CSE_E---1.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SWV580-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n012.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 05:27:00 PM UTC 2026

% Result   : Unsatisfiable 0.35s 1.52s
% Output   : CNFRefutation 0.74s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_602)

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

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

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

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

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

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

cnf(cls_fold1__singleton_0,axiom,
    c_Finite__Set_Ofold1(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__singleton_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/sandbox/benchmark/theBenchmark.p',cls_fold1__def_0) ).

cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
    hBOOL(hAPP(c_fequal(X1,X2),X1)),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_CollectD_0) ).

cnf(cls_add__nonneg__eq__0__iff_2,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).

cnf(cls_CollectI_0,axiom,
    ( hBOOL(c_in(X1,c_Collect(X2,X3),X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).

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

cnf(cls_complete__lattice_OSup__binary_0,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)) = hAPP(hAPP(X5,X2),X3)
    | ~ c_Complete__Lattice_Ocomplete__lattice(X6,X1,X7,X8,X9,X5,X10,X11,X4) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).

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

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

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

cnf(cls_complete__lattice_OSup__insert_0,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,X3,X4)) = hAPP(hAPP(X5,X2),hAPP(X1,X3))
    | ~ c_Complete__Lattice_Ocomplete__lattice(X6,X1,X7,X8,X9,X5,X10,X11,X4) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).

cnf(cls_setsum__ivl__cong_2,axiom,
    ( c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1),X1,X2) = c_Finite__Set_Osetsum(X6,c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1),X1,X2)
    | ~ class_HOL_Oord(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X2)
    | hAPP(X3,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(X4,X5,X3,X6,X1,X2)) != hAPP(X6,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(X4,X5,X3,X6,X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__ivl__cong_2) ).

cnf(cls_setsum__ivl__cong_1,axiom,
    ( c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1),X1,X2) = c_Finite__Set_Osetsum(X6,c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1),X1,X2)
    | c_HOL_Oord__class_Oless(c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(X4,X5,X3,X6,X1,X2),X5,X1)
    | ~ class_HOL_Oord(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__ivl__cong_1) ).

cnf(cls_setsum__ivl__cong_0,axiom,
    ( c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1),X1,X2) = c_Finite__Set_Osetsum(X6,c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1),X1,X2)
    | c_lessequals(X4,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(X4,X5,X3,X6,X1,X2),X1)
    | ~ class_HOL_Oord(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__ivl__cong_0) ).

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

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

cnf(cls_conjecture_0,negated_conjecture,
    c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

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

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

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

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

cnf(cls_calculation_0,axiom,
    ( c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a),t_a) = c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a)
    | ~ class_OrderedGroup_Ocomm__monoid__add(t_a) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_calculation_0) ).

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

cnf(cls_vimage__code_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_UN__iff_2) ).

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

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

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

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

cnf(cls_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).

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

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

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

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

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

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

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

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/sandbox/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).

cnf(cls_setsum__head__upt__Suc_0,axiom,
    ( c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,tc_nat),tc_nat,X1) = c_HOL_Oplus__class_Oplus(hAPP(X2,X3),c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X3),X4,tc_nat),tc_nat,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__head__upt__Suc_0) ).

cnf(cls_setsum__op__ivl__Suc_1,axiom,
    ( c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(X3,c_Suc(X4),tc_nat),tc_nat,X1) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,tc_nat),tc_nat,X1),hAPP(X2,X4),X1)
    | c_HOL_Oord__class_Oless(X4,X3,tc_nat)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__op__ivl__Suc_1) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).

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/sandbox/benchmark/theBenchmark.p',cls_UN__upper_0) ).

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

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

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

cnf(cls_setsum__shift__lb__Suc0__0__upt_0,axiom,
    ( c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat),tc_nat,X1) = c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat),tc_nat,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | hAPP(X2,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__shift__lb__Suc0__0__upt_0) ).

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

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

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

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_DiffE_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/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).

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

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

cnf(cls_INT__extend__simps_I4_J_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X1,
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_empty__fold1SetE_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/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

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/sandbox/benchmark/theBenchmark.p',cls_DiffI_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X5,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

cnf(cls_Deriv_Oadd__diff__add_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,X1),X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).

cnf(cls_ivl__disj__un_I3_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I3_J_0) ).

cnf(cls_ivl__disj__un_I5_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I5_J_0) ).

cnf(cls_ivl__disj__un_I4_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X1),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I4_J_0) ).

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

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

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

cnf(cls_ivl__disj__un_I15_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I15_J_0) ).

cnf(cls_ivl__disj__un_I19_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I19_J_0) ).

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

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

cnf(cls_ivl__disj__un_I16_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I16_J_0) ).

cnf(cls_ivl__disj__un_I20_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I20_J_0) ).

cnf(cls_ivl__disj__un_I18_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I18_J_0) ).

cnf(cls_ivl__disj__un_I22_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I22_J_0) ).

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

cnf(cls_le__add__right__mono_0,axiom,
    ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X5,X4,X1)
    | ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X5,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).

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

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

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

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

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

cnf(cls_add__less__cancel__right_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

cnf(cls_add__less__cancel__left_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

cnf(cls_add__le__cancel__right_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).

cnf(cls_add__le__cancel__left_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_setsum__op__ivl__Suc_0,axiom,
    ( c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(X3,c_Suc(X4),tc_nat),tc_nat,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__op__ivl__Suc_0) ).

cnf(cls_add__strict__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

cnf(cls_add__le__less__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).

cnf(cls_add__less__le__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).

cnf(cls_add__mono_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).

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

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

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

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

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

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

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

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

cnf(cls_add__sup__distrib__right_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__sup__distrib__right_0) ).

cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) ).

cnf(cls_add__inf__distrib__right_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__right_0) ).

cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).

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

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

cnf(cls_add__sup__distrib__left_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__sup__distrib__left_0) ).

cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) ).

cnf(cls_add__inf__distrib__left_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).

cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).

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

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

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

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

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).

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

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

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

cnf(cls_add__cancel__21_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X4,X1) = X5
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X3,X5,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

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

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

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

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).

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

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

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

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

cnf(cls_Int__insert__right_1,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool))
    | hBOOL(c_in(X2,X1,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_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/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).

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

cnf(cls_add__neg__neg_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

cnf(cls_add__nonpos__neg_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).

cnf(cls_add__neg__nonpos_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).

cnf(cls_add__nonpos__nonpos_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).

cnf(cls_add__pos__pos_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

cnf(cls_add__nonneg__pos_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).

cnf(cls_add__pos__nonneg_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).

cnf(cls_add__nonneg__nonneg_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).

cnf(cls_add__strict__left__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

cnf(cls_add__less__cancel__left_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

cnf(cls_add__strict__right__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

cnf(cls_add__less__cancel__right_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

cnf(cls_add__le__cancel__left_1,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

cnf(cls_add__left__mono_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).

cnf(cls_add__le__cancel__right_1,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

cnf(cls_add__right__mono_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).

cnf(cls_add__strict__increasing2_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).

cnf(cls_add__strict__increasing_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).

cnf(cls_add__increasing2_0,axiom,
    ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).

cnf(cls_add__increasing_0,axiom,
    ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).

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

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

cnf(cls_pos__add__strict_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).

cnf(cls_even__less__0__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).

cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).

cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).

cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

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

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

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

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

cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).

cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

cnf(cls_class__semiring_Oadd__a_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

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

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

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

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

cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

cnf(cls_add__cancel__21_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

cnf(cls_add__eq__inf__sup_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__inf__sup_0) ).

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

cnf(cls_less__iff__diff__less__0_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).

cnf(cls_le__iff__diff__le__0_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).

cnf(cls_ivl__disj__int_I9_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I9_J_0) ).

cnf(cls_ivl__disj__int_I13_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I13_J_0) ).

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

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

cnf(cls_ivl__disj__int_I10_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I10_J_0) ).

cnf(cls_ivl__disj__int_I14_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I14_J_0) ).

cnf(cls_ivl__disj__int_I12_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I12_J_0) ).

cnf(cls_ivl__disj__int_I16_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I16_J_0) ).

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

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

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

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

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

cnf(cls_less__eqI_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,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_HOL_Oord__class_Oless(X4,X5,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).

cnf(cls_less__eqI_0,axiom,
    ( c_HOL_Oord__class_Oless(X4,X5,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_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).

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

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

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

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

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

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

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

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

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

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

cnf(cls_setsum__empty_0,axiom,
    ( c_Finite__Set_Osetsum(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__empty_0) ).

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

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

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

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

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

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

cnf(cls_add__nonneg__eq__0__iff_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).

cnf(cls_add__nonneg__eq__0__iff_1,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).

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

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

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

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

cnf(cls_even__less__0__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).

cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).

cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).

cnf(cls_complete__lattice__class_OInf__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/sandbox/benchmark/theBenchmark.p',cls_complete__lattice__class_OInf__lower_0) ).

cnf(cls_complete__lattice__class_OSup__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/sandbox/benchmark/theBenchmark.p',cls_complete__lattice__class_OSup__upper_0) ).

cnf(cls_less__iff__diff__less__0_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).

cnf(cls_le__iff__diff__le__0_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).

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

cnf(cls_less__infI1_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).

cnf(cls_less__infI2_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).

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

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

cnf(cls_less__supI1_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).

cnf(cls_less__supI2_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).

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

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

cnf(cls_sup__fun__eq__raw_0,axiom,
    ( hAPP(c_Lattices_Oupper__semilattice__class_Osup(v_f,v_g,tc_fun(t_a,t_b)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(v_f,v_x),hAPP(v_g,v_x),t_b)
    | ~ class_Lattices_Olattice(t_b) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq__raw_0) ).

cnf(cls_inf__fun__eq__raw_0,axiom,
    ( hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_f,v_g,tc_fun(t_a,t_b)),v_x) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(v_f,v_x),hAPP(v_g,v_x),t_b)
    | ~ class_Lattices_Olattice(t_b) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq__raw_0) ).

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

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

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

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

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

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

cnf(cls_order__less__trans_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

cnf(cls_order__le__less__trans_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

cnf(cls_order__less__le__trans_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

cnf(cls_xt1_I10_J_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

cnf(cls_xt1_I7_J_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

cnf(cls_xt1_I8_J_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_lessequals(X4,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

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

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

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

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

cnf(cls_complete__lattice__class_OSup__singleton_0,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice__class_OSup__singleton_0) ).

cnf(cls_complete__lattice__class_OInf__singleton_0,axiom,
    ( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice__class_OInf__singleton_0) ).

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

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

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

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

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

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

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

cnf(cls_less__trans__Suc_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

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

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

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

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

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

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

cnf(cls_atLeastLessThan__empty__iff2_0,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_0) ).

cnf(cls_greaterThanAtMost__empty__iff2_0,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff2_0) ).

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

cnf(cls_atLeastLessThan__empty__iff_0,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_0) ).

cnf(cls_greaterThanAtMost__empty__iff_0,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff_0) ).

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

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

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

cnf(cls_gcd__lcm__complete__lattice__nat_OSup__singleton_0,axiom,
    c_GCD_Ogcd__class_OLCM(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_OSup__singleton_0) ).

cnf(cls_gcd__lcm__complete__lattice__nat_OInf__singleton_0,axiom,
    c_GCD_Ogcd__class_OGCD(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_OInf__singleton_0) ).

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

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

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

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

cnf(cls_less__le__not__le_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

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

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

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

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

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

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

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

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

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

cnf(cls_nat__less__cases_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | X3 = X2
    | c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).

cnf(cls_class__ringb_Oadd__cancel_0,axiom,
    ( X3 = X4
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).

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

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

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

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

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

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

cnf(cls_add__right__cancel_0,axiom,
    ( X2 = X4
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X4,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

cnf(cls_add__left__cancel_0,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

cnf(cls_add__imp__eq_0,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

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

cnf(cls_order__less__asym_0,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

cnf(cls_order__less__asym_H_0,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

cnf(cls_less__le__not__le_1,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

cnf(cls_not__less__iff__gr__or__eq_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

cnf(cls_linorder__antisym__conv2_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X2,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).

cnf(cls_linorder__not__le_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

cnf(cls_linorder__not__less_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

cnf(cls_xt1_I9_J_0,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

cnf(cls_not__less__eq_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

cnf(cls_greaterThanLessThan__empty_0,axiom,
    ( c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanLessThan__empty_0) ).

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

cnf(cls_greaterThanAtMost__empty_0,axiom,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty_0) ).

cnf(cls_atLeastatMost__empty_0,axiom,
    ( c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty_0) ).

cnf(cls_diff__add__cancel_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).

cnf(cls_add__diff__cancel_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_atLeastLessThan__singleton_0,axiom,
    c_SetInterval_Oord__class_OatLeastLessThan(X1,c_Suc(X1),tc_nat) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__singleton_0) ).

cnf(cls_Suc__less__eq_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

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

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

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).

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

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

cnf(cls_linorder__antisym__conv2_0,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

cnf(cls_linorder__antisym__conv1_0,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

cnf(cls_xt1_I11_J_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X3 = X2
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

cnf(cls_xt1_I12_J_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X3 = X2
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).

cnf(cls_order__neq__le__trans_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

cnf(cls_order__le__neq__trans_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

cnf(cls_order__le__less_0,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).

cnf(cls_order__less__le_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).

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

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

cnf(cls_less__Suc__eq__0__disj_3,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).

cnf(cls_Suc__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).

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

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

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

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

cnf(cls_less__SucE_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).

cnf(cls_not__less__less__Suc__eq_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).

cnf(cls_less__antisym_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).

cnf(cls_Suc__lessI_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
    | c_Suc(X1) = X2
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

cnf(cls_order__less__imp__le_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

cnf(cls_order__le__less_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).

cnf(cls_Suc__lessD_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).

cnf(cls_nat__lt__two__imp__zero__or__one_0,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__lt__two__imp__zero__or__one_0) ).

cnf(cls_atLeastLessThan__empty__iff2_1,axiom,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_1) ).

cnf(cls_greaterThanAtMost__empty__iff2_1,axiom,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff2_1) ).

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

cnf(cls_atLeastLessThan__empty__iff_1,axiom,
    ( c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_1) ).

cnf(cls_greaterThanAtMost__empty__iff_1,axiom,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff_1) ).

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

cnf(cls_less__SucI_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).

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

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

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

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

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

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

cnf(cls_not__less__iff__gr__or__eq_0,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

cnf(cls_linorder__antisym__conv3_0,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

cnf(cls_linorder__less__linear_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X3 = X2
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

cnf(cls_linorder__neqE_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | X3 = X2
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

cnf(cls_linorder__neqE__ordered__idom_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | X3 = X2
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

cnf(cls_linorder__antisym__conv1_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X2,X1)
    | c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).

cnf(cls_linorder__not__less_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).

cnf(cls_linorder__not__le_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

cnf(cls_not__leE_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).

