tc_fun(X5,tc_bool))),
    cls_UN__insert_0,
    [final] ).

cnf(i_0_635,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_526,c_0_522]),
    [final] ).

cnf(i_0_636,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
    | ~ hBOOL(c_in(X3,X1,X2))
    | ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)) ),
    cls_subset__insert__iff_0,
    [final] ).

cnf(i_0_637,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_638,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),X3,X4))
    | ~ hBOOL(c_in(X2,hAPP(c_Set_Ovimage(X1,X5,X4),X3),X5)) ),
    cls_vimageD_0,
    [final] ).

cnf(i_0_639,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),X3,X4))
    | ~ hBOOL(c_in(X2,hAPP(c_Set_Ovimage(X1,X5,X4),X3),X5)) ),
    cls_vimageE_0,
    [final] ).

cnf(i_0_640,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X5),X3,X4) ),
    cls_inj__on__Un_0,
    [final] ).

cnf(i_0_641,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X5),X2),X3,X4) ),
    cls_inj__on__Un_1,
    [final] ).

cnf(i_0_642,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_distrib__inf__le_0,
    [final] ).

cnf(i_0_643,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_distrib__sup__le_0,
    [final] ).

cnf(i_0_644,axiom,
    hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2),X3)),
    cls_fold1Set__sing_1,
    [final] ).

cnf(i_0_645,axiom,
    ( hAPP(c_Set_Oimage(X1,X2,X2),X3) = X3
    | ~ c_Fun_Oinj__on(X1,X3,X2,X2)
    | ~ c_lessequals(hAPP(c_Set_Oimage(X1,X2,X2),X3),X3,tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    cls_endo__inj__surj_0,
    [final] ).

cnf(i_0_646,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_647,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_648,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_649,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X3,X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),X1),X2)) ),
    cls_sup1E_0,
    [final] ).

cnf(i_0_650,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_651,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_652,axiom,
    c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X1,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))),
    cls_Un__Diff_0,
    [final] ).

cnf(i_0_653,axiom,
    c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(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_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool))),c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool))),
    cls_Diff__Un_0,
    [final] ).

cnf(i_0_654,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)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool))),c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool))),
    cls_Diff__Int_0,
    [final] ).

cnf(i_0_655,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_656,axiom,
    ( X1 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2)
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X1)) ),
    cls_Nitpick_OEx1__def_3,
    [final] ).

cnf(i_0_657,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_527,c_0_522]),
    [final] ).

cnf(i_0_658,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(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_Un__mono_0,
    [final] ).

cnf(i_0_659,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_660,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X2,X4,X5),X1),X3)) ),
    cls_vimage__code_0,
    [final] ).

cnf(i_0_661,negated_conjecture,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
    cls_conjecture_0,
    [final] ).

cnf(i_0_662,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4) = hAPP(hAPP(c_Set_Oinsert(X1),X2),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_0,
    [final] ).

cnf(i_0_663,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),
    cls_Un__left__commute_0,
    [final] ).

cnf(i_0_664,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_665,axiom,
    ( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2))
    | ~ hBOOL(c_in(X1,X3,X2)) ),
    cls_UnCI_1,
    [final] ).

cnf(i_0_666,axiom,
    ( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2))
    | ~ hBOOL(c_in(X1,X4,X2)) ),
    cls_UnCI_0,
    [final] ).

cnf(i_0_667,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
    cls_hoare__derivs_Oinsert_0,
    [final] ).

cnf(i_0_668,axiom,
    ( hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),X5),X3))
    | ~ hBOOL(c_in(hAPP(X2,X1),X5,X4)) ),
    cls_vimageI_0,
    [final] ).

cnf(i_0_669,axiom,
    ( hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),X5),X3))
    | ~ hBOOL(c_in(hAPP(X2,X1),X5,X4)) ),
    cls_vimageI2_0,
    [final] ).

cnf(i_0_670,axiom,
    ( hBOOL(c_in(X1,hAPP(c_Set_Ovimage(X2,X3,X4),X5),X3))
    | ~ hBOOL(c_in(hAPP(X2,X1),X5,X4)) ),
    cls_vimage__eq_1,
    [final] ).

cnf(i_0_671,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),X3,X4))
    | ~ hBOOL(c_in(X2,X5,X6))
    | ~ c_lessequals(hAPP(c_Set_Oimage(X1,X6,X4),X5),X3,tc_fun(X4,tc_bool)) ),
    cls_image__subset__iff_0,
    [final] ).

cnf(i_0_672,axiom,
    hAPP(c_Set_Ovimage(X1,X2,X3),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X3,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(X1,X2,X3),X4),hAPP(c_Set_Ovimage(X1,X2,X3),X5),tc_fun(X2,tc_bool)),
    cls_vimage__Diff_0,
    [final] ).

cnf(i_0_673,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_674,axiom,
    ( X1 = X2
    | ~ hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X3)) ),
    cls_singletonE_0,
    [final] ).

cnf(i_0_675,axiom,
    c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)),
    cls_Diff__insert2_0,
    [final] ).

cnf(i_0_676,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_677,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),hAPP(c_Set_Oimage(X1,X3,X4),X5),X4))
    | ~ hBOOL(c_in(X2,X5,X3)) ),
    cls_imageI_0,
    [final] ).

cnf(i_0_678,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),hAPP(c_Set_Oimage(X1,X3,X4),X5),X4))
    | ~ hBOOL(c_in(X2,X5,X3)) ),
    cls_image__eqI_0,
    [final] ).

cnf(i_0_679,axiom,
    ( hBOOL(c_in(hAPP(X4,X1),hAPP(c_Set_Oimage(X4,X3,X5),X2),X5))
    | ~ hBOOL(c_in(X1,X2,X3)) ),
    cls_image__iff_2,
    [final] ).

cnf(i_0_680,axiom,
    ( hBOOL(c_in(hAPP(X4,X1),hAPP(c_Set_Oimage(X4,X3,X5),X2),X5))
    | ~ hBOOL(c_in(X1,X2,X3)) ),
    cls_rev__image__eqI_0,
    [final] ).

cnf(i_0_681,axiom,
    ( X2 = X5
    | X2 = X4
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
    cls_doubleton__eq__iff_0,
    [final] ).

cnf(i_0_682,axiom,
    ( X3 = X4
    | X2 = X4
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
    cls_doubleton__eq__iff_1,
    [final] ).

cnf(i_0_683,axiom,
    ( X2 = X5
    | X3 = X5
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
    cls_doubleton__eq__iff_2,
    [final] ).

cnf(i_0_684,axiom,
    ( X3 = X4
    | X3 = X5
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
    cls_doubleton__eq__iff_3,
    [final] ).

cnf(i_0_685,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Fun_Oinj__on(X3,X1,X2,X4)
    | ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X3,X2,X4),X1),X4) ),
    cls_finite__imageD_0,
    [final] ).

cnf(i_0_686,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X4),tc_fun(X3,tc_bool)) ),
    cls_Diff__subset__conv_1,
    [final] ).

cnf(i_0_687,axiom,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,tc_fun(X1,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),
    cls_UN__extend__simps_I1_J_0,
    [final] ).

cnf(i_0_688,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Set_Oinsert(X3),X5),X2),X3,X4) ),
    cls_inj__on__insert_0,
    [final] ).

cnf(i_0_689,axiom,
    c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),X4,tc_fun(X3,tc_bool)),
    cls_image__vimage__subset_0,
    [final] ).

