CSE_E---1.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SCT007-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n029.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 05:05:49 PM UTC 2026

% Result   : Unsatisfiable 1.03s 1.66s
% Output   : CNFRefutation 1.09s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_604)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_trancl__Int__subset_0,axiom,
    ( c_lessequals(c_Transitive__Closure_Otrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X1,X2,X2,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__Int__subset_0) ).

cnf(cls_trancl__unfold__left_0,axiom,
    c_Transitive__Closure_Otrancl(X1,X2) = c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).

cnf(cls_wf__converse__trancl_0,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X2))
    | ~ hBOOL(c_Wellfounded_Owf(c_Relation_Oconverse(X1,X2,X2),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).

cnf(cls_trancl__unfold_0,axiom,
    c_Transitive__Closure_Otrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X1,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).

cnf(cls_rtrancl__Int__subset_0,axiom,
    ( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X1,X2,X2,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(c_Relation_OId(X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__Int__subset_0) ).

cnf(cls_rtrancl__empty_0,axiom,
    c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Relation_OId(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__empty_0) ).

cnf(cls_trancl__range_0,axiom,
    c_Relation_ORange(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ORange(X1,X2,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__range_0) ).

cnf(cls_Range__def_0,axiom,
    c_Relation_ORange(X1,X2,X3) = c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__def_0) ).

cnf(cls_wf__trancl_0,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X1,X2),X2))
    | ~ hBOOL(c_Wellfounded_Owf(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__trancl_0) ).

cnf(cls_trans__trancl_0,axiom,
    hBOOL(c_Relation_Otrans(c_Transitive__Closure_Otrancl(X1,X2),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__trancl_0) ).

cnf(cls_trancl__subset__Sigma_0,axiom,
    ( c_lessequals(c_Transitive__Closure_Otrancl(X1,X2),c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(X1,c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__subset__Sigma_0) ).

cnf(cls_trancl__converse_0,axiom,
    c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__converse_0) ).

cnf(cls_trancl__reflcl_0,axiom,
    c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).

cnf(cls_well__order__on__def_2,axiom,
    ( hBOOL(c_Order__Relation_Owell__order__on(X1,X2,X3))
    | ~ hBOOL(c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(X2,c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3))
    | ~ hBOOL(c_Order__Relation_Olinear__order__on(X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_well__order__on__def_2) ).

cnf(cls_total__on__diff__Id_0,axiom,
    ( hBOOL(c_Relation_Ototal__on(X1,X2,X3))
    | ~ hBOOL(c_Relation_Ototal__on(X1,c_HOL_Ominus__class_Ominus(X2,c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__diff__Id_0) ).

cnf(cls_reflcl__trancl_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Ortrancl(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_reflcl__trancl_0) ).

cnf(cls_rtrancl__unfold_0,axiom,
    c_Transitive__Closure_Ortrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).

cnf(cls_Nitpick_Ortrancl__def_0,axiom,
    c_Transitive__Closure_Ortrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Ortrancl__def_0) ).

cnf(cls_Range__Diff__subset_0,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(X1,X2,X3),c_Relation_ORange(X4,X2,X3),tc_fun(X3,tc_bool)),c_Relation_ORange(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Diff__subset_0) ).

cnf(cls_Range__Int__subset_0,axiom,
    c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(X1,X3,X4),c_Relation_ORange(X2,X3,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Int__subset_0) ).

cnf(cls_trancl__domain_0,axiom,
    c_Relation_ODomain(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ODomain(X1,X2,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__domain_0) ).

cnf(cls_sym__trancl_0,axiom,
    ( c_Relation_Osym(c_Transitive__Closure_Otrancl(X1,X2),X2)
    | ~ c_Relation_Osym(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__trancl_0) ).

cnf(cls_trancl__rtrancl__absorb_0,axiom,
    c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).

cnf(cls_trancl__unfold__right_0,axiom,
    c_Transitive__Closure_Otrancl(X1,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).

cnf(cls_total__on__diff__Id_1,axiom,
    ( hBOOL(c_Relation_Ototal__on(X1,c_HOL_Ominus__class_Ominus(X2,c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3))
    | ~ hBOOL(c_Relation_Ototal__on(X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__diff__Id_1) ).

cnf(cls_strict__linear__order__on__diff__Id_0,axiom,
    ( hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X1,X2),c_HOL_Ominus__class_Ominus(X3,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool))))
    | ~ hBOOL(c_Order__Relation_Olinear__order__on(X1,X3,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__diff__Id_0) ).

cnf(cls_well__order__on__def_1,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2))
    | ~ hBOOL(c_Order__Relation_Owell__order__on(X3,X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_well__order__on__def_1) ).

cnf(cls_trans__diff__Id_0,axiom,
    ( hBOOL(c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2))
    | ~ c_Relation_Oantisym(X1,X2)
    | ~ hBOOL(c_Relation_Otrans(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__diff__Id_0) ).

cnf(cls_trans__reflclI_0,axiom,
    ( hBOOL(c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2))
    | ~ hBOOL(c_Relation_Otrans(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__reflclI_0) ).

cnf(cls_irrefl__diff__Id_0,axiom,
    hBOOL(c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__diff__Id_0) ).

cnf(cls_well__order__on__def__raw_0,axiom,
    c_Order__Relation_Owell__order__on(v_A,v_r,t_a) = c_and(c_Order__Relation_Olinear__order__on(v_A,v_r,t_a),c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(t_a),tc_fun(tc_prod(t_a,t_a),tc_bool)),t_a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_well__order__on__def__raw_0) ).

cnf(cls_trancl__empty_0,axiom,
    c_Transitive__Closure_Otrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__empty_0) ).

cnf(cls_conjecture_1,negated_conjecture,
    hBOOL(c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(cls_Id__O__R_0,axiom,
    c_Relation_Orel__comp(c_Relation_OId(X1),X2,X1,X1,X3) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__O__R_0) ).

cnf(cls_R__O__Id_0,axiom,
    c_Relation_Orel__comp(X1,c_Relation_OId(X2),X3,X2,X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_R__O__Id_0) ).

cnf(cls_antisym__reflcl_0,axiom,
    ( c_Relation_Oantisym(X1,X2)
    | ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__reflcl_0) ).

cnf(cls_wf__Un_0,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2))
    | c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X2,X2),c_Relation_ORange(X3,X2,X2),tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ hBOOL(c_Wellfounded_Owf(X3,X2))
    | ~ hBOOL(c_Wellfounded_Owf(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__Un_0) ).

cnf(cls_Range__Un__eq_0,axiom,
    c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X1,X3,X4),c_Relation_ORange(X2,X3,X4),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).

cnf(cls_rtrancl__trancl__absorb_0,axiom,
    c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).

cnf(cls_trancl__id_0,axiom,
    ( c_Transitive__Closure_Otrancl(X1,X2) = X1
    | ~ hBOOL(c_Relation_Otrans(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__id_0) ).

cnf(cls_refl__reflcl_0,axiom,
    c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__reflcl_0) ).

cnf(cls_antisym__reflcl_1,axiom,
    ( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
    | ~ c_Relation_Oantisym(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).

cnf(cls_rtrancl__r__diff__Id_0,axiom,
    c_Transitive__Closure_Ortrancl(c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__r__diff__Id_0) ).

cnf(cls_rtrancl__reflcl_0,axiom,
    c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).

cnf(cls_Range__Id_0,axiom,
    c_Relation_ORange(c_Relation_OId(X1),X1,X1) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Id_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/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_0) ).

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

cnf(cls_trans__Id_0,axiom,
    hBOOL(c_Relation_Otrans(c_Relation_OId(X1),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__Id_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_2) ).

cnf(cls_Image__Id_0,axiom,
    c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Id_0) ).

cnf(cls_converse__Id_0,axiom,
    c_Relation_Oconverse(c_Relation_OId(X1),X1,X1) = c_Relation_OId(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Id_0) ).

cnf(cls_rtrancl__reflcl__absorb_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Ortrancl(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).

cnf(cls_Range__empty_0,axiom,
    c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__empty_0) ).

cnf(cls_refl__Id_0,axiom,
    c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Relation_OId(X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__Id_0) ).

cnf(cls_Range__converse_0,axiom,
    c_Relation_ORange(c_Relation_Oconverse(X1,X2,X3),X3,X2) = c_Relation_ODomain(X1,X2,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__converse_0) ).

cnf(cls_Domain__Id_0,axiom,
    c_Relation_ODomain(c_Relation_OId(X1),X1,X1) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Id_0) ).

cnf(cls_single__valued__Id_0,axiom,
    c_Relation_Osingle__valued(c_Relation_OId(X1),X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).

cnf(cls_Range__empty__iff_0,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
    | c_Relation_ORange(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__empty__iff_0) ).

cnf(cls_sym__Id_0,axiom,
    c_Relation_Osym(c_Relation_OId(X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Id_0) ).

cnf(cls_antisym__Id_0,axiom,
    c_Relation_Oantisym(c_Relation_OId(X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__Id_0) ).

cnf(cls_Range__rtrancl_0,axiom,
    c_Relation_ORange(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__rtrancl_0) ).

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

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

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

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

cnf(cls_Lin__def_0,axiom,
    c_Arrow__Order__Mirabelle_OLin = c_Collect(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lin__def_0) ).

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

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

cnf(cls_complete__lattice_OInf__UNIV_0,axiom,
    ( hAPP(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))) = X3
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X4,X5,X6,X7,X8,X3,X9,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__UNIV_0) ).

cnf(cls_complete__lattice_OSup__UNIV_0,axiom,
    ( hAPP(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))) = X3
    | ~ c_Complete__Lattice_Ocomplete__lattice(X4,X1,X5,X6,X7,X8,X9,X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__UNIV_0) ).

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

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

cnf(cls_wf__union__merge_1,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3))
    | ~ hBOOL(c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X1,X3,X3,X3),c_Relation_Orel__comp(X2,X1,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)),X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).

cnf(cls_wf__union__merge_0,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X1,X2,X2,X2),c_Relation_Orel__comp(X3,X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2))
    | ~ hBOOL(c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).

cnf(cls_wf__comp__self_1,axiom,
    ( hBOOL(c_Wellfounded_Owf(X1,X2))
    | ~ hBOOL(c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).

cnf(cls_O__assoc_0,axiom,
    c_Relation_Orel__comp(c_Relation_Orel__comp(X1,X2,X3,X4,X5),X6,X3,X5,X7) = c_Relation_Orel__comp(X1,c_Relation_Orel__comp(X2,X6,X4,X5,X7),X3,X4,X7),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_O__assoc_0) ).

cnf(cls_rel__comp__distrib2_0,axiom,
    c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X5,X3,X4,X6) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X5,X3,X4,X6),c_Relation_Orel__comp(X2,X5,X3,X4,X6),tc_fun(tc_prod(X3,X6),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).

cnf(cls_rel__comp__distrib_0,axiom,
    c_Relation_Orel__comp(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(tc_prod(X4,X5),tc_bool)),X6,X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X2,X6,X4,X5),c_Relation_Orel__comp(X1,X3,X6,X4,X5),tc_fun(tc_prod(X6,X5),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).

cnf(cls_rel__comp__subset__Sigma_0,axiom,
    ( c_lessequals(c_Relation_Orel__comp(X1,X2,X3,X4,X5),c_Product__Type_OSigma(X6,c_COMBK(X7,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool))
    | ~ c_lessequals(X2,c_Product__Type_OSigma(X8,c_COMBK(X7,tc_fun(X5,tc_bool),X4),X4,X5),tc_fun(tc_prod(X4,X5),tc_bool))
    | ~ c_lessequals(X1,c_Product__Type_OSigma(X6,c_COMBK(X8,tc_fun(X4,tc_bool),X3),X3,X4),tc_fun(tc_prod(X3,X4),tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__subset__Sigma_0) ).

cnf(cls_union__comp__emptyL_0,axiom,
    ( c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(tc_prod(X3,X3),tc_bool)),X2,X3,X3,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
    | c_Relation_Orel__comp(X1,X2,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
    | c_Relation_Orel__comp(X4,X2,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_union__comp__emptyL_0) ).

cnf(cls_union__comp__emptyR_0,axiom,
    ( c_Relation_Orel__comp(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3,X3,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
    | c_Relation_Orel__comp(X1,X2,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
    | c_Relation_Orel__comp(X1,X4,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_union__comp__emptyR_0) ).

cnf(cls_rel__comp__mono_0,axiom,
    ( c_lessequals(c_Relation_Orel__comp(X1,X2,X3,X4,X5),c_Relation_Orel__comp(X6,X7,X3,X4,X5),tc_fun(tc_prod(X3,X5),tc_bool))
    | ~ c_lessequals(X2,X7,tc_fun(tc_prod(X4,X5),tc_bool))
    | ~ c_lessequals(X1,X6,tc_fun(tc_prod(X3,X4),tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).

cnf(cls_wf__comp__self_0,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2))
    | ~ hBOOL(c_Wellfounded_Owf(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).

cnf(cls_wf__union__compatible_0,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3))
    | ~ c_lessequals(c_Relation_Orel__comp(X1,X2,X3,X3,X3),X1,tc_fun(tc_prod(X3,X3),tc_bool))
    | ~ hBOOL(c_Wellfounded_Owf(X2,X3))
    | ~ hBOOL(c_Wellfounded_Owf(X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).

cnf(cls_converse__rel__comp_0,axiom,
    c_Relation_Oconverse(c_Relation_Orel__comp(X1,X2,X3,X4,X5),X3,X5) = c_Relation_Orel__comp(c_Relation_Oconverse(X2,X4,X5),c_Relation_Oconverse(X1,X3,X4),X5,X4,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).

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

cnf(cls_rel__pow__commute_0,axiom,
    c_Relation_Orel__comp(X1,c_Nat_Ocompow(X2,X1,tc_prod(X3,X3),tc_bool),X3,X3,X3) = c_Relation_Orel__comp(c_Nat_Ocompow(X2,X1,tc_prod(X3,X3),tc_bool),X1,X3,X3,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__pow__commute_0) ).

cnf(cls_Image__subset__eq_1,axiom,
    ( c_lessequals(c_Relation_OImage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(c_Relation_OImage(c_Relation_Oconverse(X1,X3,X4),c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X4,tc_bool)),X4,X3),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__subset__eq_1) ).

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

cnf(cls_Image__Int__subset_0,axiom,
    c_lessequals(c_Relation_OImage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).

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

cnf(cls_Times__subset__cancel2_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool))
    | ~ hBOOL(c_in(X6,X4,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__subset__cancel2_0) ).

cnf(cls_refl__on__comp__subset_0,axiom,
    ( c_lessequals(X1,c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_Relation_Orefl__on(X3,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).

cnf(cls_sym__trans__comp__subset_0,axiom,
    ( c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ hBOOL(c_Relation_Otrans(X1,X2))
    | ~ c_Relation_Osym(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__trans__comp__subset_0) ).

cnf(cls_Image__subset__eq_0,axiom,
    ( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(c_Relation_OImage(c_Relation_Oconverse(X2,X3,X4),c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X4,tc_bool)),X4,X3),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Relation_OImage(X2,X1,X3,X4),X5,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__subset__eq_0) ).

cnf(cls_single__valued__rel__comp_0,axiom,
    ( c_Relation_Osingle__valued(c_Relation_Orel__comp(X1,X2,X3,X4,X5),X3,X5)
    | ~ c_Relation_Osingle__valued(X2,X4,X5)
    | ~ c_Relation_Osingle__valued(X1,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).

cnf(cls_trans__O__subset_0,axiom,
    ( c_lessequals(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ hBOOL(c_Relation_Otrans(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).

cnf(cls_r__comp__rtrancl__eq_0,axiom,
    c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__comp__rtrancl__eq_0) ).

cnf(cls_inj__image__mem__iff_0,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
    | ~ c_Fun_Oinj__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).

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

cnf(cls_Times__Diff__distrib1_0,axiom,
    c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5) = c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__Diff__distrib1_0) ).

cnf(cls_Times__Int__distrib1_0,axiom,
    c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__Int__distrib1_0) ).

cnf(cls_Times__Un__distrib1_0,axiom,
    c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__Un__distrib1_0) ).

cnf(cls_inj__image__Compl__subset_0,axiom,
    ( c_lessequals(c_Set_Oimage(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3,X4),c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(X1,X2,X3,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__Compl__subset_0) ).

cnf(cls_inj__image__subset__iff_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).

cnf(cls_INT__iff_0,axiom,
    ( hBOOL(c_in(X1,hAPP(X2,X3),X4))
    | ~ hBOOL(c_in(X3,X5,X6))
    | ~ hBOOL(c_in(X1,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X2,X6,tc_fun(X4,tc_bool)),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__iff_0) ).

cnf(cls_INT__D_0,axiom,
    ( hBOOL(c_in(X1,hAPP(X2,X3),X4))
    | ~ hBOOL(c_in(X3,X5,X6))
    | ~ hBOOL(c_in(X1,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X2,X6,tc_fun(X4,tc_bool)),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__D_0) ).

cnf(cls_INT__E_0,axiom,
    ( hBOOL(c_in(X4,hAPP(X5,X1),X6))
    | ~ hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X5,X3,tc_fun(X6,tc_bool)),X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__E_0) ).

cnf(cls_inj__on__image__set__diff_0,axiom,
    ( c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(X3,X6,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X6,tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X6,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).