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

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

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

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

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

cnf(cls_class__semiring_Oadd__c_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

cnf(cls_not__less__less__Suc__eq_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).

cnf(cls_not__less__eq_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

cnf(cls_atLeastSucLessThan__greaterThanLessThan_0,axiom,
    c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X1),X2,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastSucLessThan__greaterThanLessThan_0) ).

cnf(cls_nat__neq__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | X2 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

cnf(cls_linorder__neqE__nat_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | X2 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

cnf(cls_class__ringb_Osubr0__iff_0,axiom,
    ( X2 = X3
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).

cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | X2 != c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

cnf(cls_less__Suc0_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).

cnf(cls_double__eq__0__iff_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).

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

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

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

cnf(cls_eq__iff__diff__eq__0_1,axiom,
    ( X2 = X3
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

cnf(cls_right__minus__eq_0,axiom,
    ( X2 = X3
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).

cnf(cls_order__less__irrefl_0,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

cnf(cls_linorder__neq__iff_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

cnf(cls_order__less__le_1,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

cnf(cls_neq0__conv_1,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).

cnf(cls_not__less0_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).

cnf(cls_gr__implies__not0_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).

cnf(cls_nat__less__le_1,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

cnf(cls_less__not__refl_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).

cnf(cls_atLeastLessThan0_0,axiom,
    c_SetInterval_Oord__class_OatLeastLessThan(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan0_0) ).

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

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

cnf(cls_double__eq__0__iff_1,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

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

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).

cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
    ( X2 = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

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/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

cnf(cls_class__ringb_Osubr0__iff_1,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).

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

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

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

cnf(cls_add__0__left_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

cnf(cls_class__semiring_Oadd__0_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

cnf(cls_comm__monoid__add_Omult__1_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

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

cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

cnf(cls_diff__0__right_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

cnf(cls_less__Suc0_1,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_1) ).

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

cnf(cls_eq__iff__diff__eq__0_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

cnf(cls_right__minus__eq_1,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).

cnf(cls_diff__self_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).

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

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

cnf(cls_zero__less__Suc_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).

cnf(cls_gr0__conv__Suc_1,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).

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

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

cnf(cls_GCD__empty__nat_0,axiom,
    c_GCD_Ogcd__class_OGCD(c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD__empty__nat_0) ).

cnf(cls_gr0I_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).

cnf(cls_lessI_0,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).

cnf(cls_less__Suc__eq_2,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

cnf(cls_CHAINED_0,axiom,
    c_HOL_Oord__class_Oless(v_m,v_n,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

cnf(cls_less_0,axiom,
    c_HOL_Oord__class_Oless(v_m,v_n,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less_0) ).

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_Suc__inject_0,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).

cnf(cls_nat_Oinject_0,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

cnf(clsrel_OrderedGroup_Ocomm__monoid__add_OrderedGroup_Omonoid__add,axiom,
    ( class_OrderedGroup_Omonoid__add(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_OrderedGroup_Omonoid__add) ).

cnf(clsrel_OrderedGroup_Ocomm__monoid__add_OrderedGroup_Oab__semigroup__add,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_OrderedGroup_Oab__semigroup__add) ).

cnf(cls_Zero__neq__Suc_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).

cnf(cls_nat_Osimps_I2_J_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).

cnf(cls_nat_Osimps_I3_J_0,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).

cnf(cls_Suc__neq__Zero_0,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).

cnf(cls_Suc__n__not__n_0,axiom,
    c_Suc(X1) != X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

cnf(cls_n__not__Suc__n_0,axiom,
    X1 != c_Suc(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

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

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

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

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

cnf(tfree_tcs,negated_conjecture,
    class_OrderedGroup_Ocomm__monoid__add(t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).

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

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

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

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

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

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

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

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

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

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

cnf(i_0_601,axiom,
    c_Collect(c_fequal(X1,X2),X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    cls_singleton__conv2_0 ).

cnf(i_0_602,axiom,
    c_Collect(X1,X2) = X1,
    cls_Collect__def_0 ).

cnf(i_0_603,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,c_Collect(X4,X3),tc_fun(X3,tc_bool)),X3)) ),
    cls_Int__Collect_0 ).

cnf(i_0_604,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(c_fequal(X1,X3),X2)) ),
    cls_ATP__Linkup_Ofequal__imp__equal_0 ).

cnf(i_0_605,plain,
    c_fequal(X1,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    inference(rw,[status(thm)],[i_0_601,c_0_602]) ).

cnf(i_0_606,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,c_Collect(X1,X4),tc_fun(X4,tc_bool)),X4)) ),
    cls_Int__Collect_1 ).

cnf(i_0_607,axiom,
    ( hBOOL(c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,c_Collect(X3,X4),tc_fun(X4,tc_bool)),X4))
    | ~ hBOOL(hAPP(X3,X1))
    | ~ hBOOL(c_in(X1,X2,X4)) ),
    cls_Int__Collect_2 ).

cnf(i_0_608,axiom,
    c_Finite__Set_Ofold1(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = X2,
    cls_fold1__singleton_0 ).

cnf(i_0_609,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_610,axiom,
    hBOOL(hAPP(c_fequal(X1,X2),X1)),
    cls_ATP__Linkup_Oequal__imp__fequal_0 ).

cnf(i_0_611,axiom,
    c_The(c_fequal(X1,X2),X2) = X1,
    cls_the__sym__eq__trivial_0 ).

cnf(i_0_612,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,c_Collect(X1,X3),X3)) ),
    cls_CollectD_0 ).

cnf(i_0_613,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_add__nonneg__eq__0__iff_2 ).

cnf(i_0_614,axiom,
    ( hBOOL(c_in(X1,c_Collect(X2,X3),X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    cls_CollectI_0 ).

cnf(i_0_615,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_616,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_617,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)) = hAPP(hAPP(X5,X2),X3)
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X6,X7,X8,X5,X9,X10,X11,X4) ),
    cls_complete__lattice_OInf__binary_0,
    [final] ).

cnf(i_0_618,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)) = hAPP(hAPP(X5,X2),X3)
    | ~ c_Complete__Lattice_Ocomplete__lattice(X6,X1,X7,X8,X9,X5,X10,X11,X4) ),
    cls_complete__lattice_OSup__binary_0,
    [final] ).

cnf(i_0_619,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_620,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_621,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X4,X5,X6,X7,X8,X9,X10,X3) ),
    cls_complete__lattice_OInf__singleton_0,
    [final] ).

cnf(i_0_622,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) = X2
    | ~ c_Complete__Lattice_Ocomplete__lattice(X4,X1,X5,X6,X7,X8,X9,X10,X3) ),
    cls_complete__lattice_OSup__singleton_0,
    [final] ).

cnf(i_0_623,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,X3,X4)) = hAPP(hAPP(X5,X2),hAPP(X1,X3))
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X6,X7,X8,X5,X9,X10,X11,X4) ),
    cls_complete__lattice_OInf__insert_0,
    [final] ).

cnf(i_0_624,axiom,
    ( hAPP(X1,c_Set_Oinsert(X2,X3,X4)) = hAPP(hAPP(X5,X2),hAPP(X1,X3))
    | ~ c_Complete__Lattice_Ocomplete__lattice(X6,X1,X7,X8,X9,X5,X10,X11,X4) ),
    cls_complete__lattice_OSup__insert_0,
    [final] ).

cnf(i_0_625,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_626,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_627,axiom,
    ( c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1),X1,X2) = c_Finite__Set_Osetsum(X6,c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1),X1,X2)
    | ~ class_HOL_Oord(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X2)
    | hAPP(X3,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(X4,X5,X3,X6,X1,X2)) != hAPP(X6,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(X4,X5,X3,X6,X1,X2)) ),
    cls_setsum__ivl__cong_2,
    [final] ).

cnf(i_0_628,axiom,
    ( c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1),X1,X2) = c_Finite__Set_Osetsum(X6,c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1),X1,X2)
    | c_HOL_Oord__class_Oless(c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(X4,X5,X3,X6,X1,X2),X5,X1)
    | ~ class_HOL_Oord(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
    cls_setsum__ivl__cong_1,
    [final] ).

cnf(i_0_629,axiom,
    ( c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1),X1,X2) = c_Finite__Set_Osetsum(X6,c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1),X1,X2)
    | c_lessequals(X4,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(X4,X5,X3,X6,X1,X2),X1)
    | ~ class_HOL_Oord(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
    cls_setsum__ivl__cong_0,
    [final] ).

cnf(i_0_630,axiom,
    ( hAPP(X1,X2) = X3
    | ~ hBOOL(c_in(X2,c_Set_Ovimage(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),X5)) ),
    cls_vimage__singleton__eq_0,
    [final] ).

cnf(i_0_631,axiom,
    hBOOL(c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(hAPP(X2,X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3),X4)),
    cls_vimage__singleton__eq_1,
    [final] ).

cnf(i_0_632,negated_conjecture,
    c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
    cls_conjecture_0,
    [final] ).

cnf(i_0_633,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Un__Int__crazy_0,
    [final] ).

cnf(i_0_634,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),X3,X4))
    | ~ hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)) ),
    cls_vimageE_0,
    [final] ).

cnf(i_0_635,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),X3,X4))
    | ~ hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)) ),
    cls_vimageD_0,
    [final] ).

cnf(i_0_636,axiom,
    c_Set_Ovimage(X1,c_Set_Oinsert(X2,X3,X4),X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
    cls_vimage__insert_0,
    [final] ).

cnf(i_0_637,axiom,
    ( c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a),t_a) = c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a)
    | ~ class_OrderedGroup_Ocomm__monoid__add(t_a) ),
    cls_calculation_0,
    [final] ).

cnf(i_0_638,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4),X2)) ),
    cls_fold1Set__sing_0,
    [final] ).

cnf(i_0_639,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
    cls_vimage__code_0,
    [final] ).

cnf(i_0_640,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_641,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_642,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,X3,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X4,X3,tc_fun(X5,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
    cls_UN__Un_0,
    [final] ).

cnf(i_0_643,axiom,
    c_Set_Ovimage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
    cls_vimage__Un_0,
    [final] ).

cnf(i_0_644,axiom,
    c_Set_Ovimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
    cls_vimage__Int_0,
    [final] ).

cnf(i_0_645,axiom,
    c_Set_Ovimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
    cls_vimage__Diff_0,
    [final] ).

cnf(i_0_646,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_647,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_648,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ hBOOL(c_in(X2,X1,X4))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    cls_diff__single__insert_0,
    [final] ).

cnf(i_0_649,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ hBOOL(c_in(X2,X1,X4))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    cls_subset__insert__iff_3,
    [final] ).

cnf(i_0_650,axiom,
    ( hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4))
    | ~ hBOOL(c_in(hAPP(X2,X1),X3,X5)) ),
    cls_vimage__eq_1,
    [final] ).

cnf(i_0_651,axiom,
    ( hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4))
    | ~ hBOOL(c_in(hAPP(X2,X1),X3,X5)) ),
    cls_vimageI2_0,
    [final] ).

cnf(i_0_652,axiom,
    ( hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4))
    | ~ hBOOL(c_in(hAPP(X2,X1),X3,X5)) ),
    cls_vimageI_0,
    [final] ).

cnf(i_0_653,axiom,
    hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2))),
    cls_Nitpick_OEx1__def_2,
    [final] ).

cnf(i_0_654,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    cls_subset__insert__iff_4,
    [final] ).

cnf(i_0_655,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_656,axiom,
    ( c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,tc_nat),tc_nat,X1) = c_HOL_Oplus__class_Oplus(hAPP(X2,X3),c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X3),X4,tc_nat),tc_nat,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    cls_setsum__head__upt__Suc_0,
    [final] ).

cnf(i_0_657,axiom,
    ( c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(X3,c_Suc(X4),tc_nat),tc_nat,X1) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,tc_nat),tc_nat,X1),hAPP(X2,X4),X1)
    | c_HOL_Oord__class_Oless(X4,X3,tc_nat)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_setsum__op__ivl__Suc_1,
    [final] ).

cnf(i_0_658,axiom,
    ( c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),c_Set_Ovimage(X1,X5,X3,X4),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X4,tc_bool)) ),
    cls_vimage__mono_0,
    [final] ).

cnf(i_0_659,axiom,
    ( hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5))
    | ~ hBOOL(hAPP(X2,hAPP(X1,X5))) ),
    cls_vimage__code_1,
    [final] ).

cnf(i_0_660,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | ~ hBOOL(c_in(X2,X1,X3))
    | ~ c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool)) ),
    cls_subset__insert__iff_0,
    [final] ).

cnf(i_0_661,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(hAPP(X1,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1,X4,tc_fun(X5,tc_bool))
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    cls_UN__absorb_0,
    [final] ).

cnf(i_0_662,axiom,
    hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X2)),
    cls_fold1Set__sing_1,
    [final] ).

cnf(i_0_663,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X1,X2,X3),X4,X3,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
    cls_UN__insert_0,
    [final] ).

cnf(i_0_664,axiom,
    ( X1 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
    | ~ hBOOL(hAPP(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X1)) ),
    cls_Nitpick_OEx1__def_3,
    [final] ).

cnf(i_0_665,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1),c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_distrib__inf__le_0,
    [final] ).

cnf(i_0_666,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_distrib__sup__le_0,
    [final] ).

cnf(i_0_667,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | hBOOL(c_in(X1,X4,X3))
    | ~ hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3)) ),
    cls_UnE_0,
    [final] ).

cnf(i_0_668,axiom,
    ( X1 = X2
    | ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) ),
    cls_singletonE_0,
    [final] ).

cnf(i_0_669,axiom,
    ( X1 = X5
    | X1 = X4
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    cls_doubleton__eq__iff_0,
    [final] ).

cnf(i_0_670,axiom,
    ( X2 = X4
    | X1 = X4
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    cls_doubleton__eq__iff_1,
    [final] ).

cnf(i_0_671,axiom,
    ( X1 = X5
    | X2 = X5
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    cls_doubleton__eq__iff_2,
    [final] ).

cnf(i_0_672,axiom,
    ( X2 = X4
    | X2 = X5
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    cls_doubleton__eq__iff_3,
    [final] ).

cnf(i_0_673,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)),
    cls_Diff__insert2_0,
    [final] ).

cnf(i_0_674,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_675,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_676,axiom,
    ( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
    | ~ hBOOL(c_in(X1,X2,X3)) ),
    cls_insert__Diff_0,
    [final] ).

cnf(i_0_677,axiom,
    c_Set_Oinsert(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X4,tc_bool)),X4) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
    cls_UN__extend__simps_I1_J_0,
    [final] ).