cnf(i_0_690,axiom,
    ( hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))) = X3
    | ~ hBOOL(c_in(X2,X3,X1)) ),
    cls_insert__Diff_0,
    [final] ).

cnf(i_0_691,plain,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | c_The(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2),X2) = hAPP(hAPP(X1,X3),c_The(c_Finite__Set_Ofold1Set(X1,X4,X2),X2))
    | hBOOL(c_in(X3,X4,X2))
    | ~ c_Finite__Set_Ofinite(X4,X2)
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_528,c_0_524]),c_0_524]),
    [final] ).

cnf(i_0_692,axiom,
    ( c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X4,X5) ),
    cls_inj__on__diff_0,
    [final] ).

cnf(i_0_693,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_529,c_0_524]),
    [final] ).

cnf(i_0_694,axiom,
    hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
    cls_insert__inter__insert_0,
    [final] ).

cnf(i_0_695,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,tc_fun(X1,tc_bool))) = X2,
    cls_UN__extend__simps_I3_J_0,
    [final] ).

cnf(i_0_696,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6)
    | ~ hBOOL(c_in(X3,X4,X5))
    | ~ hBOOL(c_in(X2,X4,X5)) ),
    cls_inj__onD_0,
    [final] ).

cnf(i_0_697,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ hBOOL(c_in(X3,X4,X5))
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    cls_inj__on__def_0,
    [final] ).

cnf(i_0_698,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ hBOOL(c_in(X3,X4,X5))
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    cls_inj__on__iff_0,
    [final] ).

cnf(i_0_699,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ hBOOL(c_in(X3,X4,X5))
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    cls_inj__on__contraD_0,
    [final] ).

cnf(i_0_700,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_701,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_702,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_703,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X3)
    | ~ c_lessequals(X2,hAPP(c_Set_Oimage(X1,X3,X3),X2),tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_finite__surj__inj_0,
    [final] ).

cnf(i_0_704,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_705,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X5,X3,X4) ),
    cls_subset__inj__on_0,
    [final] ).

cnf(i_0_706,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),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_0,
    [final] ).

cnf(i_0_707,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_708,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,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool)),X3) ),
    cls_finite__Diff__insert_0,
    [final] ).

cnf(i_0_709,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = X2,
    cls_Un__Diff__Int_0,
    [final] ).

cnf(i_0_710,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),tc_fun(X2,tc_bool))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
    cls_Diff__subset__conv_0,
    [final] ).

cnf(i_0_711,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_712,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_713,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_714,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_715,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X2)) ),
    inference(rw,[status(thm)],[i_0_530,c_0_531]),
    [final] ).

cnf(i_0_716,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_717,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
    cls_Un__insert__left_0,
    [final] ).

cnf(i_0_718,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_719,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_720,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2) ),
    cls_derivs__insertD_0,
    [final] ).

cnf(i_0_721,axiom,
    ( c_lessequals(hAPP(c_Set_Ovimage(X1,X2,X3),X4),hAPP(c_Set_Ovimage(X1,X2,X3),X5),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
    cls_vimage__mono_0,
    [final] ).

cnf(i_0_722,axiom,
    ( c_lessequals(hAPP(c_Set_Oimage(X1,X2,X3),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X4,X5,tc_fun(X2,tc_bool)) ),
    cls_image__mono_0,
    [final] ).

cnf(i_0_723,axiom,
    ( c_lessequals(hAPP(c_Set_Oimage(X4,X3,X5),X1),hAPP(c_Set_Oimage(X4,X3,X5),X2),tc_fun(X5,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_subset__image__iff_2,
    [final] ).

cnf(i_0_724,axiom,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
    cls_insert__Diff__single_0,
    [final] ).

cnf(i_0_725,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_726,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
    | ~ hBOOL(hAPP(X2,X4)) ),
    cls_sup1CI_1,
    [final] ).

cnf(i_0_727,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
    | ~ hBOOL(hAPP(X3,X4)) ),
    cls_sup1CI_0,
    [final] ).

cnf(i_0_728,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2,tc_fun(X3,tc_bool)) ),
    cls_Un__subset__iff_0,
    [final] ).

cnf(i_0_729,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1),X2,tc_fun(X3,tc_bool)) ),
    cls_Un__subset__iff_1,
    [final] ).

cnf(i_0_730,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_731,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_732,axiom,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord_OatLeastAtMost(X2,X3,X4,X1)
    | ~ c_Orderings_Oorder(X2,X5,X1)
    | ~ hBOOL(hAPP(hAPP(X2,X3),X4)) ),
    cls_order_OatLeastatMost__empty__iff2_0,
    [final] ).

cnf(i_0_733,axiom,
    ( c_SetInterval_Oord_OatLeastAtMost(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | ~ c_Orderings_Oorder(X1,X5,X4)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    cls_order_OatLeastatMost__empty__iff_0,
    [final] ).

cnf(i_0_734,axiom,
    ( hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X2,X4,X1),X5)) = hAPP(c_Set_Oimage(X2,X4,X1),X5)
    | ~ hBOOL(c_in(X3,X5,X4)) ),
    cls_insert__image_0,
    [final] ).

cnf(i_0_735,axiom,
    ( hBOOL(hAPP(hAPP(c_Set_Ovimage(X1,X2,X3),X4),X5))
    | ~ hBOOL(hAPP(X4,hAPP(X1,X5))) ),
    cls_vimage__code_1,
    [final] ).

cnf(i_0_736,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2) ),
    cls_finite__Diff__insert_1,
    [final] ).

cnf(i_0_737,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_738,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    cls_sup__inf__distrib2_0,
    [final] ).

cnf(i_0_739,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    cls_inf__sup__distrib2_0,
    [final] ).

cnf(i_0_740,plain,
    ( c_The(c_Finite__Set_Ofold1Set(X4,hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))),X5),X5) = X6
    | ~ c_Orderings_Olinorder(X1,X2,X3) ),
    inference(rw,[status(thm)],[i_0_532,c_0_524]),
    [final] ).

cnf(i_0_741,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_742,axiom,
    c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),
    cls_Diff__insert_0,
    [final] ).

cnf(i_0_743,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | X1 = X4
    | ~ hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),X3)) ),
    cls_insertE_0,
    [final] ).

cnf(i_0_744,axiom,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X3),
    cls_insert__is__Un_0,
    [final] ).

cnf(i_0_745,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool))
    | ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X1,tc_bool)) ),
    cls_Un__least_0,
    [final] ).

cnf(i_0_746,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4,tc_fun(X1,tc_bool))
    | ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X1,tc_bool)) ),
    cls_Un__subset__iff_2,
    [final] ).

cnf(i_0_747,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_748,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_749,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_750,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_751,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),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_752,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
    cls_Un__Diff__cancel2_0,
    [final] ).

cnf(i_0_753,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_Sup__binary_0,
    [final] ).

cnf(i_0_754,axiom,
    ( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),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_755,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),
    cls_Un__insert__right_0,
    [final] ).

cnf(i_0_756,axiom,
    ( X1 = hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)) ),
    cls_subset__singletonD_0,
    [final] ).

cnf(i_0_757,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
    cls_Un__left__absorb_0,
    [final] ).

cnf(i_0_758,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_759,axiom,
    hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),X5)) = hAPP(hAPP(c_Set_Oinsert(X3),hAPP(X1,X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),
    cls_image__insert_0,
    [final] ).