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

cnf(cls_wf__no__loop_0,axiom,
    ( hBOOL(c_Wellfounded_Owf(X1,X2))
    | c_Relation_Orel__comp(X1,X1,X2,X2,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__no__loop_0) ).

cnf(cls_Image__subset_0,axiom,
    ( c_lessequals(c_Relation_OImage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,c_Product__Type_OSigma(X6,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4),tc_fun(tc_prod(X3,X4),tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__subset_0) ).

cnf(cls_Times__subset__cancel2_1,axiom,
    ( c_lessequals(c_Product__Type_OSigma(X1,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3),c_Product__Type_OSigma(X5,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3),tc_fun(tc_prod(X4,X3),tc_bool))
    | ~ c_lessequals(X1,X5,tc_fun(X4,tc_bool))
    | ~ hBOOL(c_in(X6,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__subset__cancel2_1) ).

cnf(cls_INF1__iff_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1,X5,tc_fun(X6,tc_bool)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INF1__iff_0) ).

cnf(cls_INF1__D_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1,X5,tc_fun(X6,tc_bool)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INF1__D_0) ).

cnf(cls_INF1__E_0,axiom,
    ( hBOOL(hAPP(hAPP(X4,X1),X5))
    | ~ hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X4,X3,tc_fun(X6,tc_bool)),X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INF1__E_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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).

cnf(cls_vimage__subsetI_0,axiom,
    ( c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),X5,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).

cnf(cls_image__set__diff_0,axiom,
    ( c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__set__diff_0) ).

cnf(cls_image__Int_0,axiom,
    ( c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Int_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/sandbox2/benchmark/theBenchmark.p',cls_vimageD_0) ).

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

cnf(cls_inj__image__mem__iff_1,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
    | ~ hBOOL(c_in(X2,X3,X4))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).

cnf(cls_wf__exp_0,axiom,
    ( hBOOL(c_Wellfounded_Owf(X1,X2))
    | ~ hBOOL(c_Wellfounded_Owf(c_Nat_Ocompow(X3,X1,tc_prod(X2,X2),tc_bool),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__exp_0) ).

cnf(cls_Image__Int__eq_0,axiom,
    ( c_Relation_OImage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X1,X4,X5),X5,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).

cnf(cls_vimage__code_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_0) ).

cnf(cls_inj__image__subset__iff_1,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).

cnf(cls_INT__Un_0,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,X3,tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X3,tc_fun(X5,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__Un_0) ).

cnf(cls_Un__Image_0,axiom,
    c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X5,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X1,X5,X3,X4),c_Relation_OImage(X2,X5,X3,X4),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Image_0) ).

cnf(cls_funpow__swap1_0,axiom,
    hAPP(X1,hAPP(c_Nat_Ocompow(X2,X1,X3,X3),X4)) = hAPP(c_Nat_Ocompow(X2,X1,X3,X3),hAPP(X1,X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funpow__swap1_0) ).

cnf(cls_endo__inj__surj_0,axiom,
    ( c_Set_Oimage(X1,X2,X3,X3) = X2
    | ~ c_Fun_Oinj__on(X1,X2,X3,X3)
    | ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X3),X2,tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).

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

cnf(cls_Sigma__Diff__distrib1_0,axiom,
    c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5) = c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(X1,X4,X3,X5),c_Product__Type_OSigma(X2,X4,X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__Diff__distrib1_0) ).

cnf(cls_Sigma__Int__distrib1_0,axiom,
    c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X1,X4,X3,X5),c_Product__Type_OSigma(X2,X4,X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__Int__distrib1_0) ).

cnf(cls_Sigma__Un__distrib1_0,axiom,
    c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X1,X4,X3,X5),c_Product__Type_OSigma(X2,X4,X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).

cnf(cls_Image__Un_0,axiom,
    c_Relation_OImage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Un_0) ).

cnf(cls_vimage__Diff_0,axiom,
    c_Set_Ovimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).

cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_vimage__Int_0) ).

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

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

cnf(cls_rel__comp__empty1_0,axiom,
    c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X3,X1,X2,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X4),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__empty1_0) ).

cnf(cls_rel__comp__empty2_0,axiom,
    c_Relation_Orel__comp(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)),X4,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X3),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__empty2_0) ).

cnf(cls_Times__eq__cancel2_0,axiom,
    ( X1 = X5
    | c_Product__Type_OSigma(X1,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3) != c_Product__Type_OSigma(X5,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3)
    | ~ hBOOL(c_in(X6,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).

cnf(cls_image__vimage__eq_0,axiom,
    c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).

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

cnf(cls_Image__mono_0,axiom,
    ( c_lessequals(c_Relation_OImage(X1,X2,X3,X4),c_Relation_OImage(X5,X6,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X6,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X5,tc_fun(tc_prod(X3,X4),tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__mono_0) ).

cnf(cls_rangeI_0,axiom,
    hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rangeI_0) ).

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

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

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

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

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

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

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

cnf(cls_Domain__Diff__subset_0,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ODomain(X1,X2,X3),c_Relation_ODomain(X4,X2,X3),tc_fun(X2,tc_bool)),c_Relation_ODomain(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Diff__subset_0) ).

cnf(cls_Domain__Int__subset_0,axiom,
    c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Int__subset_0) ).

cnf(cls_rtrancl__idemp__self__comp_0,axiom,
    c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).

cnf(cls_inj__image__eq__iff_0,axiom,
    ( X2 = X5
    | c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X5,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).

cnf(cls_INT__subset__iff_0,axiom,
    ( c_lessequals(X1,hAPP(X2,X3),tc_fun(X4,tc_bool))
    | ~ hBOOL(c_in(X3,X5,X6))
    | ~ c_lessequals(X1,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X2,X6,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__subset__iff_0) ).

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

cnf(cls_inj__vimage__image__eq_0,axiom,
    ( c_Set_Ovimage(X1,c_Set_Oimage(X1,X2,X3,X4),X3,X4) = X2
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).

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

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

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

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

cnf(cls_finite__surj__inj_0,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X3)
    | ~ c_lessequals(X2,c_Set_Oimage(X1,X2,X3,X3),tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).

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

cnf(cls_INT__absorb_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(hAPP(X1,X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1,X4,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1,X4,tc_fun(X5,tc_bool))
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__absorb_0) ).

cnf(cls_wf__inv__image_0,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Relation_Oinv__image(X1,X2,X3,X4),X4))
    | ~ hBOOL(c_Wellfounded_Owf(X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).

cnf(cls_trans__inv__image_0,axiom,
    ( hBOOL(c_Relation_Otrans(c_Relation_Oinv__image(X1,X2,X3,X4),X4))
    | ~ hBOOL(c_Relation_Otrans(X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).

cnf(cls_rtrancl__Un__subset_0,axiom,
    c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).

cnf(cls_refl__on__def_0,axiom,
    ( c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
    | ~ c_Relation_Orefl__on(X2,X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__def_0) ).

cnf(cls_finite__vimageI_0,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Ovimage(X1,X2,X3,X4),X3)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4)
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).

cnf(cls_wfE__pf_0,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,c_Relation_OImage(X3,X1,X2,X2),tc_fun(X2,tc_bool))
    | ~ hBOOL(c_Wellfounded_Owf(X3,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfE__pf_0) ).

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

cnf(cls_distrib__inf__le_0,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1),c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).

cnf(cls_converse__inv__image_0,axiom,
    c_Relation_Oconverse(c_Relation_Oinv__image(X1,X2,X3,X4),X4,X4) = c_Relation_Oinv__image(c_Relation_Oconverse(X1,X3,X3),X2,X3,X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).

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

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

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

cnf(cls_INT__extend__simps_I3_J_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__extend__simps_I3_J_0) ).

cnf(cls_vimage__Compl_0,axiom,
    c_Set_Ovimage(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X4,X3) = c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(X1,X2,X4,X3),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).

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

cnf(cls_INT__lower_0,axiom,
    ( c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X2,X3,tc_fun(X4,tc_bool)),hAPP(X2,X5),tc_fun(X4,tc_bool))
    | ~ hBOOL(c_in(X5,X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__lower_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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).

cnf(cls_finite__INT_0,axiom,
    ( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X2,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_Finite__Set_Ofinite(hAPP(X2,X5),X4)
    | ~ hBOOL(c_in(X5,X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__INT_0) ).

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

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

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

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

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

cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_Int__iff_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_IntI_0) ).

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

cnf(cls_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_IntE_1) ).

cnf(cls_subset__inj__on_0,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X5,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).

cnf(cls_INF__leI_0,axiom,
    ( c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X3,X4,X1),hAPP(X3,X5),X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(c_in(X5,X2,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INF__leI_0) ).

cnf(cls_INT__extend__simps_I1_J_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = X4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__extend__simps_I1_J_0) ).

cnf(cls_INT__extend__simps_I2_J_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__extend__simps_I2_J_0) ).

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

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

cnf(cls_INTER__UNIV__conv_I2_J_0,axiom,
    ( hAPP(X2,X5) = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool))
    | c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X2,X3,tc_fun(X4,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool))
    | ~ hBOOL(c_in(X5,X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I2_J_0) ).

cnf(cls_INTER__UNIV__conv_I1_J_0,axiom,
    ( hAPP(X3,X5) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))
    | c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X3,X4,tc_fun(X1,tc_bool))
    | ~ hBOOL(c_in(X5,X2,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I1_J_0) ).

cnf(cls_single__valued__rel__pow_0,axiom,
    ( c_Relation_Osingle__valued(c_Nat_Ocompow(X1,X2,tc_prod(X3,X3),tc_bool),X3,X3)
    | ~ c_Relation_Osingle__valued(X2,X3,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__rel__pow_0) ).

cnf(cls_converse__Int_0,axiom,
    c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X1,X3,X4),c_Relation_Oconverse(X2,X3,X4),tc_fun(tc_prod(X4,X3),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Int_0) ).

cnf(cls_converse__Un_0,axiom,
    c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(X1,X3,X4),c_Relation_Oconverse(X2,X3,X4),tc_fun(tc_prod(X4,X3),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Un_0) ).

cnf(cls_rtrancl__Un__rtrancl_0,axiom,
    c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).

cnf(cls_trans__Int_0,axiom,
    ( hBOOL(c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3))
    | ~ hBOOL(c_Relation_Otrans(X2,X3))
    | ~ hBOOL(c_Relation_Otrans(X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__Int_0) ).

cnf(cls_refl__on__Int_0,axiom,
    ( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
    | ~ c_Relation_Orefl__on(X2,X5,X3)
    | ~ c_Relation_Orefl__on(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__Int_0) ).

cnf(cls_refl__on__Un_0,axiom,
    ( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
    | ~ c_Relation_Orefl__on(X2,X5,X3)
    | ~ c_Relation_Orefl__on(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).

cnf(cls_Diff__mono_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_Int__mono_0) ).

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

cnf(cls_total__on__converse_0,axiom,
    ( hBOOL(c_Relation_Ototal__on(X1,X2,X3))
    | ~ hBOOL(c_Relation_Ototal__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__converse_0) ).

cnf(cls_linear__order__on__converse_0,axiom,
    ( hBOOL(c_Order__Relation_Olinear__order__on(X1,X2,X3))
    | ~ hBOOL(c_Order__Relation_Olinear__order__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linear__order__on__converse_0) ).

cnf(cls_partial__order__on__converse_0,axiom,
    ( hBOOL(c_Order__Relation_Opartial__order__on(X1,X2,X3))
    | ~ hBOOL(c_Order__Relation_Opartial__order__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_partial__order__on__converse_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/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).

cnf(cls_Un__Diff_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_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/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

cnf(cls_Int__Un__distrib2_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib2_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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib2_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/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int_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/sandbox2/benchmark/theBenchmark.p',cls_Diff__Un_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/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

cnf(cls_Int__Un__distrib_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib_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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).

cnf(cls_Domain__Un__eq_0,axiom,
    c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Un__eq_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/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

cnf(cls_Diff__subset__conv_0,axiom,
    ( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

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

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

cnf(cls_wf__Int1_0,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3))
    | ~ hBOOL(c_Wellfounded_Owf(X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__Int1_0) ).

cnf(cls_wf__Int2_0,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3))
    | ~ hBOOL(c_Wellfounded_Owf(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__Int2_0) ).

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

cnf(cls_Sigma__empty2_0,axiom,
    c_Product__Type_OSigma(X1,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool),X3),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__empty2_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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).

cnf(cls_ComplD_0,axiom,
    ( ~ hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplD_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).

cnf(cls_vimage__const_0,axiom,
    ( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))
    | ~ hBOOL(c_in(X1,X4,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__const_0) ).

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

cnf(cls_sym__inv__image_0,axiom,
    ( c_Relation_Osym(c_Relation_Oinv__image(X1,X2,X3,X4),X4)
    | ~ c_Relation_Osym(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).

cnf(cls_well__order__on__empty_0,axiom,
    hBOOL(c_Order__Relation_Owell__order__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_well__order__on__empty_0) ).

cnf(cls_lnear__order__on__empty_0,axiom,
    hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lnear__order__on__empty_0) ).

cnf(cls_partial__order__on__empty_0,axiom,
    hBOOL(c_Order__Relation_Opartial__order__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_partial__order__on__empty_0) ).

cnf(cls_injD_0,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_injD_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/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).

cnf(cls_INT__constant_0,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_COMBK(X2,tc_fun(X3,tc_bool),X1),X1,tc_fun(X3,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__constant_0) ).

cnf(cls_total__on__converse_1,axiom,
    ( hBOOL(c_Relation_Ototal__on(X1,c_Relation_Oconverse(X2,X3,X3),X3))
    | ~ hBOOL(c_Relation_Ototal__on(X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__converse_1) ).

cnf(cls_linear__order__on__converse_1,axiom,
    ( hBOOL(c_Order__Relation_Olinear__order__on(X1,c_Relation_Oconverse(X2,X3,X3),X3))
    | ~ hBOOL(c_Order__Relation_Olinear__order__on(X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linear__order__on__converse_1) ).

cnf(cls_partial__order__on__converse_1,axiom,
    ( hBOOL(c_Order__Relation_Opartial__order__on(X1,c_Relation_Oconverse(X2,X3,X3),X3))
    | ~ hBOOL(c_Order__Relation_Opartial__order__on(X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_partial__order__on__converse_1) ).

cnf(cls_Domain__mono_0,axiom,
    ( c_lessequals(c_Relation_ODomain(X1,X2,X3),c_Relation_ODomain(X4,X2,X3),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__mono_0) ).

cnf(cls_vimage__const_1,axiom,
    ( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | hBOOL(c_in(X1,X4,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__const_1) ).

cnf(cls_sym__Int__converse_0,axiom,
    c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X1,c_Relation_Oconverse(X1,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Int__converse_0) ).

cnf(cls_sym__Un__converse_0,axiom,
    c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_Oconverse(X1,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).

cnf(cls_rtrancl__subset_0,axiom,
    ( c_Transitive__Closure_Ortrancl(X1,X2) = c_Transitive__Closure_Ortrancl(X3,X2)
    | ~ c_lessequals(X1,c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__subset_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/sandbox2/benchmark/theBenchmark.p',cls_double__diff_0) ).

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

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

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/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).

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

cnf(cls_wf__induct__rule_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X1,X3,X4)))
    | ~ hBOOL(c_Wellfounded_Owf(X3,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__induct__rule_1) ).

cnf(cls_tfl__wf__induct_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X1,X3,X4)))
    | ~ hBOOL(c_Wellfounded_Owf(X3,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tfl__wf__induct_1) ).

cnf(cls_wf__induct_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X1,X3,X4)))
    | ~ hBOOL(c_Wellfounded_Owf(X3,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__induct_1) ).

cnf(cls_wf__def_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X1,X3,X4)))
    | ~ hBOOL(c_Wellfounded_Owf(X3,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__def_1) ).

cnf(cls_linear__order__on__def_2,axiom,
    ( hBOOL(c_Order__Relation_Olinear__order__on(X1,X2,X3))
    | ~ hBOOL(c_Relation_Ototal__on(X1,X2,X3))
    | ~ hBOOL(c_Order__Relation_Opartial__order__on(X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linear__order__on__def_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_Int__Diff_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/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

cnf(cls_Un__assoc_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_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/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

cnf(cls_Un__left__commute_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

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

cnf(cls_image__is__empty_0,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

cnf(cls_INT__constant_1,axiom,
    ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,tc_fun(X3,tc_bool)) = X2
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__constant_1) ).

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

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

cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).

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

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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib2_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/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib2_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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_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/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).

cnf(cls_image__constant__conv_0,axiom,
    c_Set_Oimage(c_COMBK(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_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/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).

cnf(cls_rtrancl__subset__rtrancl_0,axiom,
    ( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(X1,c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).

cnf(cls_Compl__subset__Compl__iff_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).

cnf(cls_trans__converse_0,axiom,
    ( hBOOL(c_Relation_Otrans(X1,X2))
    | ~ hBOOL(c_Relation_Otrans(c_Relation_Oconverse(X1,X2,X2),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__converse_0) ).

cnf(cls_Compl__Int_0,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__Int_0) ).

cnf(cls_Compl__Un_0,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__Un_0) ).

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

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

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

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

cnf(cls_conjecture_2,negated_conjecture,
    ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

cnf(cls_INF__const_0,axiom,
    ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,c_COMBK(X3,X1,X4),X4,X1) = X3
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INF__const_0) ).

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

cnf(cls_rtrancl__mono_0,axiom,
    ( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__mono_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).

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

cnf(cls_Sigma__empty1_0,axiom,
    c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__empty1_0) ).

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

cnf(cls_ComplI_0,axiom,
    ( hBOOL(c_in(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3))
    | hBOOL(c_in(X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplI_0) ).

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

cnf(cls_strict__linear__order__on__def_3,axiom,
    ( hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X1,X2),X3))
    | ~ hBOOL(c_Relation_Ototal__on(X1,X3,X2))
    | ~ hBOOL(c_Relation_Oirrefl(X3,X2))
    | ~ hBOOL(c_Relation_Otrans(X3,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_3) ).

cnf(cls_INT__empty_0,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__empty_0) ).

cnf(cls_single__valued__subset_0,axiom,
    ( c_Relation_Osingle__valued(X1,X2,X3)
    | ~ c_Relation_Osingle__valued(X4,X2,X3)
    | ~ c_lessequals(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).

cnf(cls_Compl__subset__Compl__iff_1,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).

cnf(cls_Compl__anti__mono_0,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).

cnf(cls_wf__empty_0,axiom,
    hBOOL(c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__empty_0) ).

cnf(cls_le__sup__iff_2,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

cnf(cls_sup__least_0,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).

cnf(cls_le__supI_0,axiom,
    ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).

cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_le__infI_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/sandbox2/benchmark/theBenchmark.p',cls_le__inf__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/sandbox2/benchmark/theBenchmark.p',cls_inf__greatest_0) ).

cnf(cls_disjoint__eq__subset__Compl_1,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_1) ).

cnf(cls_Compl__Diff__eq_0,axiom,
    c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__Diff__eq_0) ).