cnf(i_0_678,axiom,
    ( c_lessequals(X4,X1,tc_fun(X3,tc_bool))
    | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    cls_Un__Int__assoc__eq_0,
    [final] ).

cnf(i_0_679,axiom,
    ( c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat),tc_nat,X1) = c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat),tc_nat,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | hAPP(X2,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_setsum__shift__lb__Suc0__0__upt_0,
    [final] ).

cnf(i_0_680,axiom,
    ( hBOOL(c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4))
    | ~ hBOOL(c_in(X1,X3,X4))
    | ~ hBOOL(c_in(X1,X2,X4)) ),
    cls_IntI_0,
    [final] ).

cnf(i_0_681,axiom,
    ( hBOOL(c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4))
    | ~ hBOOL(c_in(X1,X3,X4))
    | ~ hBOOL(c_in(X1,X2,X4)) ),
    cls_Int__iff_2,
    [final] ).

cnf(i_0_682,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)) ),
    cls_IntE_0,
    [final] ).

cnf(i_0_683,plain,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)) ),
    inference(rw,[status(thm)],[i_0_603,c_0_602]),
    [final] ).

cnf(i_0_684,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3)) ),
    cls_IntE_1,
    [final] ).

cnf(i_0_685,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_686,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_687,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = X4,
    cls_UN__extend__simps_I2_J_0,
    [final] ).

cnf(i_0_688,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X1,
    cls_UN__extend__simps_I3_J_0,
    [final] ).

cnf(i_0_689,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_690,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2)) ),
    inference(rw,[status(thm)],[i_0_604,c_0_605]),
    [final] ).

cnf(i_0_691,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_692,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_693,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_694,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),X4)) ),
    inference(rw,[status(thm)],[i_0_606,c_0_602]),
    [final] ).

cnf(i_0_695,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_696,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_697,axiom,
    c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X1,X2,X3),
    cls_insert__Diff__single_0,
    [final] ).

cnf(i_0_698,plain,
    ( hBOOL(c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4))
    | ~ hBOOL(hAPP(X3,X1))
    | ~ hBOOL(c_in(X1,X2,X4)) ),
    inference(rw,[status(thm)],[i_0_607,c_0_602]),
    [final] ).

cnf(i_0_699,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    cls_Un__mono_0,
    [final] ).

cnf(i_0_700,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    cls_Int__mono_0,
    [final] ).

cnf(i_0_701,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_702,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
    cls_Diff__insert_0,
    [final] ).

cnf(i_0_703,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | X1 = X4
    | ~ hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)) ),
    cls_insertE_0,
    [final] ).

cnf(i_0_704,axiom,
    c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
    cls_Diff__Int2_0,
    [final] ).

cnf(i_0_705,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Un__Int__distrib2_0,
    [final] ).

cnf(i_0_706,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Int__Un__distrib2_0,
    [final] ).

cnf(i_0_707,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Diff__Int__distrib2_0,
    [final] ).

cnf(i_0_708,axiom,
    c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Un__Diff_0,
    [final] ).

cnf(i_0_709,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Un__Int__distrib_0,
    [final] ).

cnf(i_0_710,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Int__Un__distrib_0,
    [final] ).

cnf(i_0_711,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Diff__Int__distrib_0,
    [final] ).

cnf(i_0_712,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Diff__Un_0,
    [final] ).

cnf(i_0_713,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Diff__Int_0,
    [final] ).

cnf(i_0_714,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_715,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_716,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_Sup__binary_0,
    [final] ).

cnf(i_0_717,axiom,
    ( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_Inf__binary_0,
    [final] ).

cnf(i_0_718,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    cls_Diff__subset__conv_1,
    [final] ).

cnf(i_0_719,axiom,
    ( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    cls_Diff__subset__conv_0,
    [final] ).

cnf(i_0_720,axiom,
    ( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4))
    | ~ hBOOL(c_in(X1,X2,X4)) ),
    cls_UnCI_1,
    [final] ).

cnf(i_0_721,axiom,
    ( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4))
    | ~ hBOOL(c_in(X1,X3,X4)) ),
    cls_UnCI_0,
    [final] ).

cnf(i_0_722,axiom,
    ( X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
    cls_subset__singletonD_0,
    [final] ).

cnf(i_0_723,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X3,X2))
    | ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
    cls_sup1E_0,
    [final] ).

cnf(i_0_724,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X4,X1,tc_fun(X3,tc_bool)) ),
    cls_Un__Int__assoc__eq_1,
    [final] ).

cnf(i_0_725,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(X4,X2,X1),c_SetInterval_Oord__class_OatLeastLessThan(X5,X3,X1),tc_fun(X1,tc_bool)) ),
    cls_atLeastLessThan__subset__iff_1,
    [final] ).

cnf(i_0_726,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X4,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),c_SetInterval_Oord__class_OatLeastLessThan(X2,X5,X1),tc_fun(X1,tc_bool)) ),
    cls_atLeastLessThan__subset__iff_0,
    [final] ).

cnf(i_0_727,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
    | ~ hBOOL(c_in(X1,X4,X3)) ),
    cls_Int__insert__left_0,
    [final] ).

cnf(i_0_728,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X4)
    | ~ hBOOL(c_in(X2,X1,X4)) ),
    cls_Int__insert__right_0,
    [final] ).

cnf(i_0_729,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2)) ),
    cls_inf1E_0,
    [final] ).

cnf(i_0_730,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
    cls_inf1E_1,
    [final] ).

cnf(i_0_731,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X5,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I20_J_0,
    [final] ).

cnf(i_0_732,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,X1),X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    cls_Deriv_Oadd__diff__add_0,
    [final] ).

cnf(i_0_733,plain,
    c_The(c_Finite__Set_Ofold1Set(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X3) = X2,
    inference(rw,[status(thm)],[i_0_608,c_0_609]),
    [final] ).

cnf(i_0_734,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_ivl__disj__un_I3_J_0,
    [final] ).

cnf(i_0_735,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_ivl__disj__un_I5_J_0,
    [final] ).

cnf(i_0_736,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X1),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_ivl__disj__un_I4_J_0,
    [final] ).

cnf(i_0_737,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_ivl__disj__un_I6_J_0,
    [final] ).

cnf(i_0_738,axiom,
    hBOOL(c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)),
    cls_singleton__iff_1,
    [final] ).

cnf(i_0_739,axiom,
    c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
    cls_doubleton__eq__iff_4,
    [final] ).

cnf(i_0_740,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_ivl__disj__un_I15_J_0,
    [final] ).

cnf(i_0_741,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_ivl__disj__un_I19_J_0,
    [final] ).

cnf(i_0_742,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_ivl__disj__un_I17_J_0,
    [final] ).

cnf(i_0_743,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_ivl__disj__un_I21_J_0,
    [final] ).

cnf(i_0_744,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_ivl__disj__un_I16_J_0,
    [final] ).

cnf(i_0_745,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_ivl__disj__un_I20_J_0,
    [final] ).

cnf(i_0_746,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_ivl__disj__un_I18_J_0,
    [final] ).

cnf(i_0_747,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_ivl__disj__un_I22_J_0,
    [final] ).

cnf(i_0_748,axiom,
    ( ~ hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,X4,X3))
    | c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_disjoint__iff__not__equal_0,
    [final] ).

cnf(i_0_749,axiom,
    ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X5,X4,X1)
    | ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X5,X1),X1) ),
    cls_le__add__right__mono_0,
    [final] ).

cnf(i_0_750,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2
    | hBOOL(c_in(X1,X2,X3)) ),
    cls_Diff__insert__absorb_0,
    [final] ).

cnf(i_0_751,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)
    | hBOOL(c_in(X1,X4,X3)) ),
    cls_insert__Diff__if_1,
    [final] ).

cnf(i_0_752,axiom,
    ( hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4))
    | ~ hBOOL(c_in(X1,X3,X4)) ),
    cls_insert__iff_2,
    [final] ).

cnf(i_0_753,axiom,
    ( hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4))
    | ~ hBOOL(c_in(X1,X3,X4)) ),
    cls_insertCI_0,
    [final] ).

cnf(i_0_754,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3),
    cls_insert__inter__insert_0,
    [final] ).

cnf(i_0_755,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
    cls_add__less__cancel__right_0,
    [final] ).

cnf(i_0_756,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
    cls_add__less__cancel__left_0,
    [final] ).

cnf(i_0_757,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
    cls_add__le__cancel__right_0,
    [final] ).

cnf(i_0_758,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
    cls_add__le__cancel__left_0,
    [final] ).

cnf(i_0_759,axiom,
    ( c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
    | ~ hBOOL(c_in(X1,X4,X3)) ),
    cls_insert__subset_2,
    [final] ).

cnf(i_0_760,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | hBOOL(c_in(X4,X1,X3))
    | ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
    cls_subset__insert__iff_1,
    [final] ).

cnf(i_0_761,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | hBOOL(c_in(X4,X1,X3))
    | ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
    cls_subset__insert_0,
    [final] ).

cnf(i_0_762,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_763,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    cls_Un__subset__iff_2,
    [final] ).

cnf(i_0_764,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    cls_Un__least_0,
    [final] ).

cnf(i_0_765,axiom,
    ( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
    cls_Int__greatest_0,
    [final] ).

cnf(i_0_766,axiom,
    ( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
    cls_Int__subset__iff_2,
    [final] ).

cnf(i_0_767,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_768,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Un__assoc_0,
    [final] ).

cnf(i_0_769,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Int__assoc_0,
    [final] ).

cnf(i_0_770,axiom,
    c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Int__Diff_0,
    [final] ).

cnf(i_0_771,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Un__left__commute_0,
    [final] ).

cnf(i_0_772,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Int__left__commute_0,
    [final] ).

cnf(i_0_773,axiom,
    ( c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(X3,c_Suc(X4),tc_nat),tc_nat,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    cls_setsum__op__ivl__Suc_0,
    [final] ).

cnf(i_0_774,plain,
    hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X1)),
    inference(rw,[status(thm)],[i_0_610,c_0_605]),
    [final] ).

cnf(i_0_775,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_add__strict__mono_0,
    [final] ).

cnf(i_0_776,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_add__le__less__mono_0,
    [final] ).

cnf(i_0_777,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_add__less__le__mono_0,
    [final] ).

cnf(i_0_778,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_add__mono_0,
    [final] ).

cnf(i_0_779,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
    cls_Un__subset__iff_0,
    [final] ).

cnf(i_0_780,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
    cls_Un__subset__iff_1,
    [final] ).

cnf(i_0_781,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    cls_Int__subset__iff_0,
    [final] ).

cnf(i_0_782,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    cls_Int__subset__iff_1,
    [final] ).

cnf(i_0_783,axiom,
    ( c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X4,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_ivl__diff_0,
    [final] ).

cnf(i_0_784,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool))
    | ~ hBOOL(c_in(X1,X4,X3)) ),
    cls_insert__Diff1_0,
    [final] ).

cnf(i_0_785,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    cls_sup__inf__distrib2_0,
    [final] ).

cnf(i_0_786,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    cls_inf__sup__distrib2_0,
    [final] ).

cnf(i_0_787,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
    cls_add__sup__distrib__right_0,
    [final] ).

cnf(i_0_788,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0,
    [final] ).

cnf(i_0_789,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
    cls_add__inf__distrib__right_0,
    [final] ).

cnf(i_0_790,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,
    [final] ).

cnf(i_0_791,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    cls_sup__inf__distrib1_0,
    [final] ).

cnf(i_0_792,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    cls_inf__sup__distrib1_0,
    [final] ).

cnf(i_0_793,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
    cls_add__sup__distrib__left_0,
    [final] ).

cnf(i_0_794,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0,
    [final] ).

cnf(i_0_795,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
    cls_add__inf__distrib__left_0,
    [final] ).

cnf(i_0_796,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,
    [final] ).

cnf(i_0_797,axiom,
    ( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4))
    | ~ hBOOL(hAPP(X2,X4))
    | ~ hBOOL(hAPP(X1,X4)) ),
    cls_inf1I_0,
    [final] ).

cnf(i_0_798,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | hBOOL(c_in(X2,X1,X4))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    cls_subset__insert__iff_2,
    [final] ).

cnf(i_0_799,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | hBOOL(c_in(X2,X1,X4))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    cls_subset__insert_1,
    [final] ).

cnf(i_0_800,axiom,
    ( hBOOL(hAPP(X1,X2))
    | X3 = X2
    | ~ hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
    cls_insert__code_0,
    [final] ).

cnf(i_0_801,axiom,
    ( c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
    cls_insert__mono_0,
    [final] ).

cnf(i_0_802,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_803,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_804,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_805,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_806,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X4,X1) = X5
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X3,X5,X1) ),
    cls_add__cancel__21_0,
    [final] ).

cnf(i_0_807,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
    cls_insert__subset_0,
    [final] ).

cnf(i_0_808,axiom,
    ( hBOOL(c_in(X1,X4,X3))
    | hBOOL(c_in(X1,X2,X3))
    | X2 = X4
    | c_Set_Oinsert(X1,X2,X3) != c_Set_Oinsert(X1,X4,X3) ),
    cls_insert__ident_0,
    [final] ).

cnf(i_0_809,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3),
    cls_Un__insert__left_0,
    [final] ).

cnf(i_0_810,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X4),
    cls_Un__insert__right_0,
    [final] ).

cnf(i_0_811,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_812,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1,
    cls_Un__Diff__Int_0,
    [final] ).

cnf(i_0_813,axiom,
    ( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
    | ~ hBOOL(hAPP(X1,X4)) ),
    cls_sup1CI_1,
    [final] ).

cnf(i_0_814,axiom,
    ( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
    | ~ hBOOL(hAPP(X2,X4)) ),
    cls_sup1CI_0,
    [final] ).

cnf(i_0_815,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool))
    | hBOOL(c_in(X1,X4,X3)) ),
    cls_Int__insert__left_1,
    [final] ).

cnf(i_0_816,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool))
    | hBOOL(c_in(X2,X1,X4)) ),
    cls_Int__insert__right_1,
    [final] ).

cnf(i_0_817,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_818,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Set_Oinsert(X4,X1,X3),X2,tc_fun(X3,tc_bool)) ),
    cls_insert__subset_1,
    [final] ).

cnf(i_0_819,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_add__neg__neg_0,
    [final] ).

cnf(i_0_820,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_add__nonpos__neg_0,
    [final] ).

cnf(i_0_821,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_add__neg__nonpos_0,
    [final] ).

cnf(i_0_822,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_add__nonpos__nonpos_0,
    [final] ).

cnf(i_0_823,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__pos__pos_0,
    [final] ).

cnf(i_0_824,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__nonneg__pos_0,
    [final] ).

cnf(i_0_825,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__pos__nonneg_0,
    [final] ).

cnf(i_0_826,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__nonneg__nonneg_0,
    [final] ).