cnf(i_0_760,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_lessequals(X1,hAPP(c_Set_Oimage(X3,X4,X2),X5),tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X5,X4) ),
    cls_finite__surj_0,
    [final] ).

cnf(i_0_761,plain,
    c_The(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2),X2) = X3,
    inference(rw,[status(thm)],[i_0_533,c_0_524]),
    [final] ).

cnf(i_0_762,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_534,c_0_524]),
    [final] ).

cnf(i_0_763,axiom,
    hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2)),
    cls_singleton__iff_1,
    [final] ).

cnf(i_0_764,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    cls_sup__inf__distrib1_0,
    [final] ).

cnf(i_0_765,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    cls_inf__sup__distrib1_0,
    [final] ).

cnf(i_0_766,axiom,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
    cls_doubleton__eq__iff_4,
    [final] ).

cnf(i_0_767,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = 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_768,axiom,
    ( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)) = X3
    | hBOOL(c_in(X2,X3,X1)) ),
    cls_Diff__insert__absorb_0,
    [final] ).

cnf(i_0_769,axiom,
    ( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool)))
    | hBOOL(c_in(X2,X4,X1)) ),
    cls_insert__Diff__if_1,
    [final] ).

cnf(i_0_770,axiom,
    ( hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2))
    | ~ hBOOL(c_in(X1,X4,X2)) ),
    cls_insertCI_0,
    [final] ).

cnf(i_0_771,axiom,
    ( hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2))
    | ~ hBOOL(c_in(X1,X4,X2)) ),
    cls_insert__iff_2,
    [final] ).

cnf(i_0_772,axiom,
    ( c_SetInterval_Oord_OatLeastAtMost(X1,X2,X3,X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | ~ hBOOL(hAPP(hAPP(X5,X3),X2))
    | ~ c_Orderings_Oorder(X1,X5,X4) ),
    cls_order_OatLeastatMost__empty_0,
    [final] ).

cnf(i_0_773,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2) ),
    cls_finite__Un_0,
    [final] ).

cnf(i_0_774,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1),X2) ),
    cls_finite__Un_1,
    [final] ).

cnf(i_0_775,axiom,
    ( c_lessequals(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,tc_fun(X1,tc_bool))
    | ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool))
    | ~ hBOOL(c_in(X2,X4,X1)) ),
    cls_insert__subset_2,
    [final] ).

cnf(i_0_776,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_777,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | hBOOL(c_in(X4,X1,X3))
    | ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool)) ),
    cls_subset__insert_0,
    [final] ).

cnf(i_0_778,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | hBOOL(c_in(X4,X1,X3))
    | ~ c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool)) ),
    cls_subset__insert__iff_1,
    [final] ).

cnf(i_0_779,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_780,axiom,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord_OatLeastAtMost(X2,X3,X4,X1)
    | hBOOL(hAPP(hAPP(X2,X3),X4))
    | ~ c_Orderings_Oorder(X2,X5,X1) ),
    cls_order_OatLeastatMost__empty__iff2_1,
    [final] ).

cnf(i_0_781,axiom,
    ( c_SetInterval_Oord_OatLeastAtMost(X1,X2,X3,X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_Orderings_Oorder(X1,X5,X4) ),
    cls_order_OatLeastatMost__empty__iff_1,
    [final] ).

cnf(i_0_782,plain,
    hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X1)),
    inference(rw,[status(thm)],[i_0_535,c_0_531]),
    [final] ).

cnf(i_0_783,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
    cls_Un__Diff__cancel_0,
    [final] ).

cnf(i_0_784,axiom,
    ( c_SetInterval_Oord_OatLeastAtMost(X1,X2,X2,X3) = hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))
    | ~ c_Orderings_Oorder(X1,X4,X3) ),
    cls_order_OatLeastAtMost__singleton_0,
    [final] ).

cnf(i_0_785,axiom,
    ( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))
    | ~ hBOOL(c_in(X2,X4,X1)) ),
    cls_insert__Diff1_0,
    [final] ).

cnf(i_0_786,axiom,
    ( hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
    | ~ class_Lattices_Olattice(X1) ),
    cls_sup__fun__eq_0,
    [final] ).

cnf(i_0_787,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_788,axiom,
    ( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_SetInterval_Oord__class_OlessThan(X2,X1),tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
    | ~ class_Orderings_Oorder(X1) ),
    cls_single__Diff__lessThan_0,
    [final] ).

cnf(i_0_789,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = X3
    | ~ c_lessequals(X2,X3,tc_fun(X1,tc_bool)) ),
    cls_Diff__partition_0,
    [final] ).

cnf(i_0_790,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__assoc_0,
    [final] ).

cnf(i_0_791,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I6_J_0,
    [final] ).

cnf(i_0_792,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_793,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_794,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
    | hBOOL(c_in(X3,X1,X2))
    | ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool)) ),
    cls_subset__insert_1,
    [final] ).

cnf(i_0_795,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
    | hBOOL(c_in(X3,X1,X2))
    | ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool)) ),
    cls_subset__insert__iff_2,
    [final] ).

cnf(i_0_796,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_797,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_798,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_799,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_800,axiom,
    ( c_lessequals(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),tc_fun(X1,tc_bool))
    | ~ c_lessequals(X3,X4,tc_fun(X1,tc_bool)) ),
    cls_insert__mono_0,
    [final] ).

cnf(i_0_801,axiom,
    ( hBOOL(hAPP(X1,X2))
    | X3 = X2
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X4),X3),X1),X2)) ),
    cls_insert__code_0,
    [final] ).

cnf(i_0_802,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2,tc_fun(X3,tc_bool)) ),
    cls_insert__subset_0,
    [final] ).

cnf(i_0_803,axiom,
    ( hBOOL(c_in(X2,X4,X1))
    | hBOOL(c_in(X2,X3,X1))
    | X3 = X4
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X4) ),
    cls_insert__ident_0,
    [final] ).

cnf(i_0_804,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_805,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X4),X2),X3) ),
    cls_derivs__insertD_1,
    [final] ).

cnf(i_0_806,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_807,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1(X1,X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2(X1,X2),X2)) ),
    cls_comm__monoid__add_Ononempty__iff_1,
    [final] ).

cnf(i_0_808,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_809,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_810,axiom,
    c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),tc_fun(X2,tc_bool)),
    cls_Un__upper1_0,
    [final] ).

cnf(i_0_811,axiom,
    c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1),tc_fun(X2,tc_bool)),
    cls_Un__upper2_0,
    [final] ).

cnf(i_0_812,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2,tc_fun(X3,tc_bool)) ),
    cls_insert__subset_1,
    [final] ).

cnf(i_0_813,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_814,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(X3,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ c_Orderings_Oorder(X3,X4,X5) ),
    cls_order_Oantisym__conv_0,
    [final] ).

cnf(i_0_815,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ hBOOL(hAPP(hAPP(X3,X1),X2))
    | ~ c_Orderings_Oorder(X3,X4,X5) ),
    cls_order_Oantisym_0,
    [final] ).

cnf(i_0_816,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ hBOOL(hAPP(hAPP(X3,X1),X2))
    | ~ c_Orderings_Oorder(X3,X4,X5) ),
    cls_order_Oeq__iff_2,
    [final] ).

cnf(i_0_817,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_818,axiom,
    ( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1)
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    cls_finite__UnI_0,
    [final] ).

cnf(i_0_819,axiom,
    ( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1)
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    cls_finite__Un_2,
    [final] ).