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

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

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

cnf(cls_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

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

cnf(cls_inf__sup__aci_I6_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

cnf(cls_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

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

cnf(cls_inf__sup__aci_I7_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

cnf(cls_strict__linear__order__on__def__raw_0,axiom,
    hAPP(c_Order__Relation_Ostrict__linear__order__on(v_A,t_a),v_r) = c_and(c_Relation_Otrans(v_r,t_a),c_and(c_Relation_Oirrefl(v_r,t_a),c_Relation_Ototal__on(v_A,v_r,t_a))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__def__raw_0) ).

cnf(cls_Image__empty_0,axiom,
    c_Relation_OImage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__empty_0) ).

cnf(cls_vimage__UNIV_0,axiom,
    c_Set_Ovimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).

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

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

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

cnf(cls_subset__trans_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).

cnf(cls_le__eqI_1,axiom,
    ( c_lessequals(X3,X2,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
    | ~ c_lessequals(X5,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).

cnf(cls_le__eqI_0,axiom,
    ( c_lessequals(X5,X4,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).

cnf(cls_sym__Int_0,axiom,
    ( c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
    | ~ c_Relation_Osym(X2,X3)
    | ~ c_Relation_Osym(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Int_0) ).

cnf(cls_sym__Un_0,axiom,
    ( c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
    | ~ c_Relation_Osym(X2,X3)
    | ~ c_Relation_Osym(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Un_0) ).

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

cnf(cls_le__sup__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

cnf(cls_le__supE_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X1),X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).

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

cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

cnf(cls_le__infE_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_0) ).

cnf(cls_le__inf__iff_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).

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

cnf(cls_disjoint__eq__subset__Compl_0,axiom,
    ( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_0) ).

cnf(cls_refl__on__converse_0,axiom,
    ( c_Relation_Orefl__on(X1,X2,X3)
    | ~ c_Relation_Orefl__on(X1,c_Relation_Oconverse(X2,X3,X3),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).

cnf(cls_Diff__idemp_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

cnf(cls_Un__Diff__cancel2_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

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

cnf(cls_Un__left__absorb_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

cnf(cls_subset__Compl__self__eq_1,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_1) ).

cnf(cls_finite__Diff2_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).

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

cnf(cls_wf__mlex_0,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Wellfounded_Omlex__prod(X1,X2,X3),X3))
    | ~ hBOOL(c_Wellfounded_Owf(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__mlex_0) ).

cnf(cls_trans__converse_1,axiom,
    ( hBOOL(c_Relation_Otrans(c_Relation_Oconverse(X1,X2,X2),X2))
    | ~ hBOOL(c_Relation_Otrans(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__converse_1) ).

cnf(cls_inf__eq__neg__sup_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__eq__neg__sup_0) ).

cnf(cls_sup__eq__neg__inf_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__neg__inf_0) ).

cnf(cls_linear__order__on__def_1,axiom,
    ( hBOOL(c_Relation_Ototal__on(X1,X2,X3))
    | ~ hBOOL(c_Order__Relation_Olinear__order__on(X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linear__order__on__def_1) ).

cnf(cls_well__order__on__def_0,axiom,
    ( hBOOL(c_Order__Relation_Olinear__order__on(X1,X2,X3))
    | ~ hBOOL(c_Order__Relation_Owell__order__on(X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_well__order__on__def_0) ).

cnf(cls_linear__order__on__def_0,axiom,
    ( hBOOL(c_Order__Relation_Opartial__order__on(X1,X2,X3))
    | ~ hBOOL(c_Order__Relation_Olinear__order__on(X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linear__order__on__def_0) ).

cnf(cls_less__by__empty_0,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X2,tc_fun(tc_prod(X1,X1),tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__by__empty_0) ).

cnf(cls_wf__subset_0,axiom,
    ( hBOOL(c_Wellfounded_Owf(X1,X2))
    | ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ hBOOL(c_Wellfounded_Owf(X3,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__subset_0) ).

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

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

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

cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).

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

cnf(cls_subset__Compl__self__eq_0,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).

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

cnf(cls_refl__on__empty_0,axiom,
    c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__empty_0) ).

cnf(cls_linear__order__on__def__raw_0,axiom,
    c_Order__Relation_Olinear__order__on(v_A,v_r,t_a) = c_and(c_Order__Relation_Opartial__order__on(v_A,v_r,t_a),c_Relation_Ototal__on(v_A,v_r,t_a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linear__order__on__def__raw_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/sandbox2/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).

cnf(cls_le__infI1_0,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).

cnf(cls_le__supI1_0,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).

cnf(cls_le__supI2_0,axiom,
    ( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).

cnf(cls_refl__on__converse_1,axiom,
    ( c_Relation_Orefl__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)
    | ~ c_Relation_Orefl__on(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).

cnf(cls_set__eq__subset_2,axiom,
    ( X1 = X2
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

cnf(cls_equalityI_0,axiom,
    ( X1 = X2
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).

cnf(cls_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).

cnf(cls_acyclic__subset_0,axiom,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_Wellfounded_Oacyclic(X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).

cnf(cls_antisym__subset_0,axiom,
    ( c_Relation_Oantisym(X1,X2)
    | ~ c_Relation_Oantisym(X3,X2)
    | ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__subset_0) ).

cnf(cls_strict__linear__order__on__def_2,axiom,
    ( hBOOL(c_Relation_Ototal__on(X1,X2,X3))
    | ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X1,X3),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_2) ).

cnf(cls_Domain__empty_0,axiom,
    c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__empty_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/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).

cnf(cls_xt1_I6_J_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X4,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

cnf(cls_neg__inf__eq__sup_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__inf__eq__sup_0) ).

cnf(cls_compl__inf_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__inf_0) ).

cnf(cls_neg__sup__eq__inf_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__sup__eq__inf_0) ).

cnf(cls_compl__sup_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__sup_0) ).

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

cnf(cls_Diff__subset_0,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

cnf(cls_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

cnf(cls_Un__upper1_0,axiom,
    c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

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

cnf(cls_neg__le__iff__le_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).

cnf(cls_Diff__Compl_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Compl_0) ).

cnf(cls_Diff__eq_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__eq_0) ).

cnf(cls_finite__compl_0,axiom,
    ( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__compl_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

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

cnf(cls_inf__sup__aci_I8_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

cnf(cls_minus__le__iff_1,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).

cnf(cls_minus__le__iff_0,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).

cnf(cls_le__minus__iff_1,axiom,
    ( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).

cnf(cls_le__minus__iff_0,axiom,
    ( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).

cnf(cls_total__on__empty_0,axiom,
    hBOOL(c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__empty_0) ).

cnf(cls_UNIV__I_0,axiom,
    hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__I_0) ).

cnf(cls_finite__compl_1,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__compl_1) ).

cnf(cls_finite__Diff2_1,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).

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

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

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

cnf(cls_Domain__empty__iff_0,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
    | c_Relation_ODomain(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__empty__iff_0) ).

cnf(cls_Un__empty_2,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).

cnf(cls_compl__unique_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(X2,X1) = X3
    | ~ class_Lattices_Oboolean__algebra(X1)
    | c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__unique_0) ).

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

cnf(cls_acyclic__converse_0,axiom,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).

cnf(cls_sym__converse_0,axiom,
    ( c_Relation_Osym(X1,X2)
    | ~ c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__converse_0) ).

cnf(cls_antisym__converse_0,axiom,
    ( c_Relation_Oantisym(X1,X2)
    | ~ c_Relation_Oantisym(c_Relation_Oconverse(X1,X2,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__converse_0) ).

cnf(cls_rtrancl__converse_0,axiom,
    c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).

cnf(cls_subset__Un__eq_1,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

cnf(cls_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

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

cnf(cls_Un__absorb1_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

cnf(cls_rev__predicate1D_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool))
    | ~ hBOOL(hAPP(X3,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

cnf(cls_predicate1D_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X3,X2))
    | ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).

cnf(cls_le__imp__neg__le_0,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).

cnf(cls_conjecture_0,negated_conjecture,
    hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_Un__empty_0,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).

cnf(cls_Un__empty_1,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).

cnf(cls_finite__Diff_0,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff_0) ).

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

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

cnf(cls_partial__order__on__def_1,axiom,
    ( c_Relation_Oantisym(X1,X2)
    | ~ hBOOL(c_Order__Relation_Opartial__order__on(X3,X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_partial__order__on__def_1) ).

cnf(cls_minus__diff__eq_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Ominus__class_Ominus(X3,X2,X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).

cnf(cls_order__antisym__conv_0,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

cnf(cls_order__antisym_0,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).

cnf(cls_order__eq__iff_2,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

cnf(cls_subset__empty_1,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).

cnf(cls_eq__eqI_1,axiom,
    ( X2 = X3
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

cnf(cls_eq__eqI_0,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

cnf(cls_Compl__disjoint2_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__disjoint2_0) ).

cnf(cls_Compl__partition2_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__partition2_0) ).

cnf(cls_Compl__disjoint_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__disjoint_0) ).

cnf(cls_Compl__partition_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__partition_0) ).

cnf(cls_antisym__empty_0,axiom,
    c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__empty_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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_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/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

cnf(cls_Compl__eq__Diff__UNIV_0,axiom,
    c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__eq__Diff__UNIV_0) ).

cnf(cls_converse__converse_0,axiom,
    c_Relation_Oconverse(c_Relation_Oconverse(X1,X2,X3),X3,X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__converse_0) ).

cnf(cls_strict__linear__order__on__def_1,axiom,
    ( hBOOL(c_Relation_Oirrefl(X1,X2))
    | ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X3,X2),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_1) ).

cnf(cls_strict__linear__order__on__def_0,axiom,
    ( hBOOL(c_Relation_Otrans(X1,X2))
    | ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X3,X2),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_0) ).

cnf(cls_rev__finite__subset_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).

cnf(cls_finite__subset_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(X3,X2)
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__subset_0) ).

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

cnf(cls_empty__Diff_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

cnf(cls_Un__UNIV__left_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).

cnf(cls_Diff__UNIV_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__UNIV_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/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

cnf(cls_Un__UNIV__right_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__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/sandbox2/benchmark/theBenchmark.p',cls_bot__empty__eq_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/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).

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

cnf(cls_le__iff__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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

cnf(cls_le__iff__sup_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Oupper__semilattice(X1)
    | c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

cnf(cls_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_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/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

cnf(cls_le__iff__sup_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X3
    | ~ class_Lattices_Oupper__semilattice(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

cnf(cls_acyclic__converse_1,axiom,
    ( c_Wellfounded_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2)
    | ~ c_Wellfounded_Oacyclic(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).

cnf(cls_sym__converse_1,axiom,
    ( c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2)
    | ~ c_Relation_Osym(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__converse_1) ).

cnf(cls_antisym__converse_1,axiom,
    ( c_Relation_Oantisym(c_Relation_Oconverse(X1,X2,X2),X2)
    | ~ c_Relation_Oantisym(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__converse_1) ).

cnf(cls_diff__eq_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__eq_0) ).

cnf(cls_top1I_0,axiom,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top1I_0) ).

cnf(cls_refl__rtrancl_0,axiom,
    c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Transitive__Closure_Ortrancl(X2,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__rtrancl_0) ).

cnf(cls_Int__UNIV__left_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).

cnf(cls_Un__empty__left_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

cnf(cls_Diff__empty_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

cnf(cls_Int__UNIV__right_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).

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

cnf(cls_empty__subsetI_0,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

cnf(cls_subset__UNIV_0,axiom,
    c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).

cnf(cls_fun__Compl__def_0,axiom,
    ( hAPP(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(t_a,X1)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(X2,v_x),X1)
    | ~ class_HOL_Ouminus(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__Compl__def_0) ).

cnf(cls_COMBK__def_0,axiom,
    hAPP(c_COMBK(X1,X2,X3),X4) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

cnf(cls_Compl__eq__Compl__iff_0,axiom,
    ( X1 = X3
    | c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)) != c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).

cnf(cls_linorder__linear_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

cnf(cls_sup__commute_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).

cnf(cls_inf__sup__aci_I5_J_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

cnf(cls_Compl__UNIV__eq_0,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__UNIV__eq_0) ).

cnf(cls_Compl__empty__eq_0,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).

cnf(cls_fun__Compl__def__raw_0,axiom,
    ( hAPP(c_HOL_Ouminus__class_Ouminus(v_A,tc_fun(t_a,t_b)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(v_A,v_x),t_b)
    | ~ class_HOL_Ouminus(t_b) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__Compl__def__raw_0) ).

cnf(cls_double__complement_0,axiom,
    c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__complement_0) ).

cnf(cls_Domain__rtrancl_0,axiom,
    c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__rtrancl_0) ).

cnf(cls_inf__eq__top__eq1_0,axiom,
    ( X2 = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).

cnf(cls_sup__eq__bot__eq1_0,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

cnf(cls_inf__eq__top__eq2_0,axiom,
    ( X3 = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).

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

cnf(cls_Diff__cancel_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

cnf(cls_sym__conv__converse__eq_1,axiom,
    ( c_Relation_Osym(X1,X2)
    | c_Relation_Oconverse(X1,X2,X2) != X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).

cnf(cls_compl__inf__bot_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).

cnf(cls_compl__sup__top_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__sup__top_0) ).

cnf(cls_inf__compl__bot_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).

cnf(cls_sup__compl__top_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__compl__top_0) ).

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

cnf(cls_UNIV__not__empty_0,axiom,
    c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).

cnf(cls_wf__measures_0,axiom,
    hBOOL(c_Wellfounded_Owf(c_List_Omeasures(X1,X2),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__measures_0) ).

cnf(cls_wf__measure_0,axiom,
    hBOOL(c_Wellfounded_Owf(c_Wellfounded_Omeasure(X1,X2),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__measure_0) ).

cnf(cls_trans__rtrancl_0,axiom,
    hBOOL(c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X1,X2),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__rtrancl_0) ).

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

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

cnf(cls_sym__conv__converse__eq_0,axiom,
    ( c_Relation_Oconverse(X1,X2,X2) = X1
    | ~ c_Relation_Osym(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).

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

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

cnf(cls_Sup__UNIV_0,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).

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

cnf(cls_top__fun__eq_0,axiom,
    ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Orderings_Otop(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).

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

cnf(cls_finite__UNIV_0,axiom,
    ( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).

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

cnf(cls_sup__top__left_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X2,X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__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/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

cnf(cls_sup__top__right_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Otop__class_Otop(X1),X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__right_0) ).

cnf(cls_inf__top__left_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X2,X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__top__left_0) ).

cnf(cls_sup__bot__left_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

cnf(cls_inf__top__right_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Otop__class_Otop(X1),X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__top__right_0) ).

cnf(cls_sup__bot__right_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Obot__class_Obot(X1),X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

cnf(cls_bot__least_0,axiom,
    ( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
    | ~ class_Orderings_Obot(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).

cnf(cls_top__greatest_0,axiom,
    ( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
    | ~ class_Orderings_Otop(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__greatest_0) ).

cnf(cls_finite_OemptyI_0,axiom,
    c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).

cnf(cls_sym__rtrancl_0,axiom,
    ( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
    | ~ c_Relation_Osym(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).

cnf(cls_acyclic__impl__antisym__rtrancl_0,axiom,
    ( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
    | ~ c_Wellfounded_Oacyclic(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_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/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).

cnf(cls_sup__idem_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X2,X1) = X2
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).

cnf(cls_wf__acyclic_0,axiom,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ hBOOL(c_Wellfounded_Owf(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).

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

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

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

cnf(cls_rtrancl__idemp_0,axiom,
    c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).

cnf(cls_neg__equal__iff__equal_0,axiom,
    ( X2 = X3
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).

cnf(cls_compl__eq__compl__iff_0,axiom,
    ( X2 = X3
    | ~ class_Lattices_Oboolean__algebra(X1)
    | c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).

cnf(cls_minus__equation__iff_1,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).

cnf(cls_minus__minus_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).

cnf(cls_double__compl_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).

cnf(cls_equation__minus__iff_1,axiom,
    ( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).

cnf(cls_equation__minus__iff_0,axiom,
    ( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).