cnf(i_0_827,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    cls_add__strict__left__mono_0,
    [final] ).

cnf(i_0_828,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    cls_add__less__cancel__left_1,
    [final] ).

cnf(i_0_829,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_add__strict__right__mono_0,
    [final] ).

cnf(i_0_830,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_add__less__cancel__right_1,
    [final] ).

cnf(i_0_831,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    cls_add__le__cancel__left_1,
    [final] ).

cnf(i_0_832,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    cls_add__left__mono_0,
    [final] ).

cnf(i_0_833,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_add__le__cancel__right_1,
    [final] ).

cnf(i_0_834,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_add__right__mono_0,
    [final] ).

cnf(i_0_835,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_add__strict__increasing2_0,
    [final] ).

cnf(i_0_836,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_add__strict__increasing_0,
    [final] ).

cnf(i_0_837,axiom,
    ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
    cls_add__increasing2_0,
    [final] ).

cnf(i_0_838,axiom,
    ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_add__increasing_0,
    [final] ).

cnf(i_0_839,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_840,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X2
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_Diff__partition_0,
    [final] ).

cnf(i_0_841,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_pos__add__strict_0,
    [final] ).

cnf(i_0_842,axiom,
    c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,tc_fun(X3,tc_bool)),
    cls_insert__is__Un_0,
    [final] ).

cnf(i_0_843,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_le__supI_0,
    [final] ).

cnf(i_0_844,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_sup__least_0,
    [final] ).

cnf(i_0_845,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_le__sup__iff_2,
    [final] ).

cnf(i_0_846,axiom,
    ( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_inf__greatest_0,
    [final] ).

cnf(i_0_847,axiom,
    ( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__inf__iff_2,
    [final] ).

cnf(i_0_848,axiom,
    ( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__infI_0,
    [final] ).

cnf(i_0_849,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_850,axiom,
    ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
    cls_empty__iff_0,
    [final] ).

cnf(i_0_851,axiom,
    ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
    cls_emptyE_0,
    [final] ).

cnf(i_0_852,axiom,
    ( X1 = X3
    | c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    cls_singleton__inject_0,
    [final] ).

cnf(i_0_853,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
    cls_zero__less__double__add__iff__zero__less__single__add_0,
    [final] ).

cnf(i_0_854,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
    cls_zero__le__double__add__iff__zero__le__single__add_0,
    [final] ).

cnf(i_0_855,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_even__less__0__iff_0,
    [final] ).

cnf(i_0_856,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_double__add__less__zero__iff__single__less__zero_0,
    [final] ).

cnf(i_0_857,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_double__add__le__zero__iff__single__add__le__zero_0,
    [final] ).

cnf(i_0_858,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I23_J_0,
    [final] ).

cnf(i_0_859,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__assoc_0,
    [final] ).

cnf(i_0_860,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I6_J_0,
    [final] ).

cnf(i_0_861,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__assoc_0,
    [final] ).

cnf(i_0_862,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I2_J_0,
    [final] ).

cnf(i_0_863,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,
    [final] ).

cnf(i_0_864,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I21_J_0,
    [final] ).

cnf(i_0_865,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__assoc_0,
    [final] ).

cnf(i_0_866,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I25_J_0,
    [final] ).

cnf(i_0_867,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Oadd__a_0,
    [final] ).

cnf(i_0_868,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__left__commute_0,
    [final] ).

cnf(i_0_869,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I7_J_0,
    [final] ).

cnf(i_0_870,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__left__commute_0,
    [final] ).

cnf(i_0_871,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I3_J_0,
    [final] ).

cnf(i_0_872,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I22_J_0,
    [final] ).

cnf(i_0_873,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__left__commute_0,
    [final] ).

cnf(i_0_874,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    cls_add__cancel__21_1,
    [final] ).

cnf(i_0_875,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_add__eq__inf__sup_0,
    [final] ).

cnf(i_0_876,axiom,
    c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    cls_vimage__empty_0,
    [final] ).

cnf(i_0_877,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_less__iff__diff__less__0_1,
    [final] ).

cnf(i_0_878,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_le__iff__diff__le__0_1,
    [final] ).

cnf(i_0_879,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    cls_ivl__disj__int_I9_J_0,
    [final] ).

cnf(i_0_880,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    cls_ivl__disj__int_I13_J_0,
    [final] ).

cnf(i_0_881,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    cls_ivl__disj__int_I11_J_0,
    [final] ).

cnf(i_0_882,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    cls_ivl__disj__int_I15_J_0,
    [final] ).

cnf(i_0_883,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    cls_ivl__disj__int_I10_J_0,
    [final] ).

cnf(i_0_884,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    cls_ivl__disj__int_I14_J_0,
    [final] ).

cnf(i_0_885,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    cls_ivl__disj__int_I12_J_0,
    [final] ).

cnf(i_0_886,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1) ),
    cls_ivl__disj__int_I16_J_0,
    [final] ).

cnf(i_0_887,axiom,
    hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
    cls_insert__iff_1,
    [final] ).

cnf(i_0_888,axiom,
    hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
    cls_insertI1_0,
    [final] ).

cnf(i_0_889,axiom,
    hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
    cls_insertCI_1,
    [final] ).

cnf(i_0_890,axiom,
    c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
    cls_insert__commute_0,
    [final] ).

cnf(i_0_891,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_892,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,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_HOL_Oord__class_Oless(X4,X5,X1) ),
    cls_less__eqI_1,
    [final] ).

cnf(i_0_893,axiom,
    ( c_HOL_Oord__class_Oless(X4,X5,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_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_less__eqI_0,
    [final] ).

cnf(i_0_894,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_895,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_896,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X3,X1) ),
    cls_le__supE_0,
    [final] ).

cnf(i_0_897,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X3,X1) ),
    cls_le__sup__iff_0,
    [final] ).

cnf(i_0_898,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X1),X3,X1) ),
    cls_le__supE_1,
    [final] ).

cnf(i_0_899,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X1),X3,X1) ),
    cls_le__sup__iff_1,
    [final] ).

cnf(i_0_900,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
    cls_le__inf__iff_0,
    [final] ).

cnf(i_0_901,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
    cls_le__infE_0,
    [final] ).

cnf(i_0_902,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
    cls_le__inf__iff_1,
    [final] ).

cnf(i_0_903,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
    cls_le__infE_1,
    [final] ).

cnf(i_0_904,axiom,
    ( c_Finite__Set_Osetsum(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_setsum__empty_0,
    [final] ).

cnf(i_0_905,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
    cls_Un__Diff__cancel2_0,
    [final] ).

cnf(i_0_906,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_907,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
    cls_Un__left__absorb_0,
    [final] ).

cnf(i_0_908,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
    cls_Un__Diff__cancel_0,
    [final] ).

cnf(i_0_909,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
    cls_Int__left__absorb_0,
    [final] ).

cnf(i_0_910,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    cls_subset__insertI2_0,
    [final] ).

cnf(i_0_911,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__nonneg__eq__0__iff_0,
    [final] ).

cnf(i_0_912,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__nonneg__eq__0__iff_1,
    [final] ).

cnf(i_0_913,axiom,
    ( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
    | ~ hBOOL(hAPP(X2,X4)) ),
    cls_insert__code_2,
    [final] ).

cnf(i_0_914,axiom,
    ( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(t_a,X1)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X2,v_x),hAPP(X3,v_x),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_sup__fun__eq_0,
    [final] ).

cnf(i_0_915,axiom,
    ( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(t_a,X1)),v_x) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(X2,v_x),hAPP(X3,v_x),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__fun__eq_0,
    [final] ).

cnf(i_0_916,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_917,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_even__less__0__iff_1,
    [final] ).

cnf(i_0_918,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_double__add__less__zero__iff__single__less__zero_1,
    [final] ).

cnf(i_0_919,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_double__add__le__zero__iff__single__add__le__zero_1,
    [final] ).

cnf(i_0_920,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_zero__less__double__add__iff__zero__less__single__add_1,
    [final] ).

cnf(i_0_921,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_zero__le__double__add__iff__zero__le__single__add_1,
    [final] ).

cnf(i_0_922,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_complete__lattice__class_OInf__lower_0,
    [final] ).

cnf(i_0_923,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_complete__lattice__class_OSup__upper_0,
    [final] ).

cnf(i_0_924,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_less__iff__diff__less__0_0,
    [final] ).

cnf(i_0_925,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__iff__diff__le__0_0,
    [final] ).

cnf(i_0_926,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    cls_Diff__disjoint_0,
    [final] ).

cnf(i_0_927,axiom,
    ( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_less__infI1_0,
    [final] ).

cnf(i_0_928,axiom,
    ( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    cls_less__infI2_0,
    [final] ).

cnf(i_0_929,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_le__infI1_0,
    [final] ).

cnf(i_0_930,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    cls_le__infI2_0,
    [final] ).

cnf(i_0_931,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_less__supI1_0,
    [final] ).

cnf(i_0_932,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_less__supI2_0,
    [final] ).

cnf(i_0_933,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__supI1_0,
    [final] ).

cnf(i_0_934,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_le__supI2_0,
    [final] ).

cnf(i_0_935,axiom,
    ( hAPP(c_Lattices_Oupper__semilattice__class_Osup(v_f,v_g,tc_fun(t_a,t_b)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(v_f,v_x),hAPP(v_g,v_x),t_b)
    | ~ class_Lattices_Olattice(t_b) ),
    cls_sup__fun__eq__raw_0,
    [final] ).

cnf(i_0_936,axiom,
    ( hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_f,v_g,tc_fun(t_a,t_b)),v_x) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(v_f,v_x),hAPP(v_g,v_x),t_b)
    | ~ class_Lattices_Olattice(t_b) ),
    cls_inf__fun__eq__raw_0,
    [final] ).

cnf(i_0_937,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_938,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_939,axiom,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    cls_insert__code_1,
    [final] ).

cnf(i_0_940,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_Diff__triv_0,
    [final] ).

cnf(i_0_941,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_942,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_comm__monoid__add_Ononempty__iff_2,
    [final] ).

cnf(i_0_943,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_order__less__trans_0,
    [final] ).

cnf(i_0_944,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_order__le__less__trans_0,
    [final] ).

cnf(i_0_945,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_order__less__le__trans_0,
    [final] ).

cnf(i_0_946,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
    cls_xt1_I10_J_0,
    [final] ).

cnf(i_0_947,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
    cls_xt1_I7_J_0,
    [final] ).

cnf(i_0_948,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_lessequals(X4,X3,X1) ),
    cls_xt1_I8_J_0,
    [final] ).

cnf(i_0_949,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_950,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_951,axiom,
    ( c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    cls_Max__singleton_0,
    [final] ).

cnf(i_0_952,axiom,
    ( c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    cls_Min__singleton_0,
    [final] ).

cnf(i_0_953,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_complete__lattice__class_OSup__singleton_0,
    [final] ).

cnf(i_0_954,axiom,
    ( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_complete__lattice__class_OInf__singleton_0,
    [final] ).

cnf(i_0_955,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_956,axiom,
    ( c_Set_Oinsert(X1,X2,X3) = X2
    | ~ hBOOL(c_in(X1,X2,X3)) ),
    cls_insert__absorb_0,
    [final] ).

cnf(i_0_957,axiom,
    c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    cls_Int__lower1_0,
    [final] ).

cnf(i_0_958,axiom,
    c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
    cls_Int__lower2_0,
    [final] ).

cnf(i_0_959,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_960,axiom,
    c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Un__upper1_0,
    [final] ).

cnf(i_0_961,axiom,
    c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Un__upper2_0,
    [final] ).

cnf(i_0_962,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_less__trans__Suc_0,
    [final] ).

cnf(i_0_963,axiom,
    c_Set_Ocontents(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1,
    cls_contents__eq_0,
    [final] ).

cnf(i_0_964,axiom,
    c_The(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1,
    cls_Nitpick_OThe__psimp_0,
    [final] ).

cnf(i_0_965,plain,
    c_The(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = X1,
    inference(rw,[status(thm)],[i_0_611,c_0_605]),
    [final] ).

cnf(i_0_966,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__left__idem_0,
    [final] ).

cnf(i_0_967,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I8_J_0,
    [final] ).

cnf(i_0_968,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__left__idem_0,
    [final] ).

cnf(i_0_969,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I4_J_0,
    [final] ).

cnf(i_0_970,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_atLeastLessThan__empty__iff2_0,
    [final] ).

cnf(i_0_971,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_greaterThanAtMost__empty__iff2_0,
    [final] ).

cnf(i_0_972,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_973,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_atLeastLessThan__empty__iff_0,
    [final] ).

cnf(i_0_974,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_greaterThanAtMost__empty__iff_0,
    [final] ).

cnf(i_0_975,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_976,axiom,
    c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
    cls_insert__absorb2_0,
    [final] ).

cnf(i_0_977,axiom,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    cls_bot1E_0,
    [final] ).

cnf(i_0_978,axiom,
    c_GCD_Ogcd__class_OLCM(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = X1,
    cls_gcd__lcm__complete__lattice__nat_OSup__singleton_0,
    [final] ).

cnf(i_0_979,axiom,
    c_GCD_Ogcd__class_OGCD(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = X1,
    cls_gcd__lcm__complete__lattice__nat_OInf__singleton_0,
    [final] ).

cnf(i_0_980,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_Sup__insert_0,
    [final] ).

cnf(i_0_981,axiom,
    ( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Complete__Lattice_OInf__class_OInf(X3,X1),X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_Inf__insert_0,
    [final] ).

cnf(i_0_982,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_Un__empty_2,
    [final] ).

cnf(i_0_983,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,X1,X3)) ),
    cls_mem__def_0,
    [final] ).

cnf(i_0_984,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,X1,X3)) ),
    inference(rw,[status(thm)],[i_0_612,c_0_602]),
    [final] ).

cnf(i_0_985,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_less__le__not__le_2,
    [final] ).

cnf(i_0_986,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2 ),
    cls_subset__Un__eq_1,
    [final] ).

cnf(i_0_987,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X1
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
    cls_Un__absorb2_0,
    [final] ).

cnf(i_0_988,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_Un__absorb1_0,
    [final] ).

cnf(i_0_989,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_Int__absorb2_0,
    [final] ).

cnf(i_0_990,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X2
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
    cls_Int__absorb1_0,
    [final] ).

cnf(i_0_991,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_992,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_993,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_Un__empty_0,
    [final] ).

cnf(i_0_994,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_Un__empty_1,
    [final] ).

cnf(i_0_995,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | X3 = X2
    | c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
    cls_nat__less__cases_0,
    [final] ).

cnf(i_0_996,axiom,
    ( X3 = X4
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
    cls_class__ringb_Oadd__cancel_0,
    [final] ).

cnf(i_0_997,axiom,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    cls_subset__insertI_0,
    [final] ).