cnf(i_0_820,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
    | ~ c_Orderings_Olinorder(X1,X3,X4)
    | ~ hBOOL(hAPP(hAPP(X3,X2),X2)) ),
    cls_linorder_Oantisym__conv2_1,
    [final] ).

cnf(i_0_821,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X4,X3),X2))
    | ~ c_Orderings_Olinorder(X1,X4,X5) ),
    cls_linorder_Onot__le_1,
    [final] ).

cnf(i_0_822,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ c_Orderings_Olinorder(X4,X1,X5) ),
    cls_linorder_Onot__less__iff__gr__or__eq_1,
    [final] ).

cnf(i_0_823,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X4,X3),X2))
    | ~ c_Orderings_Olinorder(X4,X1,X5) ),
    cls_linorder_OleD_0,
    [final] ).

cnf(i_0_824,axiom,
    ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
    cls_emptyE_0,
    [final] ).

cnf(i_0_825,axiom,
    ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
    cls_empty__iff_0,
    [final] ).

cnf(i_0_826,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_827,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),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_828,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),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_829,axiom,
    ( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),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_830,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_831,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_832,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_833,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    cls_ivl__disj__int_I4_J_0,
    [final] ).

cnf(i_0_834,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_835,axiom,
    ( X2 = X3
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
    cls_singleton__inject_0,
    [final] ).

cnf(i_0_836,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_Un__empty_2,
    [final] ).

cnf(i_0_837,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_838,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_839,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_840,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_841,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_842,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_843,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__left__commute_0,
    [final] ).

cnf(i_0_844,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I7_J_0,
    [final] ).

cnf(i_0_845,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_846,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_847,axiom,
    hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X1),X3),X2)),
    cls_insertCI_1,
    [final] ).

cnf(i_0_848,axiom,
    hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X1),X3),X2)),
    cls_insertI1_0,
    [final] ).

cnf(i_0_849,axiom,
    hBOOL(c_in(X1,hAPP(hAPP(c_Set_Oinsert(X2),X1),X3),X2)),
    cls_insert__iff_1,
    [final] ).

cnf(i_0_850,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4),X3,X1) ),
    cls_le__supE_0,
    [final] ).

cnf(i_0_851,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4),X3,X1) ),
    cls_le__sup__iff_0,
    [final] ).

cnf(i_0_852,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X2),X3,X1) ),
    cls_le__supE_1,
    [final] ).

cnf(i_0_853,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X2),X3,X1) ),
    cls_le__sup__iff_1,
    [final] ).

cnf(i_0_854,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_855,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_856,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_857,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_858,axiom,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),
    cls_insert__commute_0,
    [final] ).

cnf(i_0_859,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_860,axiom,
    ( c_lessequals(X2,X3,tc_fun(X1,tc_bool))
    | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != X3 ),
    cls_subset__Un__eq_1,
    [final] ).

cnf(i_0_861,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool)) ),
    cls_subset__insertI2_0,
    [final] ).

cnf(i_0_862,axiom,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(X3,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X4,X1),X2))
    | ~ c_Orderings_Olinorder(X4,X3,X5) ),
    cls_linorder_Oantisym__conv2_0,
    [final] ).

cnf(i_0_863,axiom,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(X3,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X4,X1),X2))
    | ~ c_Orderings_Oorder(X4,X3,X5) ),
    cls_order_Ole__less_0,
    [final] ).

cnf(i_0_864,axiom,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(X4,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X3,X1),X2))
    | ~ c_Orderings_Olinorder(X3,X4,X5) ),
    cls_linorder_Oantisym__conv1_0,
    [final] ).

cnf(i_0_865,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | X2 = X3
    | ~ hBOOL(hAPP(hAPP(X4,X2),X3))
    | ~ c_Orderings_Oorder(X4,X1,X5) ),
    cls_order_Oless__le_2,
    [final] ).

cnf(i_0_866,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | X2 = X3
    | ~ hBOOL(hAPP(hAPP(X4,X2),X3))
    | ~ c_Orderings_Oorder(X4,X1,X5) ),
    cls_order_Ole__neq__trans_0,
    [final] ).

cnf(i_0_867,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | X2 = X3
    | ~ hBOOL(hAPP(hAPP(X4,X2),X3))
    | ~ c_Orderings_Oorder(X4,X1,X5) ),
    cls_order_Oneq__le__trans_0,
    [final] ).

cnf(i_0_868,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_869,axiom,
    c_Fun_Oinj__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3),
    cls_inj__on__empty_0,
    [final] ).

cnf(i_0_870,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X4,X2),X3))
    | ~ c_Orderings_Oorder(X1,X4,X5) ),
    cls_order_Ole__less_1,
    [final] ).

cnf(i_0_871,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
    cls_Un__empty_0,
    [final] ).

cnf(i_0_872,axiom,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
    cls_Un__empty_1,
    [final] ).

cnf(i_0_873,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X2),
    cls_Un__commute_0,
    [final] ).

cnf(i_0_874,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_875,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_876,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_877,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_878,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_879,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4))
    | ~ hBOOL(hAPP(X3,X4)) ),
    cls_insert__code_2,
    [final] ).

cnf(i_0_880,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_lessequals(X2,X4,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
    cls_weaken_0,
    [final] ).

cnf(i_0_881,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_lessequals(X4,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3) ),
    cls_thin_0,
    [final] ).

cnf(i_0_882,axiom,
    ( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(X1,X2,X3),X4),X3)
    | ~ c_Finite__Set_Ofinite(X4,X2) ),
    cls_finite__imageI_0,
    [final] ).

cnf(i_0_883,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_884,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_885,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = X2
    | ~ c_lessequals(X3,X2,tc_fun(X1,tc_bool)) ),
    cls_Un__absorb2_0,
    [final] ).

cnf(i_0_886,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = X3
    | ~ c_lessequals(X2,X3,tc_fun(X1,tc_bool)) ),
    cls_Un__absorb1_0,
    [final] ).

cnf(i_0_887,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_888,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_889,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OlessThan(X2,X1),c_SetInterval_Oord__class_OlessThan(X3,X1),tc_fun(X1,tc_bool)) ),
    cls_lessThan__subset__iff_0,
    [final] ).

cnf(i_0_890,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_891,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_892,axiom,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | hAPP(c_Set_Oimage(X1,X2,X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_image__is__empty_0,
    [final] ).

cnf(i_0_893,axiom,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(c_Set_Oimage(X2,X3,X1),X4) ),
    cls_empty__is__image_0,
    [final] ).

cnf(i_0_894,axiom,
    ( hBOOL(c_in(X2,X3,X1))
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ c_OrderedGroup_Oab__semigroup__mult(X4,X5) ),
    cls_ab__semigroup__mult_Ononempty__iff_2,
    [final] ).

cnf(i_0_895,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_896,axiom,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(X3,X1),X2))
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ c_Orderings_Olinorder(X4,X3,X5) ),
    cls_linorder_Oantisym__conv3_0,
    [final] ).

cnf(i_0_897,axiom,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | hBOOL(hAPP(hAPP(X3,X1),X2))
    | ~ c_Orderings_Olinorder(X4,X3,X5) ),
    cls_linorder_Onot__less__iff__gr__or__eq_0,
    [final] ).

cnf(i_0_898,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | X3 = X2
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ c_Orderings_Olinorder(X4,X1,X5) ),
    cls_linorder_Oless__linear_0,
    [final] ).