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

cnf(clsarity_prod__Finite__Set_Ofinite_Ofinite,axiom,
    ( class_Finite__Set_Ofinite_Ofinite(tc_prod(X1,X2))
    | ~ class_Finite__Set_Ofinite_Ofinite(X2)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_prod__Finite__Set_Ofinite_Ofinite) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_compl__top__eq_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(X1),X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).

cnf(cls_compl__bot__eq_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(X1),X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(i_0_603,axiom,
    ( c_lessequals(c_Transitive__Closure_Otrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X1,X2,X2,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    cls_trancl__Int__subset_0 ).

cnf(i_0_604,axiom,
    c_Transitive__Closure_Otrancl(X1,X2) = c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),
    cls_trancl__unfold__left_0 ).

cnf(i_0_605,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X2))
    | ~ hBOOL(c_Wellfounded_Owf(c_Relation_Oconverse(X1,X2,X2),X2)) ),
    cls_wf__converse__trancl_0 ).

cnf(i_0_606,axiom,
    c_Transitive__Closure_Otrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X1,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    cls_trancl__unfold_0 ).

cnf(i_0_607,axiom,
    ( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X1,X2,X2,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(c_Relation_OId(X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    cls_rtrancl__Int__subset_0 ).

cnf(i_0_608,axiom,
    c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Relation_OId(X1),
    cls_rtrancl__empty_0 ).

cnf(i_0_609,axiom,
    c_Relation_ORange(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ORange(X1,X2,X2),
    cls_trancl__range_0 ).

cnf(i_0_610,axiom,
    c_Relation_ORange(X1,X2,X3) = c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2),
    cls_Range__def_0 ).

cnf(i_0_611,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X1,X2),X2))
    | ~ hBOOL(c_Wellfounded_Owf(X1,X2)) ),
    cls_wf__trancl_0 ).

cnf(i_0_612,axiom,
    hBOOL(c_Relation_Otrans(c_Transitive__Closure_Otrancl(X1,X2),X2)),
    cls_trans__trancl_0 ).

cnf(i_0_613,axiom,
    ( c_lessequals(c_Transitive__Closure_Otrancl(X1,X2),c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(X1,c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    cls_trancl__subset__Sigma_0 ).

cnf(i_0_614,axiom,
    c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),
    cls_trancl__converse_0 ).

cnf(i_0_615,axiom,
    c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    cls_trancl__reflcl_0 ).

cnf(i_0_616,axiom,
    ( hBOOL(c_Order__Relation_Owell__order__on(X1,X2,X3))
    | ~ hBOOL(c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(X2,c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3))
    | ~ hBOOL(c_Order__Relation_Olinear__order__on(X1,X2,X3)) ),
    cls_well__order__on__def_2 ).

cnf(i_0_617,axiom,
    ( hBOOL(c_Relation_Ototal__on(X1,X2,X3))
    | ~ hBOOL(c_Relation_Ototal__on(X1,c_HOL_Ominus__class_Ominus(X2,c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3)) ),
    cls_total__on__diff__Id_0 ).

cnf(i_0_618,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Ortrancl(X1,X2),
    cls_reflcl__trancl_0 ).

cnf(i_0_619,axiom,
    c_Transitive__Closure_Ortrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    cls_rtrancl__unfold_0 ).

cnf(i_0_620,axiom,
    c_Transitive__Closure_Ortrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    cls_Nitpick_Ortrancl__def_0 ).

cnf(i_0_621,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(X1,X2,X3),c_Relation_ORange(X4,X2,X3),tc_fun(X3,tc_bool)),c_Relation_ORange(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),tc_fun(X3,tc_bool)),
    cls_Range__Diff__subset_0 ).

cnf(i_0_622,axiom,
    c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(X1,X3,X4),c_Relation_ORange(X2,X3,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Range__Int__subset_0 ).

cnf(i_0_623,axiom,
    c_Relation_ODomain(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ODomain(X1,X2,X2),
    cls_trancl__domain_0 ).

cnf(i_0_624,axiom,
    ( c_Relation_Osym(c_Transitive__Closure_Otrancl(X1,X2),X2)
    | ~ c_Relation_Osym(X1,X2) ),
    cls_sym__trancl_0 ).

cnf(i_0_625,axiom,
    c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    cls_trancl__rtrancl__absorb_0 ).

cnf(i_0_626,axiom,
    c_Transitive__Closure_Otrancl(X1,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),
    cls_trancl__unfold__right_0 ).

cnf(i_0_627,axiom,
    ( hBOOL(c_Relation_Ototal__on(X1,c_HOL_Ominus__class_Ominus(X2,c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3))
    | ~ hBOOL(c_Relation_Ototal__on(X1,X2,X3)) ),
    cls_total__on__diff__Id_1 ).

cnf(i_0_628,axiom,
    ( hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X1,X2),c_HOL_Ominus__class_Ominus(X3,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool))))
    | ~ hBOOL(c_Order__Relation_Olinear__order__on(X1,X3,X2)) ),
    cls_strict__linear__order__on__diff__Id_0 ).

cnf(i_0_629,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2))
    | ~ hBOOL(c_Order__Relation_Owell__order__on(X3,X1,X2)) ),
    cls_well__order__on__def_1 ).

cnf(i_0_630,axiom,
    ( hBOOL(c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2))
    | ~ c_Relation_Oantisym(X1,X2)
    | ~ hBOOL(c_Relation_Otrans(X1,X2)) ),
    cls_trans__diff__Id_0 ).

cnf(i_0_631,axiom,
    ( hBOOL(c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2))
    | ~ hBOOL(c_Relation_Otrans(X1,X2)) ),
    cls_trans__reflclI_0 ).

cnf(i_0_632,axiom,
    hBOOL(c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)),
    cls_irrefl__diff__Id_0 ).

cnf(i_0_633,axiom,
    c_Order__Relation_Owell__order__on(v_A,v_r,t_a) = c_and(c_Order__Relation_Olinear__order__on(v_A,v_r,t_a),c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(t_a),tc_fun(tc_prod(t_a,t_a),tc_bool)),t_a)),
    cls_well__order__on__def__raw_0 ).

cnf(i_0_634,axiom,
    c_Transitive__Closure_Otrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),
    cls_trancl__empty_0 ).

cnf(i_0_635,negated_conjecture,
    hBOOL(c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)),
    cls_conjecture_1 ).

cnf(i_0_636,axiom,
    c_Relation_Orel__comp(c_Relation_OId(X1),X2,X1,X1,X3) = X2,
    cls_Id__O__R_0 ).

cnf(i_0_637,axiom,
    c_Relation_Orel__comp(X1,c_Relation_OId(X2),X3,X2,X2) = X1,
    cls_R__O__Id_0 ).

cnf(i_0_638,axiom,
    ( c_Relation_Oantisym(X1,X2)
    | ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    cls_antisym__reflcl_0 ).

cnf(i_0_639,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2))
    | c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X2,X2),c_Relation_ORange(X3,X2,X2),tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ hBOOL(c_Wellfounded_Owf(X3,X2))
    | ~ hBOOL(c_Wellfounded_Owf(X1,X2)) ),
    cls_wf__Un_0 ).

cnf(i_0_640,axiom,
    c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X1,X3,X4),c_Relation_ORange(X2,X3,X4),tc_fun(X4,tc_bool)),
    cls_Range__Un__eq_0 ).

cnf(i_0_641,axiom,
    c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    cls_rtrancl__trancl__absorb_0 ).

cnf(i_0_642,axiom,
    ( c_Transitive__Closure_Otrancl(X1,X2) = X1
    | ~ hBOOL(c_Relation_Otrans(X1,X2)) ),
    cls_trancl__id_0 ).

cnf(i_0_643,axiom,
    c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
    cls_refl__reflcl_0 ).

cnf(i_0_644,axiom,
    ( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
    | ~ c_Relation_Oantisym(X1,X2) ),
    cls_antisym__reflcl_1 ).

cnf(i_0_645,axiom,
    c_Transitive__Closure_Ortrancl(c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    cls_rtrancl__r__diff__Id_0 ).

cnf(i_0_646,axiom,
    c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    cls_rtrancl__reflcl_0 ).

cnf(i_0_647,axiom,
    c_Relation_ORange(c_Relation_OId(X1),X1,X1) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
    cls_Range__Id_0 ).

cnf(i_0_648,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_649,axiom,
    c_Collect(X1,X2) = X1,
    cls_Collect__def_0 ).

cnf(i_0_650,axiom,
    hBOOL(c_Relation_Otrans(c_Relation_OId(X1),X1)),
    cls_trans__Id_0 ).

cnf(i_0_651,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_652,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_653,axiom,
    c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
    cls_Image__Id_0 ).

cnf(i_0_654,axiom,
    c_Relation_Oconverse(c_Relation_OId(X1),X1,X1) = c_Relation_OId(X1),
    cls_converse__Id_0 ).

cnf(i_0_655,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Ortrancl(X1,X2),
    cls_rtrancl__reflcl__absorb_0 ).

cnf(i_0_656,axiom,
    c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_Range__empty_0 ).

cnf(i_0_657,axiom,
    c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Relation_OId(X1),X1),
    cls_refl__Id_0 ).

cnf(i_0_658,axiom,
    c_Relation_ORange(c_Relation_Oconverse(X1,X2,X3),X3,X2) = c_Relation_ODomain(X1,X2,X3),
    cls_Range__converse_0 ).

cnf(i_0_659,axiom,
    c_Relation_ODomain(c_Relation_OId(X1),X1,X1) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
    cls_Domain__Id_0 ).

cnf(i_0_660,axiom,
    c_Relation_Osingle__valued(c_Relation_OId(X1),X1,X1),
    cls_single__valued__Id_0 ).

cnf(i_0_661,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
    | c_Relation_ORange(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_Range__empty__iff_0 ).

cnf(i_0_662,axiom,
    c_Relation_Osym(c_Relation_OId(X1),X1),
    cls_sym__Id_0 ).

cnf(i_0_663,axiom,
    c_Relation_Oantisym(c_Relation_OId(X1),X1),
    cls_antisym__Id_0 ).

cnf(i_0_664,axiom,
    c_Relation_ORange(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    cls_Range__rtrancl_0 ).

cnf(i_0_665,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,c_Collect(X1,X3),X3)) ),
    cls_CollectD_0 ).

cnf(i_0_666,axiom,
    ( hBOOL(c_in(X1,c_Collect(X2,X3),X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    cls_CollectI_0 ).

cnf(i_0_667,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_668,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_669,axiom,
    c_Arrow__Order__Mirabelle_OLin = c_Collect(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
    cls_Lin__def_0 ).

cnf(i_0_670,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_671,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_672,axiom,
    ( hAPP(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))) = X3
    | ~ c_Complete__Lattice_Ocomplete__lattice(X1,X4,X5,X6,X7,X8,X3,X9,X2) ),
    cls_complete__lattice_OInf__UNIV_0,
    [final] ).

cnf(i_0_673,axiom,
    ( hAPP(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))) = X3
    | ~ c_Complete__Lattice_Ocomplete__lattice(X4,X1,X5,X6,X7,X8,X9,X3,X2) ),
    cls_complete__lattice_OSup__UNIV_0,
    [final] ).

cnf(i_0_674,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_675,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_676,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3))
    | ~ hBOOL(c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X1,X3,X3,X3),c_Relation_Orel__comp(X2,X1,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)),X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)) ),
    cls_wf__union__merge_1,
    [final] ).

cnf(i_0_677,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X1,X2,X2,X2),c_Relation_Orel__comp(X3,X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2))
    | ~ hBOOL(c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)) ),
    cls_wf__union__merge_0,
    [final] ).

cnf(i_0_678,plain,
    ( c_lessequals(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X1,X2,X2,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_603,c_0_604]),c_0_604]),
    [final] ).

cnf(i_0_679,plain,
    ( hBOOL(c_Wellfounded_Owf(c_Relation_Oconverse(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X2,X2),X2))
    | ~ hBOOL(c_Wellfounded_Owf(c_Relation_Oconverse(X1,X2,X2),X2)) ),
    inference(rw,[status(thm)],[i_0_605,c_0_604]),
    [final] ).

cnf(i_0_680,plain,
    c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_Orel__comp(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_606,c_0_604]),c_0_604]),
    [final] ).

cnf(i_0_681,axiom,
    ( hBOOL(c_Wellfounded_Owf(X1,X2))
    | ~ hBOOL(c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2)) ),
    cls_wf__comp__self_1,
    [final] ).

cnf(i_0_682,axiom,
    c_Relation_Orel__comp(c_Relation_Orel__comp(X1,X2,X3,X4,X5),X6,X3,X5,X7) = c_Relation_Orel__comp(X1,c_Relation_Orel__comp(X2,X6,X4,X5,X7),X3,X4,X7),
    cls_O__assoc_0,
    [final] ).

cnf(i_0_683,axiom,
    c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X5,X3,X4,X6) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X5,X3,X4,X6),c_Relation_Orel__comp(X2,X5,X3,X4,X6),tc_fun(tc_prod(X3,X6),tc_bool)),
    cls_rel__comp__distrib2_0,
    [final] ).

cnf(i_0_684,axiom,
    c_Relation_Orel__comp(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(tc_prod(X4,X5),tc_bool)),X6,X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X2,X6,X4,X5),c_Relation_Orel__comp(X1,X3,X6,X4,X5),tc_fun(tc_prod(X6,X5),tc_bool)),
    cls_rel__comp__distrib_0,
    [final] ).

cnf(i_0_685,axiom,
    ( c_lessequals(c_Relation_Orel__comp(X1,X2,X3,X4,X5),c_Product__Type_OSigma(X6,c_COMBK(X7,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool))
    | ~ c_lessequals(X2,c_Product__Type_OSigma(X8,c_COMBK(X7,tc_fun(X5,tc_bool),X4),X4,X5),tc_fun(tc_prod(X4,X5),tc_bool))
    | ~ c_lessequals(X1,c_Product__Type_OSigma(X6,c_COMBK(X8,tc_fun(X4,tc_bool),X3),X3,X4),tc_fun(tc_prod(X3,X4),tc_bool)) ),
    cls_rel__comp__subset__Sigma_0,
    [final] ).

cnf(i_0_686,plain,
    ( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X1,X2,X2,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    inference(rw,[status(thm)],[i_0_607,c_0_608]),
    [final] ).

cnf(i_0_687,axiom,
    ( c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(tc_prod(X3,X3),tc_bool)),X2,X3,X3,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
    | c_Relation_Orel__comp(X1,X2,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
    | c_Relation_Orel__comp(X4,X2,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)) ),
    cls_union__comp__emptyL_0,
    [final] ).

cnf(i_0_688,axiom,
    ( c_Relation_Orel__comp(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3,X3,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
    | c_Relation_Orel__comp(X1,X2,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
    | c_Relation_Orel__comp(X1,X4,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)) ),
    cls_union__comp__emptyR_0,
    [final] ).

cnf(i_0_689,axiom,
    ( c_lessequals(c_Relation_Orel__comp(X1,X2,X3,X4,X5),c_Relation_Orel__comp(X6,X7,X3,X4,X5),tc_fun(tc_prod(X3,X5),tc_bool))
    | ~ c_lessequals(X2,X7,tc_fun(tc_prod(X4,X5),tc_bool))
    | ~ c_lessequals(X1,X6,tc_fun(tc_prod(X3,X4),tc_bool)) ),
    cls_rel__comp__mono_0,
    [final] ).

cnf(i_0_690,plain,
    c_Relation_ODomain(c_Relation_Oconverse(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X2,X2),X2,X2) = c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_609,c_0_604]),c_0_610]),c_0_610]),
    [final] ).

cnf(i_0_691,plain,
    ( hBOOL(c_Wellfounded_Owf(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X2))
    | ~ hBOOL(c_Wellfounded_Owf(X1,X2)) ),
    inference(rw,[status(thm)],[i_0_611,c_0_604]),
    [final] ).

cnf(i_0_692,plain,
    hBOOL(c_Relation_Otrans(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X2)),
    inference(rw,[status(thm)],[i_0_612,c_0_604]),
    [final] ).

cnf(i_0_693,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2))
    | ~ hBOOL(c_Wellfounded_Owf(X1,X2)) ),
    cls_wf__comp__self_0,
    [final] ).

cnf(i_0_694,plain,
    ( c_lessequals(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(X1,c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    inference(rw,[status(thm)],[i_0_613,c_0_604]),
    [final] ).

cnf(i_0_695,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3))
    | ~ c_lessequals(c_Relation_Orel__comp(X1,X2,X3,X3,X3),X1,tc_fun(tc_prod(X3,X3),tc_bool))
    | ~ hBOOL(c_Wellfounded_Owf(X2,X3))
    | ~ hBOOL(c_Wellfounded_Owf(X1,X3)) ),
    cls_wf__union__compatible_0,
    [final] ).

cnf(i_0_696,plain,
    c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2,X2,X2) = c_Relation_Oconverse(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X2,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_614,c_0_604]),c_0_604]),
    [final] ).

cnf(i_0_697,plain,
    c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2,X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_615,c_0_604]),c_0_608]),c_0_608]),
    [final] ).

cnf(i_0_698,axiom,
    c_Relation_Oconverse(c_Relation_Orel__comp(X1,X2,X3,X4,X5),X3,X5) = c_Relation_Orel__comp(c_Relation_Oconverse(X2,X4,X5),c_Relation_Oconverse(X1,X3,X4),X5,X4,X3),
    cls_converse__rel__comp_0,
    [final] ).

cnf(i_0_699,axiom,
    ( c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
    | c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X4,X5),tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X4,X5) ),
    cls_inj__on__Un_3,
    [final] ).

cnf(i_0_700,axiom,
    c_Relation_Orel__comp(X1,c_Nat_Ocompow(X2,X1,tc_prod(X3,X3),tc_bool),X3,X3,X3) = c_Relation_Orel__comp(c_Nat_Ocompow(X2,X1,tc_prod(X3,X3),tc_bool),X1,X3,X3,X3),
    cls_rel__pow__commute_0,
    [final] ).

cnf(i_0_701,axiom,
    ( c_lessequals(c_Relation_OImage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(c_Relation_OImage(c_Relation_Oconverse(X1,X3,X4),c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X4,tc_bool)),X4,X3),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    cls_Image__subset__eq_1,
    [final] ).

cnf(i_0_702,plain,
    ( hBOOL(c_Order__Relation_Owell__order__on(X1,X2,X3))
    | ~ hBOOL(c_Order__Relation_Olinear__order__on(X1,X2,X3))
    | ~ hBOOL(c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(X2,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3)) ),
    inference(rw,[status(thm)],[i_0_616,c_0_608]),
    [final] ).

cnf(i_0_703,plain,
    ( hBOOL(c_Relation_Ototal__on(X1,X2,X3))
    | ~ hBOOL(c_Relation_Ototal__on(X1,c_HOL_Ominus__class_Ominus(X2,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3)) ),
    inference(rw,[status(thm)],[i_0_617,c_0_608]),
    [final] ).

cnf(i_0_704,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
    cls_image__diff__subset_0,
    [final] ).

cnf(i_0_705,axiom,
    c_lessequals(c_Relation_OImage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
    cls_Image__Int__subset_0,
    [final] ).

cnf(i_0_706,axiom,
    c_lessequals(c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
    cls_image__Int__subset_0,
    [final] ).

cnf(i_0_707,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool))
    | ~ hBOOL(c_in(X6,X4,X5)) ),
    cls_Times__subset__cancel2_0,
    [final] ).

cnf(i_0_708,plain,
    c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_618,c_0_604]),c_0_608]),
    [final] ).

cnf(i_0_709,plain,
    c_Transitive__Closure_Ortrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    inference(rw,[status(thm)],[i_0_619,c_0_608]),
    [final] ).