cnf(i_0_998,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(cn,[status(thm)],[i_0_613]),
    [final] ).

cnf(i_0_999,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_1000,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_1001,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_1002,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_1003,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_1004,axiom,
    ( X2 = X4
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X4,X3,X1) ),
    cls_add__right__cancel_0,
    [final] ).

cnf(i_0_1005,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
    cls_add__left__cancel_0,
    [final] ).

cnf(i_0_1006,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
    cls_add__imp__eq_0,
    [final] ).

cnf(i_0_1007,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_1008,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    cls_order__less__asym_0,
    [final] ).

cnf(i_0_1009,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    cls_order__less__asym_H_0,
    [final] ).

cnf(i_0_1010,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    cls_less__le__not__le_1,
    [final] ).

cnf(i_0_1011,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    cls_not__less__iff__gr__or__eq_1,
    [final] ).

cnf(i_0_1012,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X2,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_linorder__antisym__conv2_1,
    [final] ).

cnf(i_0_1013,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    cls_linorder__not__le_1,
    [final] ).

cnf(i_0_1014,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_linorder__not__less_1,
    [final] ).

cnf(i_0_1015,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    cls_xt1_I9_J_0,
    [final] ).

cnf(i_0_1016,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    cls_not__less__eq_1,
    [final] ).

cnf(i_0_1017,axiom,
    ( c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_greaterThanLessThan__empty_0,
    [final] ).

cnf(i_0_1018,axiom,
    ( c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_atLeastLessThan__empty_0,
    [final] ).

cnf(i_0_1019,axiom,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_greaterThanAtMost__empty_0,
    [final] ).

cnf(i_0_1020,axiom,
    ( c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    cls_atLeastatMost__empty_0,
    [final] ).

cnf(i_0_1021,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_diff__add__cancel_0,
    [final] ).

cnf(i_0_1022,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_add__diff__cancel_0,
    [final] ).

cnf(i_0_1023,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = X2
    | ~ class_Lattices_Olattice(X1) ),
    cls_sup__inf__absorb_0,
    [final] ).

cnf(i_0_1024,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = X2
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__absorb_0,
    [final] ).

cnf(i_0_1025,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__le1_0,
    [final] ).

cnf(i_0_1026,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__ord_I1_J_0,
    [final] ).

cnf(i_0_1027,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__le2_0,
    [final] ).

cnf(i_0_1028,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__ord_I2_J_0,
    [final] ).

cnf(i_0_1029,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__ge1_0,
    [final] ).

cnf(i_0_1030,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__ord_I3_J_0,
    [final] ).

cnf(i_0_1031,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__ge2_0,
    [final] ).

cnf(i_0_1032,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__ord_I4_J_0,
    [final] ).

cnf(i_0_1033,axiom,
    ( c_SetInterval_Oord__class_OatLeastAtMost(X2,X2,X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_atLeastAtMost__singleton_0,
    [final] ).

cnf(i_0_1034,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    cls_mem__def_1,
    [final] ).

cnf(i_0_1035,plain,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    inference(rw,[status(thm)],[i_0_614,c_0_602]),
    [final] ).

cnf(i_0_1036,axiom,
    c_SetInterval_Oord__class_OatLeastLessThan(X1,c_Suc(X1),tc_nat) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),
    cls_atLeastLessThan__singleton_0,
    [final] ).

cnf(i_0_1037,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
    cls_Suc__less__eq_0,
    [final] ).

cnf(i_0_1038,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_Int__empty__left_0,
    [final] ).

cnf(i_0_1039,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_1040,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_Int__empty__right_0,
    [final] ).

cnf(i_0_1041,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_1042,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),
    cls_Un__commute_0,
    [final] ).

cnf(i_0_1043,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
    cls_Int__commute_0,
    [final] ).

cnf(i_0_1044,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_linorder__antisym__conv2_0,
    [final] ).

cnf(i_0_1045,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_linorder__antisym__conv1_0,
    [final] ).

cnf(i_0_1046,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X3 = X2
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_xt1_I11_J_0,
    [final] ).

cnf(i_0_1047,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X3 = X2
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_xt1_I12_J_0,
    [final] ).

cnf(i_0_1048,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__neq__le__trans_0,
    [final] ).

cnf(i_0_1049,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__le__neq__trans_0,
    [final] ).

cnf(i_0_1050,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__le__less_0,
    [final] ).

cnf(i_0_1051,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__less__le_2,
    [final] ).

cnf(i_0_1052,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != X3 ),
    cls_le__iff__sup_1,
    [final] ).

cnf(i_0_1053,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != X2 ),
    cls_le__iff__inf_1,
    [final] ).

cnf(i_0_1054,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_less__Suc__eq__0__disj_3,
    [final] ).

cnf(i_0_1055,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_Suc__mono_0,
    [final] ).

cnf(i_0_1056,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X2
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_sup__absorb1_0,
    [final] ).

cnf(i_0_1057,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X3
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__iff__sup_0,
    [final] ).

cnf(i_0_1058,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__iff__inf_0,
    [final] ).

cnf(i_0_1059,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X3
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_inf__absorb2_0,
    [final] ).

cnf(i_0_1060,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    cls_less__SucE_0,
    [final] ).

cnf(i_0_1061,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    cls_not__less__less__Suc__eq_0,
    [final] ).

cnf(i_0_1062,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    cls_less__antisym_0,
    [final] ).

cnf(i_0_1063,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
    | c_Suc(X1) = X2
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_Suc__lessI_0,
    [final] ).

cnf(i_0_1064,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_order__less__imp__le_0,
    [final] ).

cnf(i_0_1065,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_order__le__less_1,
    [final] ).

cnf(i_0_1066,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
    cls_Suc__lessD_0,
    [final] ).

cnf(i_0_1067,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
    cls_nat__lt__two__imp__zero__or__one_0,
    [final] ).

cnf(i_0_1068,axiom,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_atLeastLessThan__empty__iff2_1,
    [final] ).

cnf(i_0_1069,axiom,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_greaterThanAtMost__empty__iff2_1,
    [final] ).

cnf(i_0_1070,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_1071,axiom,
    ( c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_atLeastLessThan__empty__iff_1,
    [final] ).

cnf(i_0_1072,axiom,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_greaterThanAtMost__empty__iff_1,
    [final] ).

cnf(i_0_1073,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_1074,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_less__SucI_0,
    [final] ).

cnf(i_0_1075,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
    cls_Un__empty__left_0,
    [final] ).

cnf(i_0_1076,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    cls_Un__empty__right_0,
    [final] ).

cnf(i_0_1077,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_1078,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_1079,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
    cls_empty__not__insert_0,
    [final] ).

cnf(i_0_1080,axiom,
    c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    cls_insert__not__empty_0,
    [final] ).

cnf(i_0_1081,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_not__less__iff__gr__or__eq_0,
    [final] ).

cnf(i_0_1082,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__antisym__conv3_0,
    [final] ).

cnf(i_0_1083,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X3 = X2
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__less__linear_0,
    [final] ).

cnf(i_0_1084,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | X3 = X2
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__neqE_0,
    [final] ).

cnf(i_0_1085,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | X3 = X2
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    cls_linorder__neqE__ordered__idom_0,
    [final] ).

cnf(i_0_1086,axiom,
    ( c_HOL_Oord__class_Oless(X2,X2,X1)
    | c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__antisym__conv1_1,
    [final] ).

cnf(i_0_1087,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__not__less_0,
    [final] ).

cnf(i_0_1088,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__not__le_0,
    [final] ).

cnf(i_0_1089,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_not__leE_0,
    [final] ).

cnf(i_0_1090,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__linear_0,
    [final] ).

cnf(i_0_1091,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__commute_0,
    [final] ).

cnf(i_0_1092,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I5_J_0,
    [final] ).

cnf(i_0_1093,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__commute_0,
    [final] ).

cnf(i_0_1094,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I1_J_0,
    [final] ).

cnf(i_0_1095,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Oadd__c_0,
    [final] ).

cnf(i_0_1096,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I24_J_0,
    [final] ).

cnf(i_0_1097,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__commute_0,
    [final] ).

cnf(i_0_1098,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
    cls_not__less__less__Suc__eq_1,
    [final] ).

cnf(i_0_1099,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    cls_not__less__eq_0,
    [final] ).

cnf(i_0_1100,axiom,
    c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X1),X2,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,tc_nat),
    cls_atLeastSucLessThan__greaterThanLessThan_0,
    [final] ).

cnf(i_0_1101,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | X2 = X1 ),
    cls_nat__neq__iff_0,
    [final] ).

cnf(i_0_1102,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | X2 = X1 ),
    cls_linorder__neqE__nat_0,
    [final] ).

cnf(i_0_1103,axiom,
    ( X2 = X3
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_class__ringb_Osubr0__iff_0,
    [final] ).

cnf(i_0_1104,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | X2 != c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
    cls_class__ringb_Oadd__r0__iff_0,
    [final] ).

cnf(i_0_1105,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    cls_less__Suc0_0,
    [final] ).

cnf(i_0_1106,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_double__eq__0__iff_0,
    [final] ).

cnf(i_0_1107,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
    cls_sup__eq__bot__eq1_0,
    [final] ).

cnf(i_0_1108,axiom,
    ( X3 = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
    cls_sup__eq__bot__eq2_0,
    [final] ).

cnf(i_0_1109,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_1110,axiom,
    ( X2 = X3
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_eq__iff__diff__eq__0_1,
    [final] ).

cnf(i_0_1111,axiom,
    ( X2 = X3
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_right__minus__eq_0,
    [final] ).

cnf(i_0_1112,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__irrefl_0,
    [final] ).

cnf(i_0_1113,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_linorder__neq__iff_1,
    [final] ).

cnf(i_0_1114,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__le_1,
    [final] ).

cnf(i_0_1115,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_neq0__conv_1,
    [final] ).

cnf(i_0_1116,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X2
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(rw,[status(thm)],[i_0_615,c_0_602]),
    [final] ).

cnf(i_0_1117,plain,
    ( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(rw,[status(thm)],[i_0_616,c_0_602]),
    [final] ).

cnf(i_0_1118,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_not__less0_0,
    [final] ).

cnf(i_0_1119,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_gr__implies__not0_0,
    [final] ).

cnf(i_0_1120,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_nat__less__le_1,
    [final] ).

cnf(i_0_1121,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_less__not__refl_0,
    [final] ).

cnf(i_0_1122,axiom,
    c_SetInterval_Oord__class_OatLeastLessThan(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),
    cls_atLeastLessThan0_0,
    [final] ).

cnf(i_0_1123,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
    cls_Un__absorb_0,
    [final] ).

cnf(i_0_1124,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
    cls_Int__absorb_0,
    [final] ).

cnf(i_0_1125,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_double__eq__0__iff_1,
    [final] ).

cnf(i_0_1126,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    cls_equalityE_0,
    [final] ).

cnf(i_0_1127,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    cls_subset__refl_0,
    [final] ).

cnf(i_0_1128,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_1129,axiom,
    ( X2 = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    cls_class__ringb_Oadd__r0__iff_1,
    [final] ).

cnf(i_0_1130,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_1131,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    cls_class__ringb_Osubr0__iff_1,
    [final] ).

cnf(i_0_1132,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_inf__bot__left_0,
    [final] ).

cnf(i_0_1133,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Obot__class_Obot(X1),X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_inf__bot__right_0,
    [final] ).

cnf(i_0_1134,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_sup__bot__left_0,
    [final] ).

cnf(i_0_1135,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    cls_add__0__left_0,
    [final] ).

cnf(i_0_1136,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I5_J_0,
    [final] ).

cnf(i_0_1137,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Oadd__0_0,
    [final] ).

cnf(i_0_1138,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__1_0,
    [final] ).

cnf(i_0_1139,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Obot__class_Obot(X1),X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_sup__bot__right_0,
    [final] ).

cnf(i_0_1140,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    cls_monoid__add__class_Oadd__0__right_0,
    [final] ).

cnf(i_0_1141,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I6_J_0,
    [final] ).

cnf(i_0_1142,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__1__right_0,
    [final] ).

cnf(i_0_1143,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_diff__0__right_0,
    [final] ).

cnf(i_0_1144,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    cls_less__Suc0_1,
    [final] ).

cnf(i_0_1145,axiom,
    ( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
    | ~ class_Orderings_Obot(X1) ),
    cls_bot__least_0,
    [final] ).

cnf(i_0_1146,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    cls_eq__iff__diff__eq__0_0,
    [final] ).

cnf(i_0_1147,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_right__minus__eq_1,
    [final] ).

cnf(i_0_1148,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_diff__self_0,
    [final] ).

cnf(i_0_1149,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X2,X1) = X2
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__idem_0,
    [final] ).

cnf(i_0_1150,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X2,X1) = X2
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__idem_0,
    [final] ).

cnf(i_0_1151,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    cls_zero__less__Suc_0,
    [final] ).

cnf(i_0_1152,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    cls_gr0__conv__Suc_1,
    [final] ).

cnf(i_0_1153,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Opreorder(X1) ),
    cls_order__eq__refl_0,
    [final] ).

cnf(i_0_1154,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_order__eq__iff_0,
    [final] ).

cnf(i_0_1155,axiom,
    c_GCD_Ogcd__class_OGCD(c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_GCD__empty__nat_0,
    [final] ).

cnf(i_0_1156,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_gr0I_0,
    [final] ).

cnf(i_0_1157,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    cls_lessI_0,
    [final] ).

cnf(i_0_1158,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    cls_less__Suc__eq_2,
    [final] ).

cnf(i_0_1159,axiom,
    c_HOL_Oord__class_Oless(v_m,v_n,tc_nat),
    cls_CHAINED_0,
    [final] ).

cnf(i_0_1160,axiom,
    c_HOL_Oord__class_Oless(v_m,v_n,tc_nat),
    cls_less_0,
    [final] ).

cnf(i_0_1161,axiom,
    ( class_Lattices_Odistrib__lattice(tc_fun(X1,X2))
    | ~ class_Lattices_Odistrib__lattice(X2) ),
    clsarity_fun__Lattices_Odistrib__lattice,
    [final] ).

cnf(i_0_1162,axiom,
    ( class_Lattices_Oupper__semilattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Oupper__semilattice,
    [final] ).

cnf(i_0_1163,axiom,
    ( class_HOL_Ominus(tc_fun(X1,X2))
    | ~ class_HOL_Ominus(X2) ),
    clsarity_fun__HOL_Ominus,
    [final] ).

cnf(i_0_1164,axiom,
    ( class_Orderings_Obot(tc_fun(X1,X2))
    | ~ class_Orderings_Obot(X2) ),
    clsarity_fun__Orderings_Obot,
    [final] ).