cnf(i_0_899,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | X3 = X2
    | ~ c_Orderings_Olinorder(X4,X1,X5) ),
    cls_linorder_OneqE_0,
    [final] ).

cnf(i_0_900,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ c_Orderings_Olinorder(X1,X4,X5) ),
    cls_linorder_Olinear_0,
    [final] ).

cnf(i_0_901,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X2))
    | hBOOL(hAPP(hAPP(X3,X2),X2))
    | ~ c_Orderings_Olinorder(X3,X1,X4) ),
    cls_linorder_Oantisym__conv1_1,
    [final] ).

cnf(i_0_902,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(X4,X3),X2))
    | ~ c_Orderings_Olinorder(X1,X4,X5) ),
    cls_linorder_OleI_0,
    [final] ).

cnf(i_0_903,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(X4,X3),X2))
    | ~ c_Orderings_Olinorder(X4,X1,X5) ),
    cls_linorder_Onot__leE_0,
    [final] ).

cnf(i_0_904,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(X4,X3),X2))
    | ~ c_Orderings_Olinorder(X4,X1,X5) ),
    cls_linorder_Onot__le_0,
    [final] ).

cnf(i_0_905,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_906,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_907,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4),X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__supI1_0,
    [final] ).

cnf(i_0_908,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4),X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_le__supI2_0,
    [final] ).

cnf(i_0_909,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = X2,
    cls_Un__empty__left_0,
    [final] ).

cnf(i_0_910,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_911,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_912,axiom,
    ( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X2),X3)) = hAPP(hAPP(X1,X2),X3)
    | ~ c_Finite__Set_Ofun__left__comm__idem(X1,X4,X5) ),
    cls_fun__left__comm__idem_Ofun__left__idem_0,
    [final] ).

cnf(i_0_913,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_914,axiom,
    ( hBOOL(c_in(X2,X3,X1))
    | hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
    cls_comm__monoid__add_Ononempty__iff_2,
    [final] ).

cnf(i_0_915,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
    cls_insert__code_1,
    [final] ).

cnf(i_0_916,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_917,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_918,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_919,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_920,axiom,
    ( c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    cls_Min__singleton_0,
    [final] ).

cnf(i_0_921,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_Sup__singleton_0,
    [final] ).

cnf(i_0_922,axiom,
    ( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_Inf__singleton_0,
    [final] ).

cnf(i_0_923,axiom,
    ( c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    cls_Max__singleton_0,
    [final] ).

cnf(i_0_924,axiom,
    ( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3
    | ~ hBOOL(c_in(X2,X3,X1)) ),
    cls_insert__absorb_0,
    [final] ).

cnf(i_0_925,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_926,axiom,
    ( c_lessequals(c_SetInterval_Oord__class_OlessThan(X2,X1),c_SetInterval_Oord__class_OlessThan(X3,X1),tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_lessThan__subset__iff_1,
    [final] ).

cnf(i_0_927,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_928,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_929,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_930,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_931,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_932,axiom,
    c_Set_Ocontents(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2,
    cls_contents__eq_0,
    [final] ).

cnf(i_0_933,axiom,
    c_The(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2,
    cls_Nitpick_OThe__psimp_0,
    [final] ).

cnf(i_0_934,plain,
    c_The(hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X1,
    inference(rw,[status(thm)],[i_0_536,c_0_531]),
    [final] ).

cnf(i_0_935,axiom,
    ( ~ c_Orderings_Olinorder(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X2,X4),X4)) ),
    cls_linorder_Onot__less__iff__gr__or__eq_2,
    [final] ).

cnf(i_0_936,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
    | ~ c_Orderings_Olinorder(X3,X1,X4) ),
    cls_linorder_Oneq__iff_1,
    [final] ).

cnf(i_0_937,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
    | ~ c_Orderings_Oorder(X3,X1,X4) ),
    cls_order_Oless__le_1,
    [final] ).

cnf(i_0_938,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__left__idem_0,
    [final] ).

cnf(i_0_939,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I8_J_0,
    [final] ).

cnf(i_0_940,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_941,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_942,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_943,axiom,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    cls_bot1E_0,
    [final] ).

cnf(i_0_944,axiom,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
    cls_insert__absorb2_0,
    [final] ).

cnf(i_0_945,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,X1,X3)) ),
    inference(rw,[status(thm)],[i_0_537,c_0_522]),
    [final] ).

cnf(i_0_946,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,X1,X3)) ),
    cls_mem__def_0,
    [final] ).

cnf(i_0_947,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,X1))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_Sup__insert_0,
    [final] ).

cnf(i_0_948,axiom,
    ( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),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_949,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_950,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_951,axiom,
    hAPP(c_Set_Ovimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_vimage__empty_0,
    [final] ).

cnf(i_0_952,axiom,
    hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    cls_image__empty_0,
    [final] ).

cnf(i_0_953,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Set_Oimage(X2,X3,X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),
    cls_empty__is__image_1,
    [final] ).

cnf(i_0_954,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2) ),
    cls_finite__insert_0,
    [final] ).

cnf(i_0_955,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
    cls_Un__empty__right_0,
    [final] ).

cnf(i_0_956,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_lessequals(X2,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
    cls_asm_0,
    [final] ).

cnf(i_0_957,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_958,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_959,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_960,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_961,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_962,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_963,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_964,axiom,
    c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),tc_fun(X2,tc_bool)),
    cls_subset__insertI_0,
    [final] ).

cnf(i_0_965,axiom,
    ( hBOOL(hAPP(hAPP(X1,X4),X4))
    | ~ c_Orderings_Oorder(X1,X2,X3) ),
    cls_order_Oeq__iff_0,
    [final] ).

cnf(i_0_966,axiom,
    ( c_SetInterval_Oord__class_OatLeastAtMost(X2,X2,X1) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
    | ~ class_Orderings_Oorder(X1) ),
    cls_atLeastAtMost__singleton_0,
    [final] ).

cnf(i_0_967,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_968,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_969,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_970,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_971,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__ge1_0,
    [final] ).

cnf(i_0_972,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__ord_I3_J_0,
    [final] ).

cnf(i_0_973,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2),X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__ge2_0,
    [final] ).

cnf(i_0_974,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__ord_I4_J_0,
    [final] ).

cnf(i_0_975,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = X2
    | ~ class_Lattices_Olattice(X1) ),
    cls_sup__inf__absorb_0,
    [final] ).

cnf(i_0_976,axiom,
    ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__absorb_0,
    [final] ).

cnf(i_0_977,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_978,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_979,axiom,
    ( X1 = hAPP(hAPP(c_Set_Oinsert(X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1(X1,X2)),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2(X1,X2))
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
    cls_comm__monoid__add_Ononempty__iff_0,
    [final] ).

cnf(i_0_980,plain,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    inference(rw,[status(thm)],[i_0_538,c_0_522]),
    [final] ).

cnf(i_0_981,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    cls_mem__def_1,
    [final] ).

cnf(i_0_982,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_983,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_984,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X2
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_sup__absorb1_0,
    [final] ).

cnf(i_0_985,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__iff__sup_0,
    [final] ).

cnf(i_0_986,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_987,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_988,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != X3 ),
    cls_le__iff__sup_1,
    [final] ).

cnf(i_0_989,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_990,axiom,
    hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X2) = X2,
    cls_Un__absorb_0,
    [final] ).

cnf(i_0_991,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_992,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_993,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_994,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_995,axiom,
    ( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1)
    | ~ c_Finite__Set_Ofinite(X3,X1) ),
    cls_finite__insert_1,
    [final] ).