cnf(i_0_710,plain,
    c_Transitive__Closure_Ortrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_620,c_0_604]),c_0_608]),
    [final] ).

cnf(i_0_711,plain,
    c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2),c_Relation_ODomain(c_Relation_Oconverse(X4,X2,X3),X3,X2),tc_fun(X3,tc_bool)),c_Relation_ODomain(c_Relation_Oconverse(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2),tc_fun(X3,tc_bool)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_621,c_0_610]),c_0_610]),c_0_610]),
    [final] ).

cnf(i_0_712,plain,
    c_lessequals(c_Relation_ODomain(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),X4,X3),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(c_Relation_Oconverse(X1,X3,X4),X4,X3),c_Relation_ODomain(c_Relation_Oconverse(X2,X3,X4),X4,X3),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_622,c_0_610]),c_0_610]),c_0_610]),
    [final] ).

cnf(i_0_713,axiom,
    ( c_lessequals(X1,c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_Relation_Orefl__on(X3,X1,X2) ),
    cls_refl__on__comp__subset_0,
    [final] ).

cnf(i_0_714,axiom,
    ( c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ hBOOL(c_Relation_Otrans(X1,X2))
    | ~ c_Relation_Osym(X1,X2) ),
    cls_sym__trans__comp__subset_0,
    [final] ).

cnf(i_0_715,axiom,
    ( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(c_Relation_OImage(c_Relation_Oconverse(X2,X3,X4),c_HOL_Ouminus__class_Ouminus(X5,tc_fun(X4,tc_bool)),X4,X3),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Relation_OImage(X2,X1,X3,X4),X5,tc_fun(X4,tc_bool)) ),
    cls_Image__subset__eq_0,
    [final] ).

cnf(i_0_716,axiom,
    ( c_Relation_Osingle__valued(c_Relation_Orel__comp(X1,X2,X3,X4,X5),X3,X5)
    | ~ c_Relation_Osingle__valued(X2,X4,X5)
    | ~ c_Relation_Osingle__valued(X1,X3,X4) ),
    cls_single__valued__rel__comp_0,
    [final] ).

cnf(i_0_717,axiom,
    ( c_lessequals(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ hBOOL(c_Relation_Otrans(X1,X2)) ),
    cls_trans__O__subset_0,
    [final] ).

cnf(i_0_718,plain,
    c_Relation_ODomain(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X2,X2) = c_Relation_ODomain(X1,X2,X2),
    inference(rw,[status(thm)],[i_0_623,c_0_604]),
    [final] ).

cnf(i_0_719,plain,
    ( c_Relation_Osym(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X2)
    | ~ c_Relation_Osym(X1,X2) ),
    inference(rw,[status(thm)],[i_0_624,c_0_604]),
    [final] ).

cnf(i_0_720,plain,
    c_Transitive__Closure_Ortrancl(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(rw,[status(thm)],[i_0_625,c_0_604]),
    [final] ).

cnf(i_0_721,plain,
    c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),
    inference(rw,[status(thm)],[i_0_626,c_0_604]),
    [final] ).

cnf(i_0_722,axiom,
    c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),
    cls_r__comp__rtrancl__eq_0,
    [final] ).

cnf(i_0_723,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
    | ~ c_Fun_Oinj__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X5) ),
    cls_inj__image__mem__iff_0,
    [final] ).

cnf(i_0_724,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),X4,X5),tc_fun(X5,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) ),
    cls_inj__on__Un_2,
    [final] ).

cnf(i_0_725,axiom,
    c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5) = c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
    cls_Times__Diff__distrib1_0,
    [final] ).

cnf(i_0_726,axiom,
    c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
    cls_Times__Int__distrib1_0,
    [final] ).

cnf(i_0_727,axiom,
    c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
    cls_Times__Un__distrib1_0,
    [final] ).

cnf(i_0_728,axiom,
    ( c_lessequals(c_Set_Oimage(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3,X4),c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(X1,X2,X3,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    cls_inj__image__Compl__subset_0,
    [final] ).

cnf(i_0_729,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X5) ),
    cls_inj__image__subset__iff_0,
    [final] ).

cnf(i_0_730,axiom,
    ( hBOOL(c_in(X1,hAPP(X2,X3),X4))
    | ~ hBOOL(c_in(X3,X5,X6))
    | ~ hBOOL(c_in(X1,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X2,X6,tc_fun(X4,tc_bool)),X4)) ),
    cls_INT__iff_0,
    [final] ).

cnf(i_0_731,axiom,
    ( hBOOL(c_in(X1,hAPP(X2,X3),X4))
    | ~ hBOOL(c_in(X3,X5,X6))
    | ~ hBOOL(c_in(X1,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X2,X6,tc_fun(X4,tc_bool)),X4)) ),
    cls_INT__D_0,
    [final] ).

cnf(i_0_732,axiom,
    ( hBOOL(c_in(X4,hAPP(X5,X1),X6))
    | ~ hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X4,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X5,X3,tc_fun(X6,tc_bool)),X6)) ),
    cls_INT__E_0,
    [final] ).

cnf(i_0_733,plain,
    ( hBOOL(c_Relation_Ototal__on(X1,c_HOL_Ominus__class_Ominus(X2,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3))
    | ~ hBOOL(c_Relation_Ototal__on(X1,X2,X3)) ),
    inference(rw,[status(thm)],[i_0_627,c_0_608]),
    [final] ).

cnf(i_0_734,plain,
    ( hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X1,X2),c_HOL_Ominus__class_Ominus(X3,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool))))
    | ~ hBOOL(c_Order__Relation_Olinear__order__on(X1,X3,X2)) ),
    inference(rw,[status(thm)],[i_0_628,c_0_608]),
    [final] ).

cnf(i_0_735,axiom,
    ( c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(X3,X6,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X6,tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X6,X4,X5) ),
    cls_inj__on__image__set__diff_0,
    [final] ).

cnf(i_0_736,axiom,
    ( c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(X3,X6,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X6,tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X6,X4,X5) ),
    cls_inj__on__image__Int_0,
    [final] ).

cnf(i_0_737,plain,
    ( hBOOL(c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2))
    | ~ hBOOL(c_Order__Relation_Owell__order__on(X3,X1,X2)) ),
    inference(rw,[status(thm)],[i_0_629,c_0_608]),
    [final] ).

cnf(i_0_738,axiom,
    ( hBOOL(c_Wellfounded_Owf(X1,X2))
    | c_Relation_Orel__comp(X1,X1,X2,X2,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) ),
    cls_wf__no__loop_0,
    [final] ).

cnf(i_0_739,axiom,
    ( c_lessequals(c_Relation_OImage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,c_Product__Type_OSigma(X6,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4),tc_fun(tc_prod(X3,X4),tc_bool)) ),
    cls_Image__subset_0,
    [final] ).

cnf(i_0_740,axiom,
    ( c_lessequals(c_Product__Type_OSigma(X1,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3),c_Product__Type_OSigma(X5,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3),tc_fun(tc_prod(X4,X3),tc_bool))
    | ~ c_lessequals(X1,X5,tc_fun(X4,tc_bool))
    | ~ hBOOL(c_in(X6,X2,X3)) ),
    cls_Times__subset__cancel2_1,
    [final] ).

cnf(i_0_741,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1,X5,tc_fun(X6,tc_bool)),X3)) ),
    cls_INF1__iff_0,
    [final] ).

cnf(i_0_742,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1,X5,tc_fun(X6,tc_bool)),X3)) ),
    cls_INF1__D_0,
    [final] ).

cnf(i_0_743,axiom,
    ( hBOOL(hAPP(hAPP(X4,X1),X5))
    | ~ hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X4,X3,tc_fun(X6,tc_bool)),X5)) ),
    cls_INF1__E_0,
    [final] ).

cnf(i_0_744,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_745,plain,
    ( hBOOL(c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2))
    | ~ c_Relation_Oantisym(X1,X2)
    | ~ hBOOL(c_Relation_Otrans(X1,X2)) ),
    inference(rw,[status(thm)],[i_0_630,c_0_608]),
    [final] ).

cnf(i_0_746,plain,
    ( hBOOL(c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2))
    | ~ hBOOL(c_Relation_Otrans(X1,X2)) ),
    inference(rw,[status(thm)],[i_0_631,c_0_608]),
    [final] ).

cnf(i_0_747,axiom,
    ( c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),X5,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    cls_vimage__subsetI_0,
    [final] ).

cnf(i_0_748,axiom,
    ( c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    cls_image__set__diff_0,
    [final] ).

cnf(i_0_749,axiom,
    ( c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    cls_image__Int_0,
    [final] ).

cnf(i_0_750,plain,
    hBOOL(c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)),
    inference(rw,[status(thm)],[i_0_632,c_0_608]),
    [final] ).

cnf(i_0_751,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_752,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_753,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
    | ~ hBOOL(c_in(X2,X3,X4))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    cls_inj__image__mem__iff_1,
    [final] ).

cnf(i_0_754,plain,
    c_Order__Relation_Owell__order__on(v_A,v_r,t_a) = c_and(c_Order__Relation_Olinear__order__on(v_A,v_r,t_a),c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(v_r,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(t_a,t_a),tc_bool)),t_a),tc_fun(tc_prod(t_a,t_a),tc_bool)),t_a)),
    inference(rw,[status(thm)],[i_0_633,c_0_608]),
    [final] ).

cnf(i_0_755,axiom,
    ( hBOOL(c_Wellfounded_Owf(X1,X2))
    | ~ hBOOL(c_Wellfounded_Owf(c_Nat_Ocompow(X3,X1,tc_prod(X2,X2),tc_bool),X2)) ),
    cls_wf__exp_0,
    [final] ).

cnf(i_0_756,plain,
    c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1,X1,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),
    inference(rw,[status(thm)],[i_0_634,c_0_604]),
    [final] ).

cnf(i_0_757,axiom,
    ( c_Relation_OImage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X1,X4,X5),X5,X4) ),
    cls_Image__Int__eq_0,
    [final] ).

cnf(i_0_758,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_759,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    cls_inj__image__subset__iff_1,
    [final] ).

cnf(i_0_760,negated_conjecture,
    hBOOL(c_Wellfounded_Owf(c_HOL_Ominus__class_Ominus(v_r,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)),
    inference(rw,[status(thm)],[i_0_635,c_0_608]),
    [final] ).

cnf(i_0_761,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,X3,tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X4,X3,tc_fun(X5,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
    cls_INT__Un_0,
    [final] ).

cnf(i_0_762,axiom,
    c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X5,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X1,X5,X3,X4),c_Relation_OImage(X2,X5,X3,X4),tc_fun(X4,tc_bool)),
    cls_Un__Image_0,
    [final] ).

cnf(i_0_763,axiom,
    hAPP(X1,hAPP(c_Nat_Ocompow(X2,X1,X3,X3),X4)) = hAPP(c_Nat_Ocompow(X2,X1,X3,X3),hAPP(X1,X4)),
    cls_funpow__swap1_0,
    [final] ).

cnf(i_0_764,axiom,
    ( c_Set_Oimage(X1,X2,X3,X3) = X2
    | ~ c_Fun_Oinj__on(X1,X2,X3,X3)
    | ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X3),X2,tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_endo__inj__surj_0,
    [final] ).

cnf(i_0_765,axiom,
    c_lessequals(c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4),X2,tc_fun(X4,tc_bool)),
    cls_image__vimage__subset_0,
    [final] ).

cnf(i_0_766,plain,
    c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X2,X1,X1,X3) = X2,
    inference(rw,[status(thm)],[i_0_636,c_0_608]),
    [final] ).

cnf(i_0_767,plain,
    c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X3,X2,X2) = X1,
    inference(rw,[status(thm)],[i_0_637,c_0_608]),
    [final] ).

cnf(i_0_768,axiom,
    c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5) = c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(X1,X4,X3,X5),c_Product__Type_OSigma(X2,X4,X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
    cls_Sigma__Diff__distrib1_0,
    [final] ).

cnf(i_0_769,axiom,
    c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X1,X4,X3,X5),c_Product__Type_OSigma(X2,X4,X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
    cls_Sigma__Int__distrib1_0,
    [final] ).

cnf(i_0_770,axiom,
    c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X1,X4,X3,X5),c_Product__Type_OSigma(X2,X4,X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
    cls_Sigma__Un__distrib1_0,
    [final] ).

cnf(i_0_771,plain,
    ( c_Relation_Oantisym(X1,X2)
    | ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    inference(rw,[status(thm)],[i_0_638,c_0_608]),
    [final] ).

cnf(i_0_772,plain,
    ( hBOOL(c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2))
    | c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(X3,X2,X2),X2,X2),tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ hBOOL(c_Wellfounded_Owf(X3,X2))
    | ~ hBOOL(c_Wellfounded_Owf(X1,X2)) ),
    inference(rw,[status(thm)],[i_0_639,c_0_610]),
    [final] ).

cnf(i_0_773,axiom,
    c_Relation_OImage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),
    cls_Image__Un_0,
    [final] ).

cnf(i_0_774,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_775,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_776,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_777,axiom,
    c_Set_Oimage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),
    cls_image__Un_0,
    [final] ).

cnf(i_0_778,axiom,
    c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X3,X1,X2,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X4),tc_bool)),
    cls_rel__comp__empty1_0,
    [final] ).

cnf(i_0_779,axiom,
    c_Relation_Orel__comp(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)),X4,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X3),tc_bool)),
    cls_rel__comp__empty2_0,
    [final] ).

cnf(i_0_780,axiom,
    ( X1 = X5
    | c_Product__Type_OSigma(X1,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3) != c_Product__Type_OSigma(X5,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3)
    | ~ hBOOL(c_in(X6,X2,X3)) ),
    cls_Times__eq__cancel2_0,
    [final] ).

cnf(i_0_781,axiom,
    c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
    cls_image__vimage__eq_0,
    [final] ).

cnf(i_0_782,axiom,
    ( X2 = X5
    | c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X5,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),X3,X4) ),
    cls_inj__on__Un__image__eq__iff_0,
    [final] ).

cnf(i_0_783,plain,
    c_Relation_ODomain(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(c_Relation_Oconverse(X1,X3,X4),X4,X3),c_Relation_ODomain(c_Relation_Oconverse(X2,X3,X4),X4,X3),tc_fun(X4,tc_bool)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_640,c_0_610]),c_0_610]),c_0_610]),
    [final] ).

cnf(i_0_784,axiom,
    ( c_lessequals(c_Relation_OImage(X1,X2,X3,X4),c_Relation_OImage(X5,X6,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X6,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X5,tc_fun(tc_prod(X3,X4),tc_bool)) ),
    cls_Image__mono_0,
    [final] ).

cnf(i_0_785,axiom,
    hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4)),
    cls_rangeI_0,
    [final] ).

cnf(i_0_786,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_787,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_788,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_789,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    cls_imageI_0,
    [final] ).

cnf(i_0_790,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    cls_image__eqI_0,
    [final] ).

cnf(i_0_791,axiom,
    ( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
    | ~ hBOOL(c_in(X1,X2,X3)) ),
    cls_image__iff_2,
    [final] ).

cnf(i_0_792,axiom,
    ( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
    | ~ hBOOL(c_in(X1,X2,X3)) ),
    cls_rev__image__eqI_0,
    [final] ).

cnf(i_0_793,plain,
    c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2,X2,X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(rw,[status(thm)],[i_0_641,c_0_604]),
    [final] ).

cnf(i_0_794,plain,
    ( c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = X1
    | ~ hBOOL(c_Relation_Otrans(X1,X2)) ),
    inference(rw,[status(thm)],[i_0_642,c_0_604]),
    [final] ).

cnf(i_0_795,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ODomain(X1,X2,X3),c_Relation_ODomain(X4,X2,X3),tc_fun(X2,tc_bool)),c_Relation_ODomain(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),tc_fun(X2,tc_bool)),
    cls_Domain__Diff__subset_0,
    [final] ).

cnf(i_0_796,axiom,
    c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Domain__Int__subset_0,
    [final] ).

cnf(i_0_797,axiom,
    c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    cls_rtrancl__idemp__self__comp_0,
    [final] ).

cnf(i_0_798,axiom,
    ( X2 = X5
    | c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X5,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    cls_inj__image__eq__iff_0,
    [final] ).

cnf(i_0_799,axiom,
    ( c_lessequals(X1,hAPP(X2,X3),tc_fun(X4,tc_bool))
    | ~ hBOOL(c_in(X3,X5,X6))
    | ~ c_lessequals(X1,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X2,X6,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
    cls_INT__subset__iff_0,
    [final] ).

cnf(i_0_800,axiom,
    ( hBOOL(c_in(hAPP(X1,X2),X3,X4))
    | ~ hBOOL(c_in(X2,X5,X6))
    | ~ c_lessequals(c_Set_Oimage(X1,X5,X6,X4),X3,tc_fun(X4,tc_bool)) ),
    cls_image__subset__iff_0,
    [final] ).

cnf(i_0_801,axiom,
    ( c_Set_Ovimage(X1,c_Set_Oimage(X1,X2,X3,X4),X3,X4) = X2
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    cls_inj__vimage__image__eq_0,
    [final] ).

cnf(i_0_802,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Fun_Oinj__on(X3,X1,X2,X4)
    | ~ c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4) ),
    cls_finite__imageD_0,
    [final] ).

cnf(i_0_803,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_804,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
    cls_image__mono_0,
    [final] ).

cnf(i_0_805,axiom,
    ( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_subset__image__iff_2,
    [final] ).

cnf(i_0_806,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X3)
    | ~ c_lessequals(X2,c_Set_Oimage(X1,X2,X3,X3),tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_finite__surj__inj_0,
    [final] ).

cnf(i_0_807,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_808,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(hAPP(X1,X2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1,X4,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1,X4,tc_fun(X5,tc_bool))
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    cls_INT__absorb_0,
    [final] ).

cnf(i_0_809,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Relation_Oinv__image(X1,X2,X3,X4),X4))
    | ~ hBOOL(c_Wellfounded_Owf(X1,X3)) ),
    cls_wf__inv__image_0,
    [final] ).