cnf(i_0_1165,axiom,
    ( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
    | ~ class_Lattices_Obounded__lattice(X2) ),
    clsarity_fun__Lattices_Obounded__lattice,
    [final] ).

cnf(i_0_1166,axiom,
    ( class_HOL_Oord(tc_fun(X1,X2))
    | ~ class_HOL_Oord(X2) ),
    clsarity_fun__HOL_Oord,
    [final] ).

cnf(i_0_1167,axiom,
    ( class_Orderings_Opreorder(tc_fun(X1,X2))
    | ~ class_Orderings_Opreorder(X2) ),
    clsarity_fun__Orderings_Opreorder,
    [final] ).

cnf(i_0_1168,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_1169,axiom,
    ( class_Orderings_Oorder(tc_fun(X1,X2))
    | ~ class_Orderings_Oorder(X2) ),
    clsarity_fun__Orderings_Oorder,
    [final] ).

cnf(i_0_1170,axiom,
    ( class_Lattices_Olower__semilattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_1171,axiom,
    ( class_Lattices_Olattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Olattice,
    [final] ).

cnf(i_0_1172,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    cls_Suc__inject_0,
    [final] ).

cnf(i_0_1173,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    cls_nat_Oinject_0,
    [final] ).

cnf(i_0_1174,axiom,
    ( class_OrderedGroup_Omonoid__add(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    clsrel_OrderedGroup_Ocomm__monoid__add_OrderedGroup_Omonoid__add,
    [final] ).

cnf(i_0_1175,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    clsrel_OrderedGroup_Ocomm__monoid__add_OrderedGroup_Oab__semigroup__add,
    [final] ).

cnf(i_0_1176,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    cls_Zero__neq__Suc_0,
    [final] ).

cnf(i_0_1177,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    cls_nat_Osimps_I2_J_0,
    [final] ).

cnf(i_0_1178,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    cls_nat_Osimps_I3_J_0,
    [final] ).

cnf(i_0_1179,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    cls_Suc__neq__Zero_0,
    [final] ).

cnf(i_0_1180,axiom,
    c_Suc(X1) != X1,
    cls_Suc__n__not__n_0,
    [final] ).

cnf(i_0_1181,axiom,
    X1 != c_Suc(X1),
    cls_n__not__Suc__n_0,
    [final] ).

cnf(i_0_1182,axiom,
    class_Lattices_Odistrib__lattice(tc_nat),
    clsarity_nat__Lattices_Odistrib__lattice,
    [final] ).

cnf(i_0_1183,axiom,
    class_Lattices_Odistrib__lattice(tc_bool),
    clsarity_bool__Lattices_Odistrib__lattice,
    [final] ).

cnf(i_0_1184,axiom,
    class_Lattices_Oupper__semilattice(tc_nat),
    clsarity_nat__Lattices_Oupper__semilattice,
    [final] ).

cnf(i_0_1185,axiom,
    class_Lattices_Oupper__semilattice(tc_bool),
    clsarity_bool__Lattices_Oupper__semilattice,
    [final] ).

cnf(i_0_1186,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocancel__semigroup__add,
    [final] ).

cnf(i_0_1187,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,
    [final] ).

cnf(i_0_1188,axiom,
    class_HOL_Ominus(tc_nat),
    clsarity_nat__HOL_Ominus,
    [final] ).

cnf(i_0_1189,axiom,
    class_HOL_Ominus(tc_bool),
    clsarity_bool__HOL_Ominus,
    [final] ).

cnf(i_0_1190,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    clsarity_nat__Ring__and__Field_Oordered__semidom,
    [final] ).

cnf(i_0_1191,axiom,
    class_Orderings_Obot(tc_nat),
    clsarity_nat__Orderings_Obot,
    [final] ).

cnf(i_0_1192,axiom,
    class_Orderings_Obot(tc_bool),
    clsarity_bool__Orderings_Obot,
    [final] ).

cnf(i_0_1193,axiom,
    class_Lattices_Obounded__lattice(tc_bool),
    clsarity_bool__Lattices_Obounded__lattice,
    [final] ).

cnf(i_0_1194,axiom,
    class_HOL_Oord(tc_nat),
    clsarity_nat__HOL_Oord,
    [final] ).

cnf(i_0_1195,axiom,
    class_HOL_Oord(tc_bool),
    clsarity_bool__HOL_Oord,
    [final] ).

cnf(i_0_1196,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,
    [final] ).

cnf(i_0_1197,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Omonoid__add,
    [final] ).

cnf(i_0_1198,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Oab__semigroup__add,
    [final] ).

cnf(i_0_1199,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    clsarity_nat__Ring__and__Field_Ocomm__semiring__1,
    [final] ).

cnf(i_0_1200,axiom,
    class_Orderings_Opreorder(tc_nat),
    clsarity_nat__Orderings_Opreorder,
    [final] ).

cnf(i_0_1201,axiom,
    class_Orderings_Opreorder(tc_bool),
    clsarity_bool__Orderings_Opreorder,
    [final] ).

cnf(i_0_1202,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_bool),
    clsarity_bool__Complete__Lattice_Ocomplete__lattice,
    [final] ).

cnf(i_0_1203,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocomm__monoid__add,
    [final] ).

cnf(i_0_1204,negated_conjecture,
    class_OrderedGroup_Ocomm__monoid__add(t_a),
    tfree_tcs,
    [final] ).

cnf(i_0_1205,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    [final] ).

cnf(i_0_1206,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,
    [final] ).

cnf(i_0_1207,axiom,
    class_Orderings_Olinorder(tc_nat),
    clsarity_nat__Orderings_Olinorder,
    [final] ).

cnf(i_0_1208,axiom,
    class_Orderings_Oorder(tc_nat),
    clsarity_nat__Orderings_Oorder,
    [final] ).

cnf(i_0_1209,axiom,
    class_Orderings_Oorder(tc_bool),
    clsarity_bool__Orderings_Oorder,
    [final] ).

cnf(i_0_1210,axiom,
    class_Lattices_Olower__semilattice(tc_nat),
    clsarity_nat__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_1211,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    clsarity_bool__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_1212,axiom,
    class_Lattices_Olattice(tc_nat),
    clsarity_nat__Lattices_Olattice,
    [final] ).

cnf(i_0_1213,axiom,
    class_Lattices_Olattice(tc_bool),
    clsarity_bool__Lattices_Olattice,
    [final] ).

cnf(i_0_1214,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,
    [final] ).

cnf(i_0_1215,axiom,
    X1 = X1 ).

cnf(i_0_1216,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1217,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1218,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1219,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1220,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4) ) ).

cnf(i_0_1221,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X4) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) ) ).

cnf(i_0_1222,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2) ) ).

cnf(i_0_1223,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X4) ) ).

cnf(i_0_1224,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X2,X4) ) ).

cnf(i_0_1225,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X2) ) ).

cnf(i_0_1226,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4) ) ).

cnf(i_0_1227,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X4) ) ).

cnf(i_0_1228,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2) ) ).

cnf(i_0_1229,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).

cnf(i_0_1230,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).

cnf(i_0_1231,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).

cnf(i_0_1232,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_1233,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_1234,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_1235,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_1236,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_1237,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_1238,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_1239,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_1240,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_1241,axiom,
    ( X1 != X2
    | c_Suc(X1) = c_Suc(X2) ) ).

cnf(i_0_1242,axiom,
    ( X1 != X2
    | c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).

cnf(i_0_1243,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).

cnf(i_0_1244,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).

cnf(i_0_1245,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).

cnf(i_0_1246,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).

cnf(i_0_1247,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).

cnf(i_0_1248,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).

cnf(i_0_1249,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).

cnf(i_0_1250,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).

cnf(i_0_1251,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).

cnf(i_0_1252,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).

cnf(i_0_1253,axiom,
    ( X1 != X2
    | c_The(X1,X3) = c_The(X2,X3) ) ).

cnf(i_0_1254,axiom,
    ( X1 != X2
    | c_The(X3,X1) = c_The(X3,X2) ) ).

cnf(i_0_1255,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X4) ) ).

cnf(i_0_1256,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X4) ) ).

cnf(i_0_1257,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X2) ) ).

cnf(i_0_1258,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X1,X3) = c_Finite__Set_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_1259,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X3,X1) = c_Finite__Set_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_1260,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X1,X3) = c_Finite__Set_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_1261,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X3,X1) = c_Finite__Set_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_1262,axiom,
    ( X1 != X2
    | c_Set_Ocontents(X1,X3) = c_Set_Ocontents(X2,X3) ) ).

cnf(i_0_1263,axiom,
    ( X1 != X2
    | c_Set_Ocontents(X3,X1) = c_Set_Ocontents(X3,X2) ) ).

cnf(i_0_1264,axiom,
    ( X1 != X2
    | c_GCD_Ogcd__class_OLCM(X1,X3) = c_GCD_Ogcd__class_OLCM(X2,X3) ) ).

cnf(i_0_1265,axiom,
    ( X1 != X2
    | c_GCD_Ogcd__class_OLCM(X3,X1) = c_GCD_Ogcd__class_OLCM(X3,X2) ) ).

cnf(i_0_1266,axiom,
    ( X1 != X2
    | c_GCD_Ogcd__class_OGCD(X1,X3) = c_GCD_Ogcd__class_OGCD(X2,X3) ) ).

cnf(i_0_1267,axiom,
    ( X1 != X2
    | c_GCD_Ogcd__class_OGCD(X3,X1) = c_GCD_Ogcd__class_OGCD(X3,X2) ) ).

cnf(i_0_1268,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_1269,axiom,
    ( X1 != X2
    | c_in(X1,X3,X4) = c_in(X2,X3,X4) ) ).

cnf(i_0_1270,axiom,
    ( X1 != X2
    | c_in(X3,X1,X4) = c_in(X3,X2,X4) ) ).

cnf(i_0_1271,axiom,
    ( X1 != X2
    | c_in(X3,X4,X1) = c_in(X3,X4,X2) ) ).

cnf(i_0_1272,axiom,
    ( X1 != X2
    | c_Finite__Set_Osetsum(X1,X3,X4,X5) = c_Finite__Set_Osetsum(X2,X3,X4,X5) ) ).

cnf(i_0_1273,axiom,
    ( X1 != X2
    | c_Finite__Set_Osetsum(X3,X1,X4,X5) = c_Finite__Set_Osetsum(X3,X2,X4,X5) ) ).

cnf(i_0_1274,axiom,
    ( X1 != X2
    | c_Finite__Set_Osetsum(X3,X4,X1,X5) = c_Finite__Set_Osetsum(X3,X4,X2,X5) ) ).

cnf(i_0_1275,axiom,
    ( X1 != X2
    | c_Finite__Set_Osetsum(X3,X4,X5,X1) = c_Finite__Set_Osetsum(X3,X4,X5,X2) ) ).

cnf(i_0_1276,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).

cnf(i_0_1277,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).

cnf(i_0_1278,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).

cnf(i_0_1279,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X1,X3,X4,X5) = c_Set_Ovimage(X2,X3,X4,X5) ) ).

cnf(i_0_1280,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X1,X4,X5) = c_Set_Ovimage(X3,X2,X4,X5) ) ).

cnf(i_0_1281,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X1,X5) = c_Set_Ovimage(X3,X4,X2,X5) ) ).

cnf(i_0_1282,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X5,X1) = c_Set_Ovimage(X3,X4,X5,X2) ) ).

cnf(i_0_1283,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_1284,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_1285,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_1286,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_1287,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_1288,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_1289,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_1290,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_1291,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_1292,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1293,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).

cnf(i_0_1294,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1295,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_1296,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_1297,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1298,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).

cnf(i_0_1299,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_1300,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add__join(X1)
    | class_OrderedGroup_Olordered__ab__group__add__join(X2) ) ).

cnf(i_0_1301,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_1302,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1303,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1)
    | class_OrderedGroup_Olordered__ab__group__add__meet(X2) ) ).

cnf(i_0_1304,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).

cnf(i_0_1305,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_1306,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oupper__semilattice(X1)
    | class_Lattices_Oupper__semilattice(X2) ) ).

cnf(i_0_1307,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | class_Lattices_Olower__semilattice(X2) ) ).

cnf(i_0_1308,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_1309,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X2) ) ).

cnf(i_0_1310,axiom,
    ( X1 != X2
    | ~ class_HOL_Ominus(X1)
    | class_HOL_Ominus(X2) ) ).

cnf(i_0_1311,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1312,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oidom(X2) ) ).

cnf(i_0_1313,axiom,
    ( X1 != X2
    | ~ class_HOL_Oord(X1)
    | class_HOL_Oord(X2) ) ).

cnf(i_0_1314,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_1315,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_1316,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1317,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | class_OrderedGroup_Ogroup__add(X2) ) ).

cnf(i_0_1318,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_1319,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_1320,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__add(X1)
    | class_OrderedGroup_Omonoid__add(X2) ) ).

cnf(i_0_1321,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X2) ) ).

cnf(i_0_1322,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_1323,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_1324,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_1325,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_1326,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_1327,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_1328,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_1329,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_1330,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1215_001,axiom,
    X1 = X1 ).

cnf(i_0_1216_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1217_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1218_004,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1219_005,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1220_006,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4) ) ).

cnf(i_0_1221_007,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X4) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) ) ).

cnf(i_0_1222_008,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2) ) ).

cnf(i_0_1223_009,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X4) ) ).

cnf(i_0_1224_010,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X2,X4) ) ).

cnf(i_0_1225_011,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X2) ) ).

cnf(i_0_1226_012,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4) ) ).

cnf(i_0_1227_013,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X4) ) ).

cnf(i_0_1228_014,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2) ) ).

cnf(i_0_1229_015,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).

cnf(i_0_1230_016,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).

cnf(i_0_1231_017,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).

cnf(i_0_1232_018,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_1233_019,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_1234_020,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_1235_021,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_1236_022,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_1237_023,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_1238_024,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_1239_025,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_1240_026,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_1241_027,axiom,
    ( X1 != X2
    | c_Suc(X1) = c_Suc(X2) ) ).

cnf(i_0_1242_028,axiom,
    ( X1 != X2
    | c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).

cnf(i_0_1243_029,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).

cnf(i_0_1244_030,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).

cnf(i_0_1245_031,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).

cnf(i_0_1246_032,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).

cnf(i_0_1247_033,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).

cnf(i_0_1248_034,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).

cnf(i_0_1249_035,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).

cnf(i_0_1250_036,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).

cnf(i_0_1251_037,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).

cnf(i_0_1252_038,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).

cnf(i_0_1253_039,axiom,
    ( X1 != X2
    | c_The(X1,X3) = c_The(X2,X3) ) ).

cnf(i_0_1254_040,axiom,
    ( X1 != X2
    | c_The(X3,X1) = c_The(X3,X2) ) ).