cnf(i_0_996,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_997,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_998,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_999,axiom,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_insert__not__empty_0,
    [final] ).

cnf(i_0_1000,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
    cls_empty__not__insert_0,
    [final] ).

cnf(i_0_1001,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__linear_0,
    [final] ).

cnf(i_0_1002,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__commute_0,
    [final] ).

cnf(i_0_1003,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I5_J_0,
    [final] ).

cnf(i_0_1004,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_1005,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_1006,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_1007,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_1008,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != c_Orderings_Obot__class_Obot(X1) ),
    cls_sup__eq__bot__eq1_0,
    [final] ).

cnf(i_0_1009,axiom,
    ( X3 = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != c_Orderings_Obot__class_Obot(X1) ),
    cls_sup__eq__bot__eq2_0,
    [final] ).

cnf(i_0_1010,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X2
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(rw,[status(thm)],[i_0_539,c_0_522]),
    [final] ).

cnf(i_0_1011,plain,
    ( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(rw,[status(thm)],[i_0_540,c_0_522]),
    [final] ).

cnf(i_0_1012,axiom,
    c_Finite__Set_Ofun__left__comm__idem(c_Set_Oinsert(X1),X1,tc_fun(X1,tc_bool)),
    cls_fun__left__comm__idem__insert_0,
    [final] ).

cnf(i_0_1013,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    cls_subset__refl_0,
    [final] ).

cnf(i_0_1014,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    cls_equalityE_0,
    [final] ).

cnf(i_0_1015,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_1016,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_1017,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_1018,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_sup__bot__left_0,
    [final] ).

cnf(i_0_1019,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_1020,axiom,
    ( c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(X1),X1,X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_fun__left__comm__idem__sup_0,
    [final] ).

cnf(i_0_1021,axiom,
    ( c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(X1),X1,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_fun__left__comm__idem__inf_0,
    [final] ).

cnf(i_0_1022,axiom,
    ( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
    | ~ class_Orderings_Obot(X1) ),
    cls_bot__least_0,
    [final] ).

cnf(i_0_1023,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_sup__bot__right_0,
    [final] ).

cnf(i_0_1024,axiom,
    c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
    cls_finite_OemptyI_0,
    [final] ).

cnf(i_0_1025,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Opreorder(X1) ),
    cls_order__eq__refl_0,
    [final] ).

cnf(i_0_1026,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_order__eq__iff_0,
    [final] ).

cnf(i_0_1027,axiom,
    ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__idem_0,
    [final] ).

cnf(i_0_1028,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_1029,axiom,
    ( X2 = X3
    | ~ class_Orderings_Olinorder(X1)
    | c_SetInterval_Oord__class_OlessThan(X2,X1) != c_SetInterval_Oord__class_OlessThan(X3,X1) ),
    cls_lessThan__eq__iff_0,
    [final] ).

cnf(i_0_1030,axiom,
    ( X1 = X3
    | c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSemi(X3,X4) ),
    cls_com_Osimps_I3_J_0,
    [final] ).

cnf(i_0_1031,axiom,
    ( X2 = X4
    | c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSemi(X3,X4) ),
    cls_com_Osimps_I3_J_1,
    [final] ).

cnf(i_0_1032,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_1033,axiom,
    ( class_Orderings_Opreorder(tc_fun(X1,X2))
    | ~ class_Orderings_Opreorder(X2) ),
    clsarity_fun__Orderings_Opreorder,
    [final] ).

cnf(i_0_1034,axiom,
    ( class_Orderings_Obot(tc_fun(X1,X2))
    | ~ class_Orderings_Obot(X2) ),
    clsarity_fun__Orderings_Obot,
    [final] ).

cnf(i_0_1035,axiom,
    ( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
    | ~ class_Lattices_Obounded__lattice(X2) ),
    clsarity_fun__Lattices_Obounded__lattice,
    [final] ).

cnf(i_0_1036,axiom,
    ( class_HOL_Oord(tc_fun(X1,X2))
    | ~ class_HOL_Oord(X2) ),
    clsarity_fun__HOL_Oord,
    [final] ).

cnf(i_0_1037,axiom,
    ( class_HOL_Ominus(tc_fun(X1,X2))
    | ~ class_HOL_Ominus(X2) ),
    clsarity_fun__HOL_Ominus,
    [final] ).

cnf(i_0_1038,axiom,
    ( class_Orderings_Oorder(tc_fun(X1,X2))
    | ~ class_Orderings_Oorder(X2) ),
    clsarity_fun__Orderings_Oorder,
    [final] ).

cnf(i_0_1039,axiom,
    ( class_Lattices_Olower__semilattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_1040,axiom,
    ( class_Lattices_Oupper__semilattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Oupper__semilattice,
    [final] ).

cnf(i_0_1041,axiom,
    ( class_Lattices_Odistrib__lattice(tc_fun(X1,X2))
    | ~ class_Lattices_Odistrib__lattice(X2) ),
    clsarity_fun__Lattices_Odistrib__lattice,
    [final] ).

cnf(i_0_1042,axiom,
    ( class_Lattices_Olattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Olattice,
    [final] ).

cnf(i_0_1043,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_1044,axiom,
    c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
    cls_com_Osimps_I13_J_0,
    [final] ).

cnf(i_0_1045,axiom,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X2),
    cls_com_Osimps_I12_J_0,
    [final] ).

cnf(i_0_1046,axiom,
    ( c_Finite__Set_Ofinite(X2,X1)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    cls_finite_0,
    [final] ).

cnf(i_0_1047,axiom,
    class_Orderings_Opreorder(tc_bool),
    clsarity_bool__Orderings_Opreorder,
    [final] ).

cnf(i_0_1048,axiom,
    class_Orderings_Obot(tc_bool),
    clsarity_bool__Orderings_Obot,
    [final] ).

cnf(i_0_1049,axiom,
    class_Lattices_Obounded__lattice(tc_bool),
    clsarity_bool__Lattices_Obounded__lattice,
    [final] ).

cnf(i_0_1050,axiom,
    class_HOL_Oord(tc_bool),
    clsarity_bool__HOL_Oord,
    [final] ).

cnf(i_0_1051,axiom,
    class_Finite__Set_Ofinite_Ofinite(tc_bool),
    clsarity_bool__Finite__Set_Ofinite_Ofinite,
    [final] ).

cnf(i_0_1052,axiom,
    class_HOL_Ominus(tc_bool),
    clsarity_bool__HOL_Ominus,
    [final] ).

cnf(i_0_1053,axiom,
    class_Orderings_Oorder(tc_bool),
    clsarity_bool__Orderings_Oorder,
    [final] ).

cnf(i_0_1054,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    clsarity_bool__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_1055,axiom,
    class_Lattices_Oupper__semilattice(tc_bool),
    clsarity_bool__Lattices_Oupper__semilattice,
    [final] ).

cnf(i_0_1056,axiom,
    class_Lattices_Odistrib__lattice(tc_bool),
    clsarity_bool__Lattices_Odistrib__lattice,
    [final] ).

cnf(i_0_1057,axiom,
    class_Lattices_Olattice(tc_bool),
    clsarity_bool__Lattices_Olattice,
    [final] ).

cnf(i_0_1058,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_bool),
    clsarity_bool__Complete__Lattice_Ocomplete__lattice,
    [final] ).

cnf(i_0_1059,axiom,
    X1 = X1 ).