cnf(i_0_810,axiom,
    ( hBOOL(c_Relation_Otrans(c_Relation_Oinv__image(X1,X2,X3,X4),X4))
    | ~ hBOOL(c_Relation_Otrans(X1,X3)) ),
    cls_trans__inv__image_0,
    [final] ).

cnf(i_0_811,plain,
    c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
    inference(rw,[status(thm)],[i_0_643,c_0_608]),
    [final] ).

cnf(i_0_812,axiom,
    c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    cls_rtrancl__Un__subset_0,
    [final] ).

cnf(i_0_813,axiom,
    ( c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
    | ~ c_Relation_Orefl__on(X2,X1,X3) ),
    cls_refl__on__def_0,
    [final] ).

cnf(i_0_814,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Ovimage(X1,X2,X3,X4),X3)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4)
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    cls_finite__vimageI_0,
    [final] ).

cnf(i_0_815,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,c_Relation_OImage(X3,X1,X2,X2),tc_fun(X2,tc_bool))
    | ~ hBOOL(c_Wellfounded_Owf(X3,X2)) ),
    cls_wfE__pf_0,
    [final] ).

cnf(i_0_816,plain,
    ( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
    | ~ c_Relation_Oantisym(X1,X2) ),
    inference(rw,[status(thm)],[i_0_644,c_0_608]),
    [final] ).

cnf(i_0_817,plain,
    c_Transitive__Closure_Ortrancl(c_HOL_Ominus__class_Ominus(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(rw,[status(thm)],[i_0_645,c_0_608]),
    [final] ).

cnf(i_0_818,plain,
    c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(rw,[status(thm)],[i_0_646,c_0_608]),
    [final] ).

cnf(i_0_819,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X4,X5) ),
    cls_finite__surj_0,
    [final] ).

cnf(i_0_820,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_821,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_822,axiom,
    c_Relation_Oconverse(c_Relation_Oinv__image(X1,X2,X3,X4),X4,X4) = c_Relation_Oinv__image(c_Relation_Oconverse(X1,X3,X3),X2,X3,X4),
    cls_converse__inv__image_0,
    [final] ).

cnf(i_0_823,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_824,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),X3,X4) ),
    cls_inj__on__Un_0,
    [final] ).

cnf(i_0_825,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Lattices_Oupper__semilattice__class_Osup(X5,X2,tc_fun(X3,tc_bool)),X3,X4) ),
    cls_inj__on__Un_1,
    [final] ).

cnf(i_0_826,plain,
    c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1,X1),X1,X1) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_647,c_0_610]),c_0_608]),
    [final] ).

cnf(i_0_827,axiom,
    c_HOL_Ominus__class_Ominus(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
    cls_INT__extend__simps_I3_J_0,
    [final] ).

cnf(i_0_828,axiom,
    c_Set_Ovimage(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X4,X3) = c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(X1,X2,X4,X3),tc_fun(X4,tc_bool)),
    cls_vimage__Compl_0,
    [final] ).

cnf(i_0_829,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_830,axiom,
    ( c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X2,X3,tc_fun(X4,tc_bool)),hAPP(X2,X5),tc_fun(X4,tc_bool))
    | ~ hBOOL(c_in(X5,X1,X3)) ),
    cls_INT__lower_0,
    [final] ).

cnf(i_0_831,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_832,axiom,
    ( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X2,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_Finite__Set_Ofinite(hAPP(X2,X5),X4)
    | ~ hBOOL(c_in(X5,X1,X3)) ),
    cls_finite__INT_0,
    [final] ).

cnf(i_0_833,axiom,
    ( c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X4,X5) ),
    cls_inj__on__diff_0,
    [final] ).

cnf(i_0_834,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6)
    | ~ hBOOL(c_in(X3,X4,X5))
    | ~ hBOOL(c_in(X2,X4,X5)) ),
    cls_inj__onD_0,
    [final] ).

cnf(i_0_835,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ hBOOL(c_in(X3,X4,X5))
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    cls_inj__on__def_0,
    [final] ).

cnf(i_0_836,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ hBOOL(c_in(X3,X4,X5))
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    cls_inj__on__iff_0,
    [final] ).

cnf(i_0_837,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ hBOOL(c_in(X3,X4,X5))
    | ~ hBOOL(c_in(X2,X4,X5))
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    cls_inj__on__contraD_0,
    [final] ).

cnf(i_0_838,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_839,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_840,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_841,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_648,c_0_649]),
    [final] ).

cnf(i_0_842,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_843,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_844,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X5,X3,X4) ),
    cls_subset__inj__on_0,
    [final] ).

cnf(i_0_845,axiom,
    ( c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X3,X4,X1),hAPP(X3,X5),X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(c_in(X5,X2,X4)) ),
    cls_INF__leI_0,
    [final] ).

cnf(i_0_846,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(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_INT__extend__simps_I1_J_0,
    [final] ).

cnf(i_0_847,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(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_I2_J_0,
    [final] ).

cnf(i_0_848,plain,
    hBOOL(c_Relation_Otrans(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1)),
    inference(rw,[status(thm)],[i_0_650,c_0_608]),
    [final] ).

cnf(i_0_849,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_850,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_851,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_651,c_0_649]),
    [final] ).

cnf(i_0_852,axiom,
    ( hAPP(X2,X5) = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool))
    | c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X2,X3,tc_fun(X4,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool))
    | ~ hBOOL(c_in(X5,X1,X3)) ),
    cls_INTER__UNIV__conv_I2_J_0,
    [final] ).

cnf(i_0_853,axiom,
    ( hAPP(X3,X5) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))
    | c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X3,X4,tc_fun(X1,tc_bool))
    | ~ hBOOL(c_in(X5,X2,X4)) ),
    cls_INTER__UNIV__conv_I1_J_0,
    [final] ).

cnf(i_0_854,axiom,
    ( c_Relation_Osingle__valued(c_Nat_Ocompow(X1,X2,tc_prod(X3,X3),tc_bool),X3,X3)
    | ~ c_Relation_Osingle__valued(X2,X3,X3) ),
    cls_single__valued__rel__pow_0,
    [final] ).

cnf(i_0_855,axiom,
    c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X1,X3,X4),c_Relation_Oconverse(X2,X3,X4),tc_fun(tc_prod(X4,X3),tc_bool)),
    cls_converse__Int_0,
    [final] ).

cnf(i_0_856,axiom,
    c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(X1,X3,X4),c_Relation_Oconverse(X2,X3,X4),tc_fun(tc_prod(X4,X3),tc_bool)),
    cls_converse__Un_0,
    [final] ).

cnf(i_0_857,axiom,
    c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    cls_rtrancl__Un__rtrancl_0,
    [final] ).

cnf(i_0_858,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_652,c_0_649]),
    [final] ).

cnf(i_0_859,axiom,
    ( hBOOL(c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3))
    | ~ hBOOL(c_Relation_Otrans(X2,X3))
    | ~ hBOOL(c_Relation_Otrans(X1,X3)) ),
    cls_trans__Int_0,
    [final] ).

cnf(i_0_860,axiom,
    ( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
    | ~ c_Relation_Orefl__on(X2,X5,X3)
    | ~ c_Relation_Orefl__on(X1,X4,X3) ),
    cls_refl__on__Int_0,
    [final] ).

cnf(i_0_861,axiom,
    ( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
    | ~ c_Relation_Orefl__on(X2,X5,X3)
    | ~ c_Relation_Orefl__on(X1,X4,X3) ),
    cls_refl__on__Un_0,
    [final] ).

cnf(i_0_862,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_863,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_864,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_865,axiom,
    ( hBOOL(c_Relation_Ototal__on(X1,X2,X3))
    | ~ hBOOL(c_Relation_Ototal__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)) ),
    cls_total__on__converse_0,
    [final] ).

cnf(i_0_866,axiom,
    ( hBOOL(c_Order__Relation_Olinear__order__on(X1,X2,X3))
    | ~ hBOOL(c_Order__Relation_Olinear__order__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)) ),
    cls_linear__order__on__converse_0,
    [final] ).

cnf(i_0_867,axiom,
    ( hBOOL(c_Order__Relation_Opartial__order__on(X1,X2,X3))
    | ~ hBOOL(c_Order__Relation_Opartial__order__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)) ),
    cls_partial__order__on__converse_0,
    [final] ).

cnf(i_0_868,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_869,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_870,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_871,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_872,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_873,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_874,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_875,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_876,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_877,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_878,axiom,
    c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool)),
    cls_Domain__Un__eq_0,
    [final] ).

cnf(i_0_879,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_880,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_881,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_882,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_883,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3))
    | ~ hBOOL(c_Wellfounded_Owf(X1,X3)) ),
    cls_wf__Int1_0,
    [final] ).

cnf(i_0_884,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3))
    | ~ hBOOL(c_Wellfounded_Owf(X2,X3)) ),
    cls_wf__Int2_0,
    [final] ).

cnf(i_0_885,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_886,plain,
    c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X2,X1,X1) = X2,
    inference(rw,[status(thm)],[i_0_653,c_0_608]),
    [final] ).

cnf(i_0_887,axiom,
    c_Product__Type_OSigma(X1,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool),X3),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_bool)),
    cls_Sigma__empty2_0,
    [final] ).

cnf(i_0_888,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_889,axiom,
    ( ~ hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(c_in(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3)) ),
    cls_ComplD_0,
    [final] ).

cnf(i_0_890,plain,
    c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1,X1) = c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_654,c_0_608]),c_0_608]),
    [final] ).

cnf(i_0_891,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_892,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_893,axiom,
    ( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))
    | ~ hBOOL(c_in(X1,X4,X2)) ),
    cls_vimage__const_0,
    [final] ).

cnf(i_0_894,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_finite__imageI_0,
    [final] ).

cnf(i_0_895,axiom,
    ( c_Relation_Osym(c_Relation_Oinv__image(X1,X2,X3,X4),X4)
    | ~ c_Relation_Osym(X1,X3) ),
    cls_sym__inv__image_0,
    [final] ).

cnf(i_0_896,axiom,
    hBOOL(c_Order__Relation_Owell__order__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)),
    cls_well__order__on__empty_0,
    [final] ).

cnf(i_0_897,axiom,
    hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)),
    cls_lnear__order__on__empty_0,
    [final] ).

cnf(i_0_898,axiom,
    hBOOL(c_Order__Relation_Opartial__order__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)),
    cls_partial__order__on__empty_0,
    [final] ).

cnf(i_0_899,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    cls_injD_0,
    [final] ).

cnf(i_0_900,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_901,plain,
    c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Ortrancl(X1,X2),
    inference(rw,[status(thm)],[i_0_655,c_0_608]),
    [final] ).

cnf(i_0_902,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_COMBK(X2,tc_fun(X3,tc_bool),X1),X1,tc_fun(X3,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
    cls_INT__constant_0,
    [final] ).

cnf(i_0_903,axiom,
    ( hBOOL(c_Relation_Ototal__on(X1,c_Relation_Oconverse(X2,X3,X3),X3))
    | ~ hBOOL(c_Relation_Ototal__on(X1,X2,X3)) ),
    cls_total__on__converse_1,
    [final] ).

cnf(i_0_904,axiom,
    ( hBOOL(c_Order__Relation_Olinear__order__on(X1,c_Relation_Oconverse(X2,X3,X3),X3))
    | ~ hBOOL(c_Order__Relation_Olinear__order__on(X1,X2,X3)) ),
    cls_linear__order__on__converse_1,
    [final] ).

cnf(i_0_905,axiom,
    ( hBOOL(c_Order__Relation_Opartial__order__on(X1,c_Relation_Oconverse(X2,X3,X3),X3))
    | ~ hBOOL(c_Order__Relation_Opartial__order__on(X1,X2,X3)) ),
    cls_partial__order__on__converse_1,
    [final] ).

cnf(i_0_906,plain,
    c_Relation_ODomain(c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    inference(rw,[status(thm)],[i_0_656,c_0_610]),
    [final] ).

cnf(i_0_907,axiom,
    ( c_lessequals(c_Relation_ODomain(X1,X2,X3),c_Relation_ODomain(X4,X2,X3),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)) ),
    cls_Domain__mono_0,
    [final] ).

cnf(i_0_908,axiom,
    ( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | hBOOL(c_in(X1,X4,X2)) ),
    cls_vimage__const_1,
    [final] ).

cnf(i_0_909,axiom,
    c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X1,c_Relation_Oconverse(X1,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    cls_sym__Int__converse_0,
    [final] ).

cnf(i_0_910,axiom,
    c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_Oconverse(X1,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    cls_sym__Un__converse_0,
    [final] ).

cnf(i_0_911,axiom,
    ( c_Transitive__Closure_Ortrancl(X1,X2) = c_Transitive__Closure_Ortrancl(X3,X2)
    | ~ c_lessequals(X1,c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    cls_rtrancl__subset_0,
    [final] ).

cnf(i_0_912,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_913,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_914,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_915,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_916,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_917,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X1,X3,X4)))
    | ~ hBOOL(c_Wellfounded_Owf(X3,X4)) ),
    cls_wf__induct__rule_1,
    [final] ).

cnf(i_0_918,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X1,X3,X4)))
    | ~ hBOOL(c_Wellfounded_Owf(X3,X4)) ),
    cls_tfl__wf__induct_1,
    [final] ).

cnf(i_0_919,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X1,X3,X4)))
    | ~ hBOOL(c_Wellfounded_Owf(X3,X4)) ),
    cls_wf__induct_1,
    [final] ).

cnf(i_0_920,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X1,X3,X4)))
    | ~ hBOOL(c_Wellfounded_Owf(X3,X4)) ),
    cls_wf__def_1,
    [final] ).

cnf(i_0_921,axiom,
    ( hBOOL(c_Order__Relation_Olinear__order__on(X1,X2,X3))
    | ~ hBOOL(c_Relation_Ototal__on(X1,X2,X3))
    | ~ hBOOL(c_Order__Relation_Opartial__order__on(X1,X2,X3)) ),
    cls_linear__order__on__def_2,
    [final] ).

cnf(i_0_922,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_923,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_924,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_925,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_926,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_927,axiom,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oimage(X2,X3,X4,X1) ),
    cls_empty__is__image_0,
    [final] ).

cnf(i_0_928,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
    cls_image__is__empty_0,
    [final] ).

cnf(i_0_929,axiom,
    ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,tc_fun(X3,tc_bool)) = X2
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
    cls_INT__constant_1,
    [final] ).

cnf(i_0_930,plain,
    c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1),
    inference(rw,[status(thm)],[i_0_657,c_0_608]),
    [final] ).

cnf(i_0_931,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_932,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_933,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_934,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_935,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_936,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_937,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_938,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_939,axiom,
    c_Set_Oimage(c_COMBK(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_image__constant__conv_0,
    [final] ).

cnf(i_0_940,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_941,plain,
    c_Relation_ODomain(c_Relation_Oconverse(c_Relation_Oconverse(X1,X2,X3),X3,X2),X2,X3) = c_Relation_ODomain(X1,X2,X3),
    inference(rw,[status(thm)],[i_0_658,c_0_610]),
    [final] ).

cnf(i_0_942,axiom,
    ( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(X1,c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    cls_rtrancl__subset__rtrancl_0,
    [final] ).

cnf(i_0_943,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    cls_Compl__subset__Compl__iff_0,
    [final] ).

cnf(i_0_944,plain,
    c_Relation_ODomain(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1,X1) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
    inference(rw,[status(thm)],[i_0_659,c_0_608]),
    [final] ).

cnf(i_0_945,axiom,
    ( hBOOL(c_Relation_Otrans(X1,X2))
    | ~ hBOOL(c_Relation_Otrans(c_Relation_Oconverse(X1,X2,X2),X2)) ),
    cls_trans__converse_0,
    [final] ).

cnf(i_0_946,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Compl__Int_0,
    [final] ).

cnf(i_0_947,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Compl__Un_0,
    [final] ).

cnf(i_0_948,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_949,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_950,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_951,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_952,negated_conjecture,
    ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),X1)),
    cls_conjecture_2,
    [final] ).

cnf(i_0_953,plain,
    c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1,X1),
    inference(rw,[status(thm)],[i_0_660,c_0_608]),
    [final] ).

cnf(i_0_954,axiom,
    ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,c_COMBK(X3,X1,X4),X4,X1) = X3
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_INF__const_0,
    [final] ).

cnf(i_0_955,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_956,axiom,
    ( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    cls_rtrancl__mono_0,
    [final] ).

cnf(i_0_957,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_958,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_959,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_960,axiom,
    c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_bool)),
    cls_Sigma__empty1_0,
    [final] ).

cnf(i_0_961,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
    | c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    inference(rw,[status(thm)],[i_0_661,c_0_610]),
    [final] ).

cnf(i_0_962,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_963,axiom,
    ( hBOOL(c_in(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),X3))
    | hBOOL(c_in(X1,X2,X3)) ),
    cls_ComplI_0,
    [final] ).

cnf(i_0_964,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_965,axiom,
    ( hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X1,X2),X3))
    | ~ hBOOL(c_Relation_Ototal__on(X1,X3,X2))
    | ~ hBOOL(c_Relation_Oirrefl(X3,X2))
    | ~ hBOOL(c_Relation_Otrans(X3,X2)) ),
    cls_strict__linear__order__on__def_3,
    [final] ).

cnf(i_0_966,plain,
    c_Relation_Osym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1),
    inference(rw,[status(thm)],[i_0_662,c_0_608]),
    [final] ).

cnf(i_0_967,plain,
    c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1),
    inference(rw,[status(thm)],[i_0_663,c_0_608]),
    [final] ).

cnf(i_0_968,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
    cls_INT__empty_0,
    [final] ).

cnf(i_0_969,axiom,
    ( c_Relation_Osingle__valued(X1,X2,X3)
    | ~ c_Relation_Osingle__valued(X4,X2,X3)
    | ~ c_lessequals(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)) ),
    cls_single__valued__subset_0,
    [final] ).

cnf(i_0_970,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
    cls_Compl__subset__Compl__iff_1,
    [final] ).

cnf(i_0_971,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
    cls_Compl__anti__mono_0,
    [final] ).

cnf(i_0_972,axiom,
    hBOOL(c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)),
    cls_wf__empty_0,
    [final] ).