cnf(i_0_1255_041,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X4) ) ).

cnf(i_0_1256_042,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X4) ) ).

cnf(i_0_1257_043,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X2) ) ).

cnf(i_0_1258_044,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X1,X3) = c_Finite__Set_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_1259_045,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X3,X1) = c_Finite__Set_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_1260_046,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X1,X3) = c_Finite__Set_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_1261_047,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X3,X1) = c_Finite__Set_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_1262_048,axiom,
    ( X1 != X2
    | c_Set_Ocontents(X1,X3) = c_Set_Ocontents(X2,X3) ) ).

cnf(i_0_1263_049,axiom,
    ( X1 != X2
    | c_Set_Ocontents(X3,X1) = c_Set_Ocontents(X3,X2) ) ).

cnf(i_0_1264_050,axiom,
    ( X1 != X2
    | c_GCD_Ogcd__class_OLCM(X1,X3) = c_GCD_Ogcd__class_OLCM(X2,X3) ) ).

cnf(i_0_1265_051,axiom,
    ( X1 != X2
    | c_GCD_Ogcd__class_OLCM(X3,X1) = c_GCD_Ogcd__class_OLCM(X3,X2) ) ).

cnf(i_0_1266_052,axiom,
    ( X1 != X2
    | c_GCD_Ogcd__class_OGCD(X1,X3) = c_GCD_Ogcd__class_OGCD(X2,X3) ) ).

cnf(i_0_1267_053,axiom,
    ( X1 != X2
    | c_GCD_Ogcd__class_OGCD(X3,X1) = c_GCD_Ogcd__class_OGCD(X3,X2) ) ).

cnf(i_0_1268_054,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_1269_055,axiom,
    ( X1 != X2
    | c_in(X1,X3,X4) = c_in(X2,X3,X4) ) ).

cnf(i_0_1270_056,axiom,
    ( X1 != X2
    | c_in(X3,X1,X4) = c_in(X3,X2,X4) ) ).

cnf(i_0_1271_057,axiom,
    ( X1 != X2
    | c_in(X3,X4,X1) = c_in(X3,X4,X2) ) ).

cnf(i_0_1272_058,axiom,
    ( X1 != X2
    | c_Finite__Set_Osetsum(X1,X3,X4,X5) = c_Finite__Set_Osetsum(X2,X3,X4,X5) ) ).

cnf(i_0_1273_059,axiom,
    ( X1 != X2
    | c_Finite__Set_Osetsum(X3,X1,X4,X5) = c_Finite__Set_Osetsum(X3,X2,X4,X5) ) ).

cnf(i_0_1274_060,axiom,
    ( X1 != X2
    | c_Finite__Set_Osetsum(X3,X4,X1,X5) = c_Finite__Set_Osetsum(X3,X4,X2,X5) ) ).

cnf(i_0_1275_061,axiom,
    ( X1 != X2
    | c_Finite__Set_Osetsum(X3,X4,X5,X1) = c_Finite__Set_Osetsum(X3,X4,X5,X2) ) ).

cnf(i_0_1276_062,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).

cnf(i_0_1277_063,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).

cnf(i_0_1278_064,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).

cnf(i_0_1279_065,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X1,X3,X4,X5) = c_Set_Ovimage(X2,X3,X4,X5) ) ).

cnf(i_0_1280_066,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X1,X4,X5) = c_Set_Ovimage(X3,X2,X4,X5) ) ).

cnf(i_0_1281_067,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X1,X5) = c_Set_Ovimage(X3,X4,X2,X5) ) ).

cnf(i_0_1282_068,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X5,X1) = c_Set_Ovimage(X3,X4,X5,X2) ) ).

cnf(i_0_1283_069,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_1284_070,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_1285_071,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_1286_072,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_1287_073,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_1288_074,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_1289_075,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_1290_076,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_1291_077,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_1292_078,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1293_079,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).

cnf(i_0_1294_080,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1295_081,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_1296_082,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_1297_083,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1298_084,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).

cnf(i_0_1299_085,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_1300_086,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add__join(X1)
    | class_OrderedGroup_Olordered__ab__group__add__join(X2) ) ).

cnf(i_0_1301_087,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_1302_088,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1303_089,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1)
    | class_OrderedGroup_Olordered__ab__group__add__meet(X2) ) ).

cnf(i_0_1304_090,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).

cnf(i_0_1305_091,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_1306_092,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oupper__semilattice(X1)
    | class_Lattices_Oupper__semilattice(X2) ) ).

cnf(i_0_1307_093,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | class_Lattices_Olower__semilattice(X2) ) ).

cnf(i_0_1308_094,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_1309_095,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X2) ) ).

cnf(i_0_1310_096,axiom,
    ( X1 != X2
    | ~ class_HOL_Ominus(X1)
    | class_HOL_Ominus(X2) ) ).

cnf(i_0_1311_097,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1312_098,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oidom(X2) ) ).

cnf(i_0_1313_099,axiom,
    ( X1 != X2
    | ~ class_HOL_Oord(X1)
    | class_HOL_Oord(X2) ) ).

cnf(i_0_1314_100,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_1315_101,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_1316_102,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1317_103,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | class_OrderedGroup_Ogroup__add(X2) ) ).

cnf(i_0_1318_104,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_1319_105,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_1320_106,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__add(X1)
    | class_OrderedGroup_Omonoid__add(X2) ) ).

cnf(i_0_1321_107,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X2) ) ).

cnf(i_0_1322_108,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_1323_109,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_1324_110,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_1325_111,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_1326_112,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_1327_113,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_1328_114,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_1329_115,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_1330_116,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1331,plain,
    ( ~ class_HOL_Oord(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X2)
    | c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1),X1,X2) = c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1),X1,X2) ),
    inference(equality_inference,[],[627]) ).

cnf(i_0_1332,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[669]) ).

cnf(i_0_1333,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[670]) ).

cnf(i_0_1334,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[671]) ).

cnf(i_0_1335,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[672]) ).

cnf(i_0_1336,plain,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
    inference(equality_inference,[],[806]) ).

cnf(i_0_1337,plain,
    ( X1 = X1
    | hBOOL(c_in(X2,X1,X3))
    | hBOOL(c_in(X2,X1,X3)) ),
    inference(equality_inference,[],[808]) ).

cnf(i_0_1338,plain,
    X1 = X1,
    inference(equality_inference,[],[852]) ).

cnf(i_0_1339,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | X2 = X2
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(equality_inference,[],[996]) ).

cnf(i_0_1340,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[1003]) ).

cnf(i_0_1341,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[1004]) ).

cnf(i_0_1342,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[1005]) ).

cnf(i_0_1343,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
    inference(equality_inference,[],[1006]) ).

cnf(i_0_1344,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[1007]) ).

cnf(i_0_1345,plain,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    inference(equality_inference,[],[1116]) ).

cnf(i_0_1346,plain,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    inference(equality_inference,[],[1117]) ).

cnf(i_0_1347,plain,
    X1 = X1,
    inference(equality_inference,[],[1173]) ).

cnf(i_0_1348,plain,
    c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a),t_a) = c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a),
    inference(scs_inference,[],[i_0_1204,i_0_637]) ).

cnf(i_0_1349,plain,
    X1 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),
    inference(scs_inference,[],[i_0_653,i_0_690]) ).

cnf(i_0_1350,plain,
    ( ~ hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3))
    | X1 = X3 ),
    inference(rename_variables,[],[i_0_690]) ).

cnf(i_0_1351,plain,
    class_OrderedGroup_Omonoid__add(t_a),
    inference(scs_inference,[],[i_0_1204,i_0_653,i_0_690,i_0_1174]) ).

cnf(i_0_1352,plain,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Omonoid__add(X1) ),
    inference(rename_variables,[],[i_0_1174]) ).

cnf(i_0_1353,plain,
    class_OrderedGroup_Oab__semigroup__add(t_a),
    inference(scs_inference,[],[i_0_1204,i_0_653,i_0_690,i_0_1174,i_0_1175]) ).

cnf(i_0_1354,plain,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(rename_variables,[],[i_0_1175]) ).

cnf(i_0_1355,plain,
    c_Set_Oinsert(X1,X2,X3) = c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3),
    inference(scs_inference,[],[i_0_1204,i_0_976,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216]) ).

cnf(i_0_1356,plain,
    c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_976,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273]) ).

cnf(i_0_1357,plain,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1,
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_976,i_0_926,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940]) ).

cnf(i_0_1358,plain,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1 ),
    inference(rename_variables,[],[i_0_940]) ).

cnf(i_0_1359,plain,
    c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_976,i_0_687,i_0_926,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986]) ).

cnf(i_0_1360,plain,
    ( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2
    | c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    inference(rename_variables,[],[i_0_986]) ).

cnf(i_0_1361,plain,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_976,i_0_687,i_0_926,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993]) ).

cnf(i_0_1362,plain,
    c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = X4,
    inference(rename_variables,[],[i_0_687]) ).

cnf(i_0_1363,plain,
    ( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    inference(rename_variables,[],[i_0_993]) ).

cnf(i_0_1364,plain,
    ~ hBOOL(hAPP(c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X3)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_976,i_0_687,i_0_926,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116]) ).

cnf(i_0_1365,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X2
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(rename_variables,[],[i_0_1116]) ).

cnf(i_0_1366,plain,
    ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),X4)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_976,i_0_812,i_0_687,i_0_926,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117]) ).

cnf(i_0_1367,plain,
    c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1,
    inference(rename_variables,[],[i_0_812]) ).

cnf(i_0_1368,plain,
    ( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(rename_variables,[],[i_0_1117]) ).

cnf(i_0_1369,plain,
    ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,c_Suc(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)))),X8),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1181,i_0_976,i_0_812,i_0_687,i_0_926,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625]) ).

cnf(i_0_1370,plain,
    X1 != c_Suc(X1),
    inference(rename_variables,[],[i_0_1181]) ).

cnf(i_0_1371,plain,
    ( 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) ),
    inference(rename_variables,[],[i_0_625]) ).

cnf(i_0_1372,plain,
    ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,c_Suc(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)))),X8,X7),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1181,i_0_1370,i_0_976,i_0_812,i_0_687,i_0_926,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626]) ).

cnf(i_0_1373,plain,
    X1 != c_Suc(X1),
    inference(rename_variables,[],[i_0_1181]) ).

cnf(i_0_1374,plain,
    ( 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) ),
    inference(rename_variables,[],[i_0_626]) ).

cnf(i_0_1375,plain,
    ~ hBOOL(hAPP(c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),X5)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1181,i_0_1370,i_0_976,i_0_812,i_0_687,i_0_926,i_0_977,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639]) ).

cnf(i_0_1376,plain,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    inference(rename_variables,[],[i_0_977]) ).

cnf(i_0_1377,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
    inference(rename_variables,[],[i_0_639]) ).

cnf(i_0_1378,plain,
    hBOOL(c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(hAPP(X2,X1),X3,X4),X5,X4),X5)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1181,i_0_1370,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_977,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652]) ).

cnf(i_0_1379,plain,
    hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
    inference(rename_variables,[],[i_0_889]) ).

cnf(i_0_1380,plain,
    ( ~ hBOOL(c_in(hAPP(X1,X2),X3,X4))
    | hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)) ),
    inference(rename_variables,[],[i_0_652]) ).

cnf(i_0_1381,plain,
    c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),c_Set_Ovimage(X1,c_Set_Oinsert(X5,X2,X4),X3,X4),tc_fun(X3,tc_bool)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1181,i_0_1370,i_0_997,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_977,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658]) ).

cnf(i_0_1382,plain,
    ( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_lessequals(c_Set_Ovimage(X4,X1,X5,X3),c_Set_Ovimage(X4,X2,X5,X3),tc_fun(X5,tc_bool)) ),
    inference(rename_variables,[],[i_0_658]) ).

cnf(i_0_1383,plain,
    hBOOL(hAPP(c_Set_Ovimage(X1,c_Set_Oinsert(hAPP(X1,X2),X3,X4),X5,X6),X2)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1181,i_0_1370,i_0_997,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_939,i_0_977,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659]) ).

cnf(i_0_1384,plain,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    inference(rename_variables,[],[i_0_939]) ).

cnf(i_0_1385,plain,
    ( ~ hBOOL(hAPP(X1,hAPP(X2,X3)))
    | hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
    inference(rename_variables,[],[i_0_659]) ).

cnf(i_0_1386,plain,
    c_lessequals(hAPP(X1,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X2,X3,X4),X1,X4,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1181,i_0_1370,i_0_997,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_977,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675]) ).

cnf(i_0_1387,plain,
    ( ~ hBOOL(c_in(X1,X2,X3))
    | c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
    inference(rename_variables,[],[i_0_675]) ).

cnf(i_0_1388,plain,
    c_lessequals(X1,c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1181,i_0_1370,i_0_997,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_977,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779]) ).

cnf(i_0_1389,plain,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_997]) ).

cnf(i_0_1390,plain,
    ( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    inference(rename_variables,[],[i_0_779]) ).

cnf(i_0_1391,plain,
    c_lessequals(X1,c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1181,i_0_1370,i_0_997,i_0_1389,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_977,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780]) ).

cnf(i_0_1392,plain,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_997]) ).

cnf(i_0_1393,plain,
    ( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
    inference(rename_variables,[],[i_0_780]) ).

cnf(i_0_1394,plain,
    c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1181,i_0_1370,i_0_997,i_0_1389,i_0_957,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_977,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781]) ).

cnf(i_0_1395,plain,
    c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_957]) ).

cnf(i_0_1396,plain,
    ( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
    inference(rename_variables,[],[i_0_781]) ).

cnf(i_0_1397,plain,
    c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1181,i_0_1370,i_0_997,i_0_1389,i_0_957,i_0_1395,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_977,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782]) ).

cnf(i_0_1398,plain,
    c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_957]) ).

cnf(i_0_1399,plain,
    ( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    inference(rename_variables,[],[i_0_782]) ).

cnf(i_0_1400,plain,
    ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1181,i_0_1370,i_0_997,i_0_1389,i_0_957,i_0_1395,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_851,i_0_977,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807]) ).

cnf(i_0_1401,plain,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
    inference(rename_variables,[],[i_0_807]) ).

cnf(i_0_1402,plain,
    ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X3,tc_bool)),X4)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1181,i_0_1370,i_0_997,i_0_1389,i_0_957,i_0_1395,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_851,i_0_977,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813]) ).

cnf(i_0_1403,plain,
    ( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
    | ~ hBOOL(hAPP(X1,X4)) ),
    inference(rename_variables,[],[i_0_813]) ).

cnf(i_0_1404,plain,
    ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X3,tc_bool)),X4)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1181,i_0_1370,i_0_997,i_0_1389,i_0_957,i_0_1395,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_851,i_0_977,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814]) ).