cnf(i_0_1060,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1061,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1062,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1063,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1064,axiom,
    ( X1 != X2
    | c_Com_Ocom_OSemi(X1,X3) = c_Com_Ocom_OSemi(X2,X3) ) ).

cnf(i_0_1065,axiom,
    ( X1 != X2
    | c_Com_Ocom_OSemi(X3,X1) = c_Com_Ocom_OSemi(X3,X2) ) ).

cnf(i_0_1066,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_1067,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_1068,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_1069,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_1070,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_1071,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_1072,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_1073,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_1074,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X1,X3,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X2,X3,X4,X5) ) ).

cnf(i_0_1075,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X1,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X2,X4,X5) ) ).

cnf(i_0_1076,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X4,X1,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X2,X5) ) ).

cnf(i_0_1077,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X2) ) ).

cnf(i_0_1078,axiom,
    ( X1 != X2
    | c_The(X1,X3) = c_The(X2,X3) ) ).

cnf(i_0_1079,axiom,
    ( X1 != X2
    | c_The(X3,X1) = c_The(X3,X2) ) ).

cnf(i_0_1080,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_1081,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_1082,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).

cnf(i_0_1083,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).

cnf(i_0_1084,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).

cnf(i_0_1085,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).

cnf(i_0_1086,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).

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

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

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

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

cnf(i_0_1091,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X1,X3) = c_Finite__Set_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_1092,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X3,X1) = c_Finite__Set_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_1093,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X1,X3) = c_Finite__Set_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_1094,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X3,X1) = c_Finite__Set_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_1095,axiom,
    ( X1 != X2
    | c_Set_Ocontents(X1,X3) = c_Set_Ocontents(X2,X3) ) ).

cnf(i_0_1096,axiom,
    ( X1 != X2
    | c_Set_Ocontents(X3,X1) = c_Set_Ocontents(X3,X2) ) ).

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

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

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

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

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

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

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

cnf(i_0_1104,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_1105,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_1106,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_1107,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_1108,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_1109,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_1110,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_1111,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_1112,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_1113,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_1114,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | class_Lattices_Olower__semilattice(X2) ) ).

cnf(i_0_1115,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_1116,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_1117,axiom,
    ( X1 != X2
    | ~ c_Orderings_Olinorder(X1,X3,X4)
    | c_Orderings_Olinorder(X2,X3,X4) ) ).

cnf(i_0_1118,axiom,
    ( X1 != X2
    | ~ c_Orderings_Olinorder(X3,X1,X4)
    | c_Orderings_Olinorder(X3,X2,X4) ) ).

cnf(i_0_1119,axiom,
    ( X1 != X2
    | ~ c_Orderings_Olinorder(X3,X4,X1)
    | c_Orderings_Olinorder(X3,X4,X2) ) ).

cnf(i_0_1120,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1121,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oupper__semilattice(X1)
    | class_Lattices_Oupper__semilattice(X2) ) ).

cnf(i_0_1122,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_1123,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1124,axiom,
    ( X1 != X2
    | ~ class_HOL_Ominus(X1)
    | class_HOL_Ominus(X2) ) ).

cnf(i_0_1125,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1126,axiom,
    ( X1 != X2
    | ~ class_HOL_Oord(X1)
    | class_HOL_Oord(X2) ) ).

cnf(i_0_1127,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1128,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1129,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__valids(X2,X3,X4) ) ).

cnf(i_0_1130,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__valids(X3,X2,X4) ) ).

cnf(i_0_1131,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X2) ) ).

cnf(i_0_1132,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_1133,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_1134,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite_Ofinite(X1)
    | class_Finite__Set_Ofinite_Ofinite(X2) ) ).

cnf(i_0_1135,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).

cnf(i_0_1136,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).

cnf(i_0_1137,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).

cnf(i_0_1138,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_1139,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_1140,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_1141,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_1142,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_1143,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_1144,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_1145,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm__idem(X1,X3,X4)
    | c_Finite__Set_Ofun__left__comm__idem(X2,X3,X4) ) ).

cnf(i_0_1146,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm__idem(X3,X1,X4)
    | c_Finite__Set_Ofun__left__comm__idem(X3,X2,X4) ) ).

cnf(i_0_1147,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm__idem(X3,X4,X1)
    | c_Finite__Set_Ofun__left__comm__idem(X3,X4,X2) ) ).

cnf(i_0_1148,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder(X1,X3,X4)
    | c_Orderings_Oorder(X2,X3,X4) ) ).

cnf(i_0_1149,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder(X3,X1,X4)
    | c_Orderings_Oorder(X3,X2,X4) ) ).

cnf(i_0_1150,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder(X3,X4,X1)
    | c_Orderings_Oorder(X3,X4,X2) ) ).

cnf(i_0_1151,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | c_Finite__Set_Ofinite(X2,X3) ) ).

cnf(i_0_1152,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | c_Finite__Set_Ofinite(X3,X2) ) ).

cnf(i_0_1153,axiom,
    ( X1 != X2
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X3)
    | c_OrderedGroup_Oab__semigroup__mult(X2,X3) ) ).

cnf(i_0_1154,axiom,
    ( X1 != X2
    | ~ c_OrderedGroup_Oab__semigroup__mult(X3,X1)
    | c_OrderedGroup_Oab__semigroup__mult(X3,X2) ) ).

cnf(i_0_1059_001,axiom,
    X1 = X1 ).

cnf(i_0_1060_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1061_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1062_004,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1063_005,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1064_006,axiom,
    ( X1 != X2
    | c_Com_Ocom_OSemi(X1,X3) = c_Com_Ocom_OSemi(X2,X3) ) ).

cnf(i_0_1065_007,axiom,
    ( X1 != X2
    | c_Com_Ocom_OSemi(X3,X1) = c_Com_Ocom_OSemi(X3,X2) ) ).

cnf(i_0_1066_008,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_1067_009,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_1068_010,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_1069_011,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_1070_012,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_1071_013,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_1072_014,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_1073_015,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_1074_016,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X1,X3,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X2,X3,X4,X5) ) ).

cnf(i_0_1075_017,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X1,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X2,X4,X5) ) ).

cnf(i_0_1076_018,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X4,X1,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X2,X5) ) ).

cnf(i_0_1077_019,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X2) ) ).

cnf(i_0_1078_020,axiom,
    ( X1 != X2
    | c_The(X1,X3) = c_The(X2,X3) ) ).

cnf(i_0_1079_021,axiom,
    ( X1 != X2
    | c_The(X3,X1) = c_The(X3,X2) ) ).

cnf(i_0_1080_022,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_1081_023,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_1082_024,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).

cnf(i_0_1083_025,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).

cnf(i_0_1084_026,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).

cnf(i_0_1085_027,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).

cnf(i_0_1086_028,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).

cnf(i_0_1087_029,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).

cnf(i_0_1088_030,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).

cnf(i_0_1089_031,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OlessThan(X1,X3) = c_SetInterval_Oord__class_OlessThan(X2,X3) ) ).

cnf(i_0_1090_032,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OlessThan(X3,X1) = c_SetInterval_Oord__class_OlessThan(X3,X2) ) ).

cnf(i_0_1091_033,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X1,X3) = c_Finite__Set_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_1092_034,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X3,X1) = c_Finite__Set_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_1093_035,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X1,X3) = c_Finite__Set_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_1094_036,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X3,X1) = c_Finite__Set_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_1095_037,axiom,
    ( X1 != X2
    | c_Set_Ocontents(X1,X3) = c_Set_Ocontents(X2,X3) ) ).