cnf(i_0_973,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_974,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_975,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_976,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_977,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_978,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_979,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    cls_disjoint__eq__subset__Compl_1,
    [final] ).

cnf(i_0_980,axiom,
    c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
    cls_Compl__Diff__eq_0,
    [final] ).

cnf(i_0_981,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_982,axiom,
    ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
    cls_empty__iff_0,
    [final] ).

cnf(i_0_983,axiom,
    ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
    cls_emptyE_0,
    [final] ).

cnf(i_0_984,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_985,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_986,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_987,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_988,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_989,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_990,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_991,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_992,axiom,
    hAPP(c_Order__Relation_Ostrict__linear__order__on(v_A,t_a),v_r) = c_and(c_Relation_Otrans(v_r,t_a),c_and(c_Relation_Oirrefl(v_r,t_a),c_Relation_Ototal__on(v_A,v_r,t_a))),
    cls_strict__linear__order__on__def__raw_0,
    [final] ).

cnf(i_0_993,axiom,
    c_Relation_OImage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    cls_Image__empty_0,
    [final] ).

cnf(i_0_994,axiom,
    c_Set_Ovimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
    cls_vimage__UNIV_0,
    [final] ).

cnf(i_0_995,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_996,axiom,
    c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    cls_image__empty_0,
    [final] ).

cnf(i_0_997,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1),
    cls_empty__is__image_1,
    [final] ).

cnf(i_0_998,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_999,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_1000,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_1001,axiom,
    ( c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
    | ~ c_Relation_Osym(X2,X3)
    | ~ c_Relation_Osym(X1,X3) ),
    cls_sym__Int_0,
    [final] ).

cnf(i_0_1002,axiom,
    ( c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
    | ~ c_Relation_Osym(X2,X3)
    | ~ c_Relation_Osym(X1,X3) ),
    cls_sym__Un_0,
    [final] ).

cnf(i_0_1003,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_1004,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_1005,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_1006,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_1007,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_1008,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_1009,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_1010,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_1011,axiom,
    ( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_disjoint__eq__subset__Compl_0,
    [final] ).

cnf(i_0_1012,axiom,
    ( c_Relation_Orefl__on(X1,X2,X3)
    | ~ c_Relation_Orefl__on(X1,c_Relation_Oconverse(X2,X3,X3),X3) ),
    cls_refl__on__converse_0,
    [final] ).

cnf(i_0_1013,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_1014,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_1015,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_1016,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_1017,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_1018,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
    cls_subset__Compl__self__eq_1,
    [final] ).

cnf(i_0_1019,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    cls_finite__Diff2_0,
    [final] ).

cnf(i_0_1020,axiom,
    c_Fun_Oinj__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3),
    cls_inj__on__empty_0,
    [final] ).

cnf(i_0_1021,axiom,
    ( hBOOL(c_Wellfounded_Owf(c_Wellfounded_Omlex__prod(X1,X2,X3),X3))
    | ~ hBOOL(c_Wellfounded_Owf(X2,X3)) ),
    cls_wf__mlex_0,
    [final] ).

cnf(i_0_1022,axiom,
    ( hBOOL(c_Relation_Otrans(c_Relation_Oconverse(X1,X2,X2),X2))
    | ~ hBOOL(c_Relation_Otrans(X1,X2)) ),
    cls_trans__converse_1,
    [final] ).

cnf(i_0_1023,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_inf__eq__neg__sup_0,
    [final] ).

cnf(i_0_1024,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_sup__eq__neg__inf_0,
    [final] ).

cnf(i_0_1025,axiom,
    ( hBOOL(c_Relation_Ototal__on(X1,X2,X3))
    | ~ hBOOL(c_Order__Relation_Olinear__order__on(X1,X2,X3)) ),
    cls_linear__order__on__def_1,
    [final] ).

cnf(i_0_1026,axiom,
    ( hBOOL(c_Order__Relation_Olinear__order__on(X1,X2,X3))
    | ~ hBOOL(c_Order__Relation_Owell__order__on(X1,X2,X3)) ),
    cls_well__order__on__def_0,
    [final] ).

cnf(i_0_1027,axiom,
    ( hBOOL(c_Order__Relation_Opartial__order__on(X1,X2,X3))
    | ~ hBOOL(c_Order__Relation_Olinear__order__on(X1,X2,X3)) ),
    cls_linear__order__on__def_0,
    [final] ).

cnf(i_0_1028,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X2,tc_fun(tc_prod(X1,X1),tc_bool)),
    cls_less__by__empty_0,
    [final] ).

cnf(i_0_1029,axiom,
    ( hBOOL(c_Wellfounded_Owf(X1,X2))
    | ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ hBOOL(c_Wellfounded_Owf(X3,X2)) ),
    cls_wf__subset_0,
    [final] ).

cnf(i_0_1030,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2) ),
    cls_finite__Un_0,
    [final] ).

cnf(i_0_1031,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)),X2) ),
    cls_finite__Un_1,
    [final] ).

cnf(i_0_1032,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_1033,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_1034,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_1035,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    cls_subset__Compl__self__eq_0,
    [final] ).

cnf(i_0_1036,axiom,
    ( c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ hBOOL(c_in(X2,X3,X1)) ),
    cls_Sup__upper_0,
    [final] ).

cnf(i_0_1037,axiom,
    c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
    cls_refl__on__empty_0,
    [final] ).

cnf(i_0_1038,axiom,
    c_Order__Relation_Olinear__order__on(v_A,v_r,t_a) = c_and(c_Order__Relation_Opartial__order__on(v_A,v_r,t_a),c_Relation_Ototal__on(v_A,v_r,t_a)),
    cls_linear__order__on__def__raw_0,
    [final] ).

cnf(i_0_1039,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_1040,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_1041,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_1042,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_1043,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_1044,axiom,
    ( c_Relation_Orefl__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)
    | ~ c_Relation_Orefl__on(X1,X2,X3) ),
    cls_refl__on__converse_1,
    [final] ).

cnf(i_0_1045,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_1046,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_1047,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_1048,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_1049,axiom,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ c_Wellfounded_Oacyclic(X3,X2) ),
    cls_acyclic__subset_0,
    [final] ).

cnf(i_0_1050,axiom,
    ( c_Relation_Oantisym(X1,X2)
    | ~ c_Relation_Oantisym(X3,X2)
    | ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    cls_antisym__subset_0,
    [final] ).

cnf(i_0_1051,axiom,
    ( hBOOL(c_Relation_Ototal__on(X1,X2,X3))
    | ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X1,X3),X2)) ),
    cls_strict__linear__order__on__def_2,
    [final] ).

cnf(i_0_1052,plain,
    c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    inference(rw,[status(thm)],[i_0_664,c_0_610]),
    [final] ).

cnf(i_0_1053,axiom,
    c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_Domain__empty_0,
    [final] ).

cnf(i_0_1054,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_1055,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_1056,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_neg__inf__eq__sup_0,
    [final] ).

cnf(i_0_1057,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_compl__inf_0,
    [final] ).

cnf(i_0_1058,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_neg__sup__eq__inf_0,
    [final] ).

cnf(i_0_1059,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_compl__sup_0,
    [final] ).

cnf(i_0_1060,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_1061,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_1062,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_1063,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_1064,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_1065,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_1066,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
    cls_neg__le__iff__le_0,
    [final] ).

cnf(i_0_1067,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
    cls_Diff__Compl_0,
    [final] ).

cnf(i_0_1068,axiom,
    c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Diff__eq_0,
    [final] ).

cnf(i_0_1069,axiom,
    ( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(X1,tc_bool)),X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    cls_finite__compl_0,
    [final] ).

cnf(i_0_1070,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_1071,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_1072,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_1073,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_1074,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
    cls_minus__le__iff_1,
    [final] ).

cnf(i_0_1075,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
    cls_minus__le__iff_0,
    [final] ).

cnf(i_0_1076,axiom,
    ( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
    cls_le__minus__iff_1,
    [final] ).

cnf(i_0_1077,axiom,
    ( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
    cls_le__minus__iff_0,
    [final] ).

cnf(i_0_1078,axiom,
    hBOOL(c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1)),
    cls_total__on__empty_0,
    [final] ).

cnf(i_0_1079,axiom,
    hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)),
    cls_UNIV__I_0,
    [final] ).

cnf(i_0_1080,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    cls_finite__compl_1,
    [final] ).

cnf(i_0_1081,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_finite__Diff2_1,
    [final] ).

cnf(i_0_1082,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X2,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    cls_finite__UnI_0,
    [final] ).

cnf(i_0_1083,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X2,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    cls_finite__Un_2,
    [final] ).

cnf(i_0_1084,axiom,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    cls_bot1E_0,
    [final] ).

cnf(i_0_1085,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
    | c_Relation_ODomain(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
    cls_Domain__empty__iff_0,
    [final] ).

cnf(i_0_1086,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_1087,axiom,
    ( c_HOL_Ouminus__class_Ouminus(X2,X1) = X3
    | ~ class_Lattices_Oboolean__algebra(X1)
    | c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
    cls_compl__unique_0,
    [final] ).

cnf(i_0_1088,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,X1,X3)) ),
    inference(rw,[status(thm)],[i_0_665,c_0_649]),
    [final] ).

cnf(i_0_1089,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,X1,X3)) ),
    cls_mem__def_0,
    [final] ).

cnf(i_0_1090,axiom,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2) ),
    cls_acyclic__converse_0,
    [final] ).

cnf(i_0_1091,axiom,
    ( c_Relation_Osym(X1,X2)
    | ~ c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2) ),
    cls_sym__converse_0,
    [final] ).

cnf(i_0_1092,axiom,
    ( c_Relation_Oantisym(X1,X2)
    | ~ c_Relation_Oantisym(c_Relation_Oconverse(X1,X2,X2),X2) ),
    cls_antisym__converse_0,
    [final] ).

cnf(i_0_1093,axiom,
    c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),
    cls_rtrancl__converse_0,
    [final] ).

cnf(i_0_1094,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_1095,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_1096,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_1097,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_1098,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_1099,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_1100,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_1101,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_le__imp__neg__le_0,
    [final] ).

cnf(i_0_1102,negated_conjecture,
    hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt)),
    cls_conjecture_0,
    [final] ).

cnf(i_0_1103,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_1104,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_1105,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    cls_finite__Diff_0,
    [final] ).

cnf(i_0_1106,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    cls_finite__Int_0,
    [final] ).

cnf(i_0_1107,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_finite__Int_1,
    [final] ).

cnf(i_0_1108,axiom,
    ( c_Relation_Oantisym(X1,X2)
    | ~ hBOOL(c_Order__Relation_Opartial__order__on(X3,X1,X2)) ),
    cls_partial__order__on__def_1,
    [final] ).

cnf(i_0_1109,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Ominus__class_Ominus(X3,X2,X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    cls_minus__diff__eq_0,
    [final] ).

cnf(i_0_1110,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_1111,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_1112,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_1113,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_1114,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_1115,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_1116,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_Compl__disjoint2_0,
    [final] ).

cnf(i_0_1117,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    cls_Compl__partition2_0,
    [final] ).

cnf(i_0_1118,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_Compl__disjoint_0,
    [final] ).

cnf(i_0_1119,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    cls_Compl__partition_0,
    [final] ).

cnf(i_0_1120,axiom,
    c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
    cls_antisym__empty_0,
    [final] ).

cnf(i_0_1121,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_1122,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_1123,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_1124,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_1125,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_1126,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_1127,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_1128,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_1129,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_1130,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_1131,axiom,
    c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
    cls_Compl__eq__Diff__UNIV_0,
    [final] ).

cnf(i_0_1132,axiom,
    c_Relation_Oconverse(c_Relation_Oconverse(X1,X2,X3),X3,X2) = X1,
    cls_converse__converse_0,
    [final] ).

cnf(i_0_1133,axiom,
    ( hBOOL(c_Relation_Oirrefl(X1,X2))
    | ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X3,X2),X1)) ),
    cls_strict__linear__order__on__def_1,
    [final] ).

cnf(i_0_1134,axiom,
    ( hBOOL(c_Relation_Otrans(X1,X2))
    | ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(X3,X2),X1)) ),
    cls_strict__linear__order__on__def_0,
    [final] ).

cnf(i_0_1135,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    cls_rev__finite__subset_0,
    [final] ).

cnf(i_0_1136,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(X3,X2)
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
    cls_finite__subset_0,
    [final] ).

cnf(i_0_1137,plain,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    inference(rw,[status(thm)],[i_0_666,c_0_649]),
    [final] ).

cnf(i_0_1138,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    cls_mem__def_1,
    [final] ).

cnf(i_0_1139,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_1140,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_1141,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
    cls_Un__UNIV__left_0,
    [final] ).

cnf(i_0_1142,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_Diff__UNIV_0,
    [final] ).

cnf(i_0_1143,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_1144,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    cls_Un__UNIV__right_0,
    [final] ).

cnf(i_0_1145,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_1146,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_1147,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_1148,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_1149,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_1150,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_1151,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_1152,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_1153,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_1154,axiom,
    ( c_Wellfounded_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2)
    | ~ c_Wellfounded_Oacyclic(X1,X2) ),
    cls_acyclic__converse_1,
    [final] ).

cnf(i_0_1155,axiom,
    ( c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2)
    | ~ c_Relation_Osym(X1,X2) ),
    cls_sym__converse_1,
    [final] ).

cnf(i_0_1156,axiom,
    ( c_Relation_Oantisym(c_Relation_Oconverse(X1,X2,X2),X2)
    | ~ c_Relation_Oantisym(X1,X2) ),
    cls_antisym__converse_1,
    [final] ).

cnf(i_0_1157,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_diff__eq_0,
    [final] ).

cnf(i_0_1158,axiom,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
    cls_top1I_0,
    [final] ).

cnf(i_0_1159,axiom,
    c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Transitive__Closure_Ortrancl(X2,X1),X1),
    cls_refl__rtrancl_0,
    [final] ).

cnf(i_0_1160,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
    cls_Int__UNIV__left_0,
    [final] ).

cnf(i_0_1161,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_1162,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_1163,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    cls_Int__UNIV__right_0,
    [final] ).

cnf(i_0_1164,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_1165,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_1166,axiom,
    c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    cls_subset__UNIV_0,
    [final] ).

cnf(i_0_1167,axiom,
    ( hAPP(c_HOL_Ouminus__class_Ouminus(X2,tc_fun(t_a,X1)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(X2,v_x),X1)
    | ~ class_HOL_Ouminus(X1) ),
    cls_fun__Compl__def_0,
    [final] ).

cnf(i_0_1168,axiom,
    hAPP(c_COMBK(X1,X2,X3),X4) = X1,
    cls_COMBK__def_0,
    [final] ).

cnf(i_0_1169,axiom,
    ( X1 = X3
    | c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)) != c_HOL_Ouminus__class_Ouminus(X3,tc_fun(X2,tc_bool)) ),
    cls_Compl__eq__Compl__iff_0,
    [final] ).

cnf(i_0_1170,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__linear_0,
    [final] ).

cnf(i_0_1171,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_1172,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_1173,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_1174,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_1175,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_Compl__UNIV__eq_0,
    [final] ).

cnf(i_0_1176,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
    cls_Compl__empty__eq_0,
    [final] ).

cnf(i_0_1177,axiom,
    ( hAPP(c_HOL_Ouminus__class_Ouminus(v_A,tc_fun(t_a,t_b)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(v_A,v_x),t_b)
    | ~ class_HOL_Ouminus(t_b) ),
    cls_fun__Compl__def__raw_0,
    [final] ).

cnf(i_0_1178,axiom,
    c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    cls_double__complement_0,
    [final] ).

cnf(i_0_1179,axiom,
    c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
    cls_Domain__rtrancl_0,
    [final] ).

cnf(i_0_1180,axiom,
    ( X2 = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
    cls_inf__eq__top__eq1_0,
    [final] ).

cnf(i_0_1181,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_1182,axiom,
    ( X3 = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
    cls_inf__eq__top__eq2_0,
    [final] ).

cnf(i_0_1183,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_1184,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_1185,axiom,
    ( c_Relation_Osym(X1,X2)
    | c_Relation_Oconverse(X1,X2,X2) != X1 ),
    cls_sym__conv__converse__eq_1,
    [final] ).

cnf(i_0_1186,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != X2
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(rw,[status(thm)],[i_0_667,c_0_649]),
    [final] ).

cnf(i_0_1187,plain,
    ( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(rw,[status(thm)],[i_0_668,c_0_649]),
    [final] ).

cnf(i_0_1188,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_compl__inf__bot_0,
    [final] ).

cnf(i_0_1189,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_compl__sup__top_0,
    [final] ).

cnf(i_0_1190,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_inf__compl__bot_0,
    [final] ).

cnf(i_0_1191,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_sup__compl__top_0,
    [final] ).

cnf(i_0_1192,axiom,
    ( X1 = X2
    | ~ c_fequal(X1,X2,X3) ),
    cls_ATP__Linkup_Ofequal__imp__equal_0,
    [final] ).

cnf(i_0_1193,axiom,
    c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_UNIV__not__empty_0,
    [final] ).

cnf(i_0_1194,axiom,
    hBOOL(c_Wellfounded_Owf(c_List_Omeasures(X1,X2),X2)),
    cls_wf__measures_0,
    [final] ).

cnf(i_0_1195,axiom,
    hBOOL(c_Wellfounded_Owf(c_Wellfounded_Omeasure(X1,X2),X2)),
    cls_wf__measure_0,
    [final] ).

cnf(i_0_1196,axiom,
    hBOOL(c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X1,X2),X2)),
    cls_trans__rtrancl_0,
    [final] ).

cnf(i_0_1197,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
    cls_Int__absorb_0,
    [final] ).

cnf(i_0_1198,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
    cls_Un__absorb_0,
    [final] ).

cnf(i_0_1199,axiom,
    ( c_Relation_Oconverse(X1,X2,X2) = X1
    | ~ c_Relation_Osym(X1,X2) ),
    cls_sym__conv__converse__eq_0,
    [final] ).