cnf(i_0_1405,plain,
    ( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
    | ~ hBOOL(hAPP(X2,X4)) ),
    inference(rename_variables,[],[i_0_814]) ).

cnf(i_0_1406,plain,
    ~ c_lessequals(c_Suc(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)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1181,i_0_1370,i_0_997,i_0_1389,i_0_957,i_0_1395,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_851,i_0_977,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955]) ).

cnf(i_0_1407,plain,
    c_Suc(X1) != X1,
    inference(rename_variables,[],[i_0_1180]) ).

cnf(i_0_1408,plain,
    ( 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)) ),
    inference(rename_variables,[],[i_0_955]) ).

cnf(i_0_1409,plain,
    c_Set_Oinsert(X1,c_Set_Ovimage(X2,c_Set_Oinsert(hAPP(X2,X1),X3,X4),X5,X4),X5) = c_Set_Ovimage(X2,c_Set_Oinsert(hAPP(X2,X1),X3,X4),X5,X4),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1181,i_0_1370,i_0_997,i_0_1389,i_0_957,i_0_1395,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_851,i_0_977,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956]) ).

cnf(i_0_1410,plain,
    ( ~ hBOOL(c_in(X1,X2,X3))
    | c_Set_Oinsert(X1,X2,X3) = X2 ),
    inference(rename_variables,[],[i_0_956]) ).

cnf(i_0_1411,plain,
    ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1181,i_0_1370,i_0_997,i_0_1389,i_0_957,i_0_1395,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984]) ).

cnf(i_0_1412,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,X1,X3)) ),
    inference(rename_variables,[],[i_0_984]) ).

cnf(i_0_1413,plain,
    hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X4)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1181,i_0_1370,i_0_997,i_0_1389,i_0_957,i_0_1395,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_1384,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984,i_0_1035]) ).

cnf(i_0_1414,plain,
    ( ~ hBOOL(hAPP(X1,X2))
    | hBOOL(c_in(X2,X1,X3)) ),
    inference(rename_variables,[],[i_0_1035]) ).

cnf(i_0_1415,plain,
    c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(X1)),tc_nat),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1181,i_0_1370,i_0_997,i_0_1389,i_0_1158,i_0_957,i_0_1395,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_1384,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984,i_0_1035,i_0_1066]) ).

cnf(i_0_1416,plain,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    inference(rename_variables,[],[i_0_1158]) ).

cnf(i_0_1417,plain,
    ( ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rename_variables,[],[i_0_1066]) ).

cnf(i_0_1418,plain,
    ~ c_HOL_Oord__class_Oless(c_Suc(X1),X1,tc_nat),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1181,i_0_1370,i_0_1121,i_0_997,i_0_1389,i_0_1158,i_0_957,i_0_1395,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_1384,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984,i_0_1035,i_0_1066,i_0_1074]) ).

cnf(i_0_1419,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_1121]) ).

cnf(i_0_1420,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rename_variables,[],[i_0_1074]) ).

cnf(i_0_1421,plain,
    c_lessequals(X1,X1,tc_nat),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1181,i_0_1370,i_0_1121,i_0_997,i_0_1389,i_0_1158,i_0_957,i_0_1395,i_0_1200,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_1384,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984,i_0_1035,i_0_1066,i_0_1074,i_0_1153]) ).

cnf(i_0_1422,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | c_lessequals(X2,X2,X1) ),
    inference(rename_variables,[],[i_0_1153]) ).

cnf(i_0_1423,plain,
    c_lessequals(X1,X1,tc_bool),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1181,i_0_1370,i_0_1121,i_0_997,i_0_1389,i_0_1158,i_0_957,i_0_1395,i_0_1200,i_0_1209,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_1384,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984,i_0_1035,i_0_1066,i_0_1074,i_0_1153,i_0_1154]) ).

cnf(i_0_1424,plain,
    ( ~ class_Orderings_Oorder(X1)
    | c_lessequals(X2,X2,X1) ),
    inference(rename_variables,[],[i_0_1154]) ).

cnf(i_0_1425,plain,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1181,i_0_1370,i_0_1121,i_0_997,i_0_1389,i_0_1158,i_0_957,i_0_1395,i_0_1398,i_0_1078,i_0_1200,i_0_1209,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_1384,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984,i_0_1035,i_0_1066,i_0_1074,i_0_1153,i_0_1154,i_0_938]) ).

cnf(i_0_1426,plain,
    c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_957]) ).

cnf(i_0_1427,plain,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
    inference(rename_variables,[],[i_0_1078]) ).

cnf(i_0_1428,plain,
    ( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
    | X2 = X1 ),
    inference(rename_variables,[],[i_0_938]) ).

cnf(i_0_1429,plain,
    c_Suc(c_Set_Oinsert(X1,X2,X3)) != c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1407,i_0_1181,i_0_1370,i_0_1121,i_0_997,i_0_1389,i_0_1158,i_0_957,i_0_1395,i_0_1398,i_0_1078,i_0_1200,i_0_1209,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_1384,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984,i_0_1035,i_0_1066,i_0_1074,i_0_1153,i_0_1154,i_0_938,i_0_1217]) ).

cnf(i_0_1430,plain,
    c_Suc(X1) != X1,
    inference(rename_variables,[],[i_0_1180]) ).

cnf(i_0_1431,plain,
    ~ hBOOL(c_in(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,X3,X4),tc_fun(X4,tc_bool)),X4)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1407,i_0_1181,i_0_1370,i_0_1121,i_0_997,i_0_1389,i_0_1158,i_0_957,i_0_1395,i_0_1398,i_0_1078,i_0_1200,i_0_1209,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_1384,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984,i_0_1035,i_0_1066,i_0_1074,i_0_1153,i_0_1154,i_0_938,i_0_1217,i_0_748]) ).

cnf(i_0_1432,plain,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_926]) ).

cnf(i_0_1433,plain,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | ~ hBOOL(c_in(X4,X2,X3))
    | ~ hBOOL(c_in(X4,X1,X3)) ),
    inference(rename_variables,[],[i_0_748]) ).

cnf(i_0_1434,plain,
    ~ c_Complete__Lattice_Ocomplete__lattice(c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3),X4,X5,X6,X7,X8,X9,c_Suc(hAPP(c_Set_Oinsert(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)))),X10),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1407,i_0_1181,i_0_1370,i_0_1121,i_0_997,i_0_1389,i_0_1158,i_0_957,i_0_1395,i_0_1398,i_0_1078,i_0_1200,i_0_1209,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_1384,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984,i_0_1035,i_0_1066,i_0_1074,i_0_1153,i_0_1154,i_0_938,i_0_1217,i_0_748,i_0_1283]) ).

cnf(i_0_1435,plain,
    ~ c_Complete__Lattice_Ocomplete__lattice(X1,c_Set_Oinsert(X2,c_Set_Oinsert(X2,X3,X4),X4),X5,X6,X7,X8,c_Suc(hAPP(c_Set_Oinsert(X2,X3,X4),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))),X10,X9),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1407,i_0_1181,i_0_1370,i_0_1121,i_0_997,i_0_1389,i_0_1158,i_0_957,i_0_1395,i_0_1398,i_0_1078,i_0_1200,i_0_1209,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_1384,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984,i_0_1035,i_0_1066,i_0_1074,i_0_1153,i_0_1154,i_0_938,i_0_1217,i_0_748,i_0_1283,i_0_1284]) ).

cnf(i_0_1436,plain,
    ~ c_Complete__Lattice_Ocomplete__lattice(c_Set_Oinsert(X1,X2,X3),X4,X5,X6,X7,X8,X9,c_Suc(hAPP(c_Set_Oinsert(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(c_Set_Oinsert(X1,X2,X3),tc_bool)))),c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1407,i_0_1181,i_0_1370,i_0_1121,i_0_997,i_0_1389,i_0_1158,i_0_957,i_0_1395,i_0_1398,i_0_1078,i_0_1200,i_0_1209,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_1384,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984,i_0_1035,i_0_1066,i_0_1074,i_0_1153,i_0_1154,i_0_938,i_0_1217,i_0_748,i_0_1283,i_0_1284,i_0_1291]) ).

cnf(i_0_1437,plain,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3) != c_in(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1407,i_0_1181,i_0_1370,i_0_1121,i_0_997,i_0_1389,i_0_1158,i_0_957,i_0_1395,i_0_1398,i_0_1078,i_0_1200,i_0_1209,i_0_976,i_0_812,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_1384,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984,i_0_1035,i_0_1066,i_0_1074,i_0_1153,i_0_1154,i_0_938,i_0_1217,i_0_748,i_0_1283,i_0_1284,i_0_1291,i_0_1302]) ).

cnf(i_0_1438,plain,
    ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool),X4,tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool),X4,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1407,i_0_1181,i_0_1370,i_0_1121,i_0_997,i_0_1389,i_0_1158,i_0_957,i_0_1395,i_0_1398,i_0_1078,i_0_1200,i_0_1209,i_0_976,i_0_812,i_0_1367,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_1384,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984,i_0_1035,i_0_1066,i_0_1074,i_0_1153,i_0_1154,i_0_938,i_0_1217,i_0_748,i_0_1283,i_0_1284,i_0_1291,i_0_1302,i_0_1327]) ).

cnf(i_0_1439,plain,
    c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1,
    inference(rename_variables,[],[i_0_812]) ).

cnf(i_0_1440,plain,
    c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3),X3),tc_fun(X3,tc_bool)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1407,i_0_1181,i_0_1370,i_0_1121,i_0_997,i_0_1389,i_0_1392,i_0_1158,i_0_957,i_0_1395,i_0_1398,i_0_1078,i_0_1200,i_0_1209,i_0_976,i_0_812,i_0_1367,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_939,i_0_1384,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984,i_0_1035,i_0_1066,i_0_1074,i_0_1153,i_0_1154,i_0_938,i_0_1217,i_0_748,i_0_1283,i_0_1284,i_0_1291,i_0_1302,i_0_1327,i_0_649]) ).

cnf(i_0_1441,plain,
    hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
    inference(rename_variables,[],[i_0_889]) ).

cnf(i_0_1442,plain,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_997]) ).

cnf(i_0_1443,plain,
    ( ~ hBOOL(c_in(X1,X2,X3))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
    inference(rename_variables,[],[i_0_649]) ).

cnf(i_0_1444,plain,
    c_lessequals(hAPP(X1,X2),c_Set_Oinsert(X3,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X2,X4,X5),X1,X5,tc_fun(X6,tc_bool)),X6),tc_fun(X6,tc_bool)),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1407,i_0_1181,i_0_1370,i_0_1121,i_0_997,i_0_1389,i_0_1392,i_0_1442,i_0_1158,i_0_957,i_0_1395,i_0_1398,i_0_1078,i_0_1200,i_0_1209,i_0_976,i_0_812,i_0_1367,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_1441,i_0_939,i_0_1384,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984,i_0_1035,i_0_1066,i_0_1074,i_0_1153,i_0_1154,i_0_938,i_0_1217,i_0_748,i_0_1283,i_0_1284,i_0_1291,i_0_1302,i_0_1327,i_0_649,i_0_655]) ).

cnf(i_0_1445,plain,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_997]) ).

cnf(i_0_1446,plain,
    ( ~ hBOOL(c_in(X1,X2,X3))
    | ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,tc_fun(X5,tc_bool)),X6,tc_fun(X5,tc_bool))
    | c_lessequals(hAPP(X4,X1),X6,tc_fun(X5,tc_bool)) ),
    inference(rename_variables,[],[i_0_655]) ).

cnf(i_0_1447,plain,
    c_lessequals(hAPP(X1,X2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X2,X3,X4),X1,X4,tc_bool),tc_bool),
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1407,i_0_1181,i_0_1370,i_0_1121,i_0_997,i_0_1389,i_0_1392,i_0_1442,i_0_1158,i_0_957,i_0_1395,i_0_1398,i_0_1078,i_0_1200,i_0_1202,i_0_1209,i_0_976,i_0_812,i_0_1367,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_1441,i_0_939,i_0_1384,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984,i_0_1035,i_0_1066,i_0_1074,i_0_1153,i_0_1154,i_0_938,i_0_1217,i_0_748,i_0_1283,i_0_1284,i_0_1291,i_0_1302,i_0_1327,i_0_649,i_0_655,i_0_686]) ).

cnf(i_0_1448,plain,
    ( ~ hBOOL(c_in(X1,X2,X3))
    | c_lessequals(hAPP(X4,X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X4,X3,X5),X5)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
    inference(rename_variables,[],[i_0_686]) ).

cnf(i_0_1449,plain,
    $false,
    inference(scs_inference,[],[i_0_632,i_0_1204,i_0_1180,i_0_1407,i_0_1181,i_0_1370,i_0_1121,i_0_1160,i_0_997,i_0_1389,i_0_1392,i_0_1442,i_0_1158,i_0_957,i_0_1395,i_0_1398,i_0_1078,i_0_1200,i_0_1202,i_0_1207,i_0_1209,i_0_976,i_0_812,i_0_1367,i_0_687,i_0_926,i_0_889,i_0_1379,i_0_1441,i_0_939,i_0_1384,i_0_851,i_0_977,i_0_1376,i_0_653,i_0_690,i_0_1174,i_0_1175,i_0_1216,i_0_1273,i_0_940,i_0_986,i_0_993,i_0_1116,i_0_1117,i_0_625,i_0_626,i_0_639,i_0_652,i_0_658,i_0_659,i_0_675,i_0_779,i_0_780,i_0_781,i_0_782,i_0_807,i_0_813,i_0_814,i_0_955,i_0_956,i_0_984,i_0_1035,i_0_1066,i_0_1074,i_0_1153,i_0_1154,i_0_938,i_0_1217,i_0_748,i_0_1283,i_0_1284,i_0_1291,i_0_1302,i_0_1327,i_0_649,i_0_655,i_0_686,i_0_734]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06  % Problem    : SWV580-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.06  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.07/0.25  % Computer : n012.cluster.edu
% 0.07/0.25  % Model    : x86_64 x86_64
% 0.07/0.25  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25  % Memory   : 8042.1875MB
% 0.07/0.25  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25  % CPULimit   : 300
% 0.07/0.25  % WCLimit    : 300
% 0.07/0.25  % DateTime   : Tue May  5 05:36:00 EDT 2026
% 0.07/0.25  % CPUTime    : 
% 0.07/0.25  % start to proof: theBenchmark
% 0.35/1.52  % Version  : CSE_E---1.7
% 0.35/1.52  % Problem  : theBenchmark.p
% 0.35/1.52  % SZS status Unsatisfiable for theBenchmark.p
% 0.35/1.52  % SZS output start CNFRefutation
% See solution above
% 0.74/1.99  % Total time : 1.265s
%------------------------------------------------------------------------------