cnf(i_0_1096_038,axiom,
    ( X1 != X2
    | c_Set_Ocontents(X3,X1) = c_Set_Ocontents(X3,X2) ) ).

cnf(i_0_1097_039,axiom,
    ( X1 != X2
    | c_in(X1,X3,X4) = c_in(X2,X3,X4) ) ).

cnf(i_0_1098_040,axiom,
    ( X1 != X2
    | c_in(X3,X1,X4) = c_in(X3,X2,X4) ) ).

cnf(i_0_1099_041,axiom,
    ( X1 != X2
    | c_in(X3,X4,X1) = c_in(X3,X4,X2) ) ).

cnf(i_0_1100_042,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple(X1,X3,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,X5) ) ).

cnf(i_0_1101_043,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple(X3,X1,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple(X3,X2,X4,X5) ) ).

cnf(i_0_1102_044,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X1,X5) = c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X2,X5) ) ).

cnf(i_0_1103_045,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,X1) = c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,X2) ) ).

cnf(i_0_1104_046,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_1105_047,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_1106_048,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_1107_049,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_1108_050,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_1109_051,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_1110_052,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_1111_053,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_1112_054,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_1113_055,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_1114_056,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | class_Lattices_Olower__semilattice(X2) ) ).

cnf(i_0_1115_057,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_1116_058,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_1117_059,axiom,
    ( X1 != X2
    | ~ c_Orderings_Olinorder(X1,X3,X4)
    | c_Orderings_Olinorder(X2,X3,X4) ) ).

cnf(i_0_1118_060,axiom,
    ( X1 != X2
    | ~ c_Orderings_Olinorder(X3,X1,X4)
    | c_Orderings_Olinorder(X3,X2,X4) ) ).

cnf(i_0_1119_061,axiom,
    ( X1 != X2
    | ~ c_Orderings_Olinorder(X3,X4,X1)
    | c_Orderings_Olinorder(X3,X4,X2) ) ).

cnf(i_0_1120_062,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1121_063,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oupper__semilattice(X1)
    | class_Lattices_Oupper__semilattice(X2) ) ).

cnf(i_0_1122_064,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_1123_065,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1124_066,axiom,
    ( X1 != X2
    | ~ class_HOL_Ominus(X1)
    | class_HOL_Ominus(X2) ) ).

cnf(i_0_1125_067,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1126_068,axiom,
    ( X1 != X2
    | ~ class_HOL_Oord(X1)
    | class_HOL_Oord(X2) ) ).

cnf(i_0_1127_069,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1128_070,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1129_071,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__valids(X2,X3,X4) ) ).

cnf(i_0_1130_072,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__valids(X3,X2,X4) ) ).

cnf(i_0_1131_073,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X2) ) ).

cnf(i_0_1132_074,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_1133_075,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_1134_076,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite_Ofinite(X1)
    | class_Finite__Set_Ofinite_Ofinite(X2) ) ).

cnf(i_0_1135_077,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).

cnf(i_0_1136_078,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).

cnf(i_0_1137_079,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).

cnf(i_0_1138_080,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_1139_081,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_1140_082,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_1141_083,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_1142_084,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_1143_085,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_1144_086,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_1145_087,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm__idem(X1,X3,X4)
    | c_Finite__Set_Ofun__left__comm__idem(X2,X3,X4) ) ).

cnf(i_0_1146_088,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm__idem(X3,X1,X4)
    | c_Finite__Set_Ofun__left__comm__idem(X3,X2,X4) ) ).

cnf(i_0_1147_089,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm__idem(X3,X4,X1)
    | c_Finite__Set_Ofun__left__comm__idem(X3,X4,X2) ) ).

cnf(i_0_1148_090,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder(X1,X3,X4)
    | c_Orderings_Oorder(X2,X3,X4) ) ).

cnf(i_0_1149_091,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder(X3,X1,X4)
    | c_Orderings_Oorder(X3,X2,X4) ) ).

cnf(i_0_1150_092,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder(X3,X4,X1)
    | c_Orderings_Oorder(X3,X4,X2) ) ).

cnf(i_0_1151_093,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | c_Finite__Set_Ofinite(X2,X3) ) ).

cnf(i_0_1152_094,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | c_Finite__Set_Ofinite(X3,X2) ) ).

cnf(i_0_1153_095,axiom,
    ( X1 != X2
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X3)
    | c_OrderedGroup_Oab__semigroup__mult(X2,X3) ) ).

cnf(i_0_1154_096,axiom,
    ( X1 != X2
    | ~ c_OrderedGroup_Oab__semigroup__mult(X3,X1)
    | c_OrderedGroup_Oab__semigroup__mult(X3,X2) ) ).

cnf(i_0_1155,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X1),X3,X4) ),
    inference(equality_inference,[],[626]) ).

cnf(i_0_1156,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[681]) ).

cnf(i_0_1157,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[682]) ).

cnf(i_0_1158,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[683]) ).

cnf(i_0_1159,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[684]) ).

cnf(i_0_1160,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,X5)
    | ~ hBOOL(c_in(X1,X3,X4))
    | ~ hBOOL(c_in(X1,X3,X4)) ),
    inference(equality_inference,[],[699]) ).

cnf(i_0_1161,plain,
    X1 = X1,
    inference(equality_inference,[],[700]) ).

cnf(i_0_1162,plain,
    X1 = X1,
    inference(equality_inference,[],[701]) ).

cnf(i_0_1163,plain,
    X1 = X1,
    inference(equality_inference,[],[702]) ).

cnf(i_0_1164,plain,
    ( X1 = X1
    | hBOOL(c_in(X2,X1,X3))
    | hBOOL(c_in(X2,X1,X3)) ),
    inference(equality_inference,[],[803]) ).

cnf(i_0_1165,plain,
    X1 = X1,
    inference(equality_inference,[],[835]) ).

cnf(i_0_1166,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[962]) ).

cnf(i_0_1167,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[963]) ).

cnf(i_0_1168,plain,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    inference(equality_inference,[],[1010]) ).

cnf(i_0_1169,plain,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    inference(equality_inference,[],[1011]) ).

cnf(i_0_1170,plain,
    ( X1 = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(equality_inference,[],[1029]) ).

cnf(i_0_1171,plain,
    X1 = X1,
    inference(equality_inference,[],[1030]) ).

cnf(i_0_1172,plain,
    X1 = X1,
    inference(equality_inference,[],[1031]) ).

cnf(i_0_1173,plain,
    $false,
    inference(scs_inference,[],[i_0_661,i_0_1014,i_0_956]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SWV913-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.11  % 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
% 0.12/0.31  % Computer : n005.cluster.edu
% 0.12/0.31  % Model    : x86_64 x86_64
% 0.12/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31  % Memory   : 8042.1875MB
% 0.12/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31  % CPULimit   : 300
% 0.12/0.31  % WCLimit    : 300
% 0.12/0.31  % DateTime   : Tue May  5 06:09:15 EDT 2026
% 0.12/0.31  % CPUTime    : 
% 0.12/0.32  % start to proof: theBenchmark
% 1.26/1.65  % Version  : CSE_E---1.7
% 1.26/1.65  % Problem  : theBenchmark.p
% 1.26/1.65  % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.65  % SZS output start CNFRefutation
% See solution above
% 1.32/1.70  % Total time : 1.324s
%------------------------------------------------------------------------------