cnf(i_0_1200,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    cls_subset__refl_0,
    [final] ).

cnf(i_0_1201,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    cls_equalityE_0,
    [final] ).

cnf(i_0_1202,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    cls_Sup__UNIV_0,
    [final] ).

cnf(i_0_1203,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_1204,axiom,
    ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Orderings_Otop(X1) ),
    cls_top__fun__eq_0,
    [final] ).

cnf(i_0_1205,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_1206,axiom,
    ( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    cls_finite__UNIV_0,
    [final] ).

cnf(i_0_1207,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_1208,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X2,X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_sup__top__left_0,
    [final] ).

cnf(i_0_1209,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_1210,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Otop__class_Otop(X1),X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_sup__top__right_0,
    [final] ).

cnf(i_0_1211,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X2,X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_inf__top__left_0,
    [final] ).

cnf(i_0_1212,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_1213,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Otop__class_Otop(X1),X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_inf__top__right_0,
    [final] ).

cnf(i_0_1214,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_1215,axiom,
    ( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
    | ~ class_Orderings_Obot(X1) ),
    cls_bot__least_0,
    [final] ).

cnf(i_0_1216,axiom,
    ( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
    | ~ class_Orderings_Otop(X1) ),
    cls_top__greatest_0,
    [final] ).

cnf(i_0_1217,axiom,
    c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
    cls_finite_OemptyI_0,
    [final] ).

cnf(i_0_1218,axiom,
    ( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
    | ~ c_Relation_Osym(X1,X2) ),
    cls_sym__rtrancl_0,
    [final] ).

cnf(i_0_1219,axiom,
    ( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
    | ~ c_Wellfounded_Oacyclic(X1,X2) ),
    cls_acyclic__impl__antisym__rtrancl_0,
    [final] ).

cnf(i_0_1220,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X2,X1) = X2
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__idem_0,
    [final] ).

cnf(i_0_1221,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(X2,X2,X1) = X2
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__idem_0,
    [final] ).

cnf(i_0_1222,axiom,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ hBOOL(c_Wellfounded_Owf(X1,X2)) ),
    cls_wf__acyclic_0,
    [final] ).

cnf(i_0_1223,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Opreorder(X1) ),
    cls_order__eq__refl_0,
    [final] ).

cnf(i_0_1224,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_order__eq__iff_0,
    [final] ).

cnf(i_0_1225,plain,
    c_Arrow__Order__Mirabelle_OLin = c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),
    inference(rw,[status(thm)],[i_0_669,c_0_649]),
    [final] ).

cnf(i_0_1226,axiom,
    c_fequal(X1,X1,X2),
    cls_ATP__Linkup_Oequal__imp__fequal_0,
    [final] ).

cnf(i_0_1227,axiom,
    c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
    cls_rtrancl__idemp_0,
    [final] ).

cnf(i_0_1228,axiom,
    ( X2 = X3
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
    cls_neg__equal__iff__equal_0,
    [final] ).

cnf(i_0_1229,axiom,
    ( X2 = X3
    | ~ class_Lattices_Oboolean__algebra(X1)
    | c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
    cls_compl__eq__compl__iff_0,
    [final] ).

cnf(i_0_1230,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_minus__equation__iff_1,
    [final] ).

cnf(i_0_1231,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_minus__minus_0,
    [final] ).

cnf(i_0_1232,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_double__compl_0,
    [final] ).

cnf(i_0_1233,axiom,
    ( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_equation__minus__iff_1,
    [final] ).

cnf(i_0_1234,axiom,
    ( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_equation__minus__iff_0,
    [final] ).

cnf(i_0_1235,axiom,
    ( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
    | ~ class_Finite__Set_Ofinite_Ofinite(X2)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    clsarity_fun__Finite__Set_Ofinite_Ofinite,
    [final] ).

cnf(i_0_1236,axiom,
    ( class_Finite__Set_Ofinite_Ofinite(tc_prod(X1,X2))
    | ~ class_Finite__Set_Ofinite_Ofinite(X2)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    clsarity_prod__Finite__Set_Ofinite_Ofinite,
    [final] ).

cnf(i_0_1237,axiom,
    ( class_HOL_Ominus(tc_fun(X1,X2))
    | ~ class_HOL_Ominus(X2) ),
    clsarity_fun__HOL_Ominus,
    [final] ).

cnf(i_0_1238,axiom,
    ( class_Orderings_Opreorder(tc_fun(X1,X2))
    | ~ class_Orderings_Opreorder(X2) ),
    clsarity_fun__Orderings_Opreorder,
    [final] ).

cnf(i_0_1239,axiom,
    ( class_Orderings_Otop(tc_fun(X1,X2))
    | ~ class_Orderings_Otop(X2) ),
    clsarity_fun__Orderings_Otop,
    [final] ).

cnf(i_0_1240,axiom,
    ( class_HOL_Oord(tc_fun(X1,X2))
    | ~ class_HOL_Oord(X2) ),
    clsarity_fun__HOL_Oord,
    [final] ).

cnf(i_0_1241,axiom,
    ( class_HOL_Ouminus(tc_fun(X1,X2))
    | ~ class_HOL_Ouminus(X2) ),
    clsarity_fun__HOL_Ouminus,
    [final] ).

cnf(i_0_1242,axiom,
    ( class_Orderings_Oorder(tc_fun(X1,X2))
    | ~ class_Orderings_Oorder(X2) ),
    clsarity_fun__Orderings_Oorder,
    [final] ).

cnf(i_0_1243,axiom,
    ( class_Lattices_Olower__semilattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_1244,axiom,
    ( class_Lattices_Oupper__semilattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Oupper__semilattice,
    [final] ).

cnf(i_0_1245,axiom,
    ( class_Lattices_Odistrib__lattice(tc_fun(X1,X2))
    | ~ class_Lattices_Odistrib__lattice(X2) ),
    clsarity_fun__Lattices_Odistrib__lattice,
    [final] ).

cnf(i_0_1246,axiom,
    ( class_Lattices_Olattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Olattice,
    [final] ).

cnf(i_0_1247,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_1248,axiom,
    ( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
    | ~ class_Lattices_Obounded__lattice(X2) ),
    clsarity_fun__Lattices_Obounded__lattice,
    [final] ).

cnf(i_0_1249,axiom,
    ( class_Lattices_Oboolean__algebra(tc_fun(X1,X2))
    | ~ class_Lattices_Oboolean__algebra(X2) ),
    clsarity_fun__Lattices_Oboolean__algebra,
    [final] ).

cnf(i_0_1250,axiom,
    ( class_Orderings_Obot(tc_fun(X1,X2))
    | ~ class_Orderings_Obot(X2) ),
    clsarity_fun__Orderings_Obot,
    [final] ).

cnf(i_0_1251,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(X1),X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_compl__top__eq_0,
    [final] ).

cnf(i_0_1252,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(X1),X1) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    cls_compl__bot__eq_0,
    [final] ).

cnf(i_0_1253,axiom,
    ( c_Finite__Set_Ofinite(X2,X1)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    cls_finite_0,
    [final] ).

cnf(i_0_1254,axiom,
    class_HOL_Ominus(tc_bool),
    clsarity_bool__HOL_Ominus,
    [final] ).

cnf(i_0_1255,axiom,
    class_Orderings_Opreorder(tc_bool),
    clsarity_bool__Orderings_Opreorder,
    [final] ).

cnf(i_0_1256,axiom,
    class_Orderings_Otop(tc_bool),
    clsarity_bool__Orderings_Otop,
    [final] ).

cnf(i_0_1257,axiom,
    class_HOL_Oord(tc_bool),
    clsarity_bool__HOL_Oord,
    [final] ).

cnf(i_0_1258,axiom,
    class_Finite__Set_Ofinite_Ofinite(tc_bool),
    clsarity_bool__Finite__Set_Ofinite_Ofinite,
    [final] ).

cnf(i_0_1259,axiom,
    class_HOL_Ouminus(tc_bool),
    clsarity_bool__HOL_Ouminus,
    [final] ).

cnf(i_0_1260,axiom,
    class_Orderings_Oorder(tc_bool),
    clsarity_bool__Orderings_Oorder,
    [final] ).

cnf(i_0_1261,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    clsarity_bool__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_1262,axiom,
    class_Lattices_Oupper__semilattice(tc_bool),
    clsarity_bool__Lattices_Oupper__semilattice,
    [final] ).

cnf(i_0_1263,axiom,
    class_Lattices_Odistrib__lattice(tc_bool),
    clsarity_bool__Lattices_Odistrib__lattice,
    [final] ).

cnf(i_0_1264,axiom,
    class_Lattices_Olattice(tc_bool),
    clsarity_bool__Lattices_Olattice,
    [final] ).

cnf(i_0_1265,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_bool),
    clsarity_bool__Complete__Lattice_Ocomplete__lattice,
    [final] ).

cnf(i_0_1266,axiom,
    class_Lattices_Obounded__lattice(tc_bool),
    clsarity_bool__Lattices_Obounded__lattice,
    [final] ).

cnf(i_0_1267,axiom,
    class_Lattices_Oboolean__algebra(tc_bool),
    clsarity_bool__Lattices_Oboolean__algebra,
    [final] ).

cnf(i_0_1268,axiom,
    class_Orderings_Obot(tc_bool),
    clsarity_bool__Orderings_Obot,
    [final] ).

cnf(i_0_1269,axiom,
    X1 = X1 ).

cnf(i_0_1270,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1271,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1272,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1273,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1274,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).

cnf(i_0_1275,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).

cnf(i_0_1276,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4) ) ).

cnf(i_0_1277,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X4) ) ).

cnf(i_0_1278,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2) ) ).

cnf(i_0_1279,axiom,
    ( X1 != X2
    | c_Relation_Oconverse(X1,X3,X4) = c_Relation_Oconverse(X2,X3,X4) ) ).

cnf(i_0_1280,axiom,
    ( X1 != X2
    | c_Relation_Oconverse(X3,X1,X4) = c_Relation_Oconverse(X3,X2,X4) ) ).

cnf(i_0_1281,axiom,
    ( X1 != X2
    | c_Relation_Oconverse(X3,X4,X1) = c_Relation_Oconverse(X3,X4,X2) ) ).

cnf(i_0_1282,axiom,
    ( X1 != X2
    | c_Product__Type_OSigma(X1,X3,X4,X5) = c_Product__Type_OSigma(X2,X3,X4,X5) ) ).

cnf(i_0_1283,axiom,
    ( X1 != X2
    | c_Product__Type_OSigma(X3,X1,X4,X5) = c_Product__Type_OSigma(X3,X2,X4,X5) ) ).

cnf(i_0_1284,axiom,
    ( X1 != X2
    | c_Product__Type_OSigma(X3,X4,X1,X5) = c_Product__Type_OSigma(X3,X4,X2,X5) ) ).

cnf(i_0_1285,axiom,
    ( X1 != X2
    | c_Product__Type_OSigma(X3,X4,X5,X1) = c_Product__Type_OSigma(X3,X4,X5,X2) ) ).

cnf(i_0_1286,axiom,
    ( X1 != X2
    | c_Relation_ODomain(X1,X3,X4) = c_Relation_ODomain(X2,X3,X4) ) ).

cnf(i_0_1287,axiom,
    ( X1 != X2
    | c_Relation_ODomain(X3,X1,X4) = c_Relation_ODomain(X3,X2,X4) ) ).

cnf(i_0_1288,axiom,
    ( X1 != X2
    | c_Relation_ODomain(X3,X4,X1) = c_Relation_ODomain(X3,X4,X2) ) ).

cnf(i_0_1289,axiom,
    ( X1 != X2
    | c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).

cnf(i_0_1290,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).

cnf(i_0_1291,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).

cnf(i_0_1292,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).

cnf(i_0_1293,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_1294,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_1295,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_1296,axiom,
    ( X1 != X2
    | c_in(X1,X3,X4) = c_in(X2,X3,X4) ) ).

cnf(i_0_1297,axiom,
    ( X1 != X2
    | c_in(X3,X1,X4) = c_in(X3,X2,X4) ) ).

cnf(i_0_1298,axiom,
    ( X1 != X2
    | c_in(X3,X4,X1) = c_in(X3,X4,X2) ) ).

cnf(i_0_1299,axiom,
    ( X1 != X2
    | c_Relation_OImage(X1,X3,X4,X5) = c_Relation_OImage(X2,X3,X4,X5) ) ).

cnf(i_0_1300,axiom,
    ( X1 != X2
    | c_Relation_OImage(X3,X1,X4,X5) = c_Relation_OImage(X3,X2,X4,X5) ) ).

cnf(i_0_1301,axiom,
    ( X1 != X2
    | c_Relation_OImage(X3,X4,X1,X5) = c_Relation_OImage(X3,X4,X2,X5) ) ).

cnf(i_0_1302,axiom,
    ( X1 != X2
    | c_Relation_OImage(X3,X4,X5,X1) = c_Relation_OImage(X3,X4,X5,X2) ) ).

cnf(i_0_1303,axiom,
    ( X1 != X2
    | c_HOL_Ouminus__class_Ouminus(X1,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3) ) ).

cnf(i_0_1304,axiom,
    ( X1 != X2
    | c_HOL_Ouminus__class_Ouminus(X3,X1) = c_HOL_Ouminus__class_Ouminus(X3,X2) ) ).

cnf(i_0_1305,axiom,
    ( X1 != X2
    | c_Order__Relation_Owell__order__on(X1,X3,X4) = c_Order__Relation_Owell__order__on(X2,X3,X4) ) ).

cnf(i_0_1306,axiom,
    ( X1 != X2
    | c_Order__Relation_Owell__order__on(X3,X1,X4) = c_Order__Relation_Owell__order__on(X3,X2,X4) ) ).

cnf(i_0_1307,axiom,
    ( X1 != X2
    | c_Order__Relation_Owell__order__on(X3,X4,X1) = c_Order__Relation_Owell__order__on(X3,X4,X2) ) ).

cnf(i_0_1308,axiom,
    ( X1 != X2
    | c_Order__Relation_Olinear__order__on(X1,X3,X4) = c_Order__Relation_Olinear__order__on(X2,X3,X4) ) ).

cnf(i_0_1309,axiom,
    ( X1 != X2
    | c_Order__Relation_Olinear__order__on(X3,X1,X4) = c_Order__Relation_Olinear__order__on(X3,X2,X4) ) ).

cnf(i_0_1310,axiom,
    ( X1 != X2
    | c_Order__Relation_Olinear__order__on(X3,X4,X1) = c_Order__Relation_Olinear__order__on(X3,X4,X2) ) ).

cnf(i_0_1311,axiom,
    ( X1 != X2
    | c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X3,X4,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X3,X4,X5) ) ).

cnf(i_0_1312,axiom,
    ( X1 != X2
    | c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1,X4,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X2,X4,X5) ) ).

cnf(i_0_1313,axiom,
    ( X1 != X2
    | c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X4,X1,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X4,X2,X5) ) ).

cnf(i_0_1314,axiom,
    ( X1 != X2
    | c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X4,X5,X1) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X4,X5,X2) ) ).

cnf(i_0_1315,axiom,
    ( X1 != X2
    | c_Order__Relation_Ostrict__linear__order__on(X1,X3) = c_Order__Relation_Ostrict__linear__order__on(X2,X3) ) ).

cnf(i_0_1316,axiom,
    ( X1 != X2
    | c_Order__Relation_Ostrict__linear__order__on(X3,X1) = c_Order__Relation_Ostrict__linear__order__on(X3,X2) ) ).

cnf(i_0_1317,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X1,X3,X4,X5) = c_Set_Ovimage(X2,X3,X4,X5) ) ).

cnf(i_0_1318,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X1,X4,X5) = c_Set_Ovimage(X3,X2,X4,X5) ) ).

cnf(i_0_1319,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X1,X5) = c_Set_Ovimage(X3,X4,X2,X5) ) ).

cnf(i_0_1320,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X5,X1) = c_Set_Ovimage(X3,X4,X5,X2) ) ).

cnf(i_0_1321,axiom,
    ( X1 != X2
    | c_and(X1,X3) = c_and(X2,X3) ) ).

cnf(i_0_1322,axiom,
    ( X1 != X2
    | c_and(X3,X1) = c_and(X3,X2) ) ).

cnf(i_0_1323,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_1324,axiom,
    ( X1 != X2
    | c_Relation_Oinv__image(X1,X3,X4,X5) = c_Relation_Oinv__image(X2,X3,X4,X5) ) ).

cnf(i_0_1325,axiom,
    ( X1 != X2
    | c_Relation_Oinv__image(X3,X1,X4,X5) = c_Relation_Oinv__image(X3,X2,X4,X5) ) ).

cnf(i_0_1326,axiom,
    ( X1 != X2
    | c_Relation_Oinv__image(X3,X4,X1,X5) = c_Relation_Oinv__image(X3,X4,X2,X5) ) ).

cnf(i_0_1327,axiom,
    ( X1 != X2
    | c_Relation_Oinv__image(X3,X4,X5,X1) = c_Relation_Oinv__image(X3,X4,X5,X2) ) ).

cnf(i_0_1328,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).

cnf(i_0_1329,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).

cnf(i_0_1330,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_1331,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4) ) ).

cnf(i_0_1332,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X4) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) ) ).

cnf(i_0_1333,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2) ) ).

cnf(i_0_1334,axiom,
    ( X1 != X2
    | c_Relation_Orel__comp(X1,X3,X4,X5,X6) = c_Relation_Orel__comp(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1335,axiom,
    ( X1 != X2
    | c_Relation_Orel__comp(X3,X1,X4,X5,X6) = c_Relation_Orel__comp(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1336,axiom,
    ( X1 != X2
    | c_Relation_Orel__comp(X3,X4,X1,X5,X6) = c_Relation_Orel__comp(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1337,axiom,
    ( X1 != X2
    | c_Relation_Orel__comp(X3,X4,X5,X1,X6) = c_Relation_Orel__comp(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1338,axiom,
    ( X1 != X2
    | c_Relation_Orel__comp(X3,X4,X5,X6,X1) = c_Relation_Orel__comp(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1339,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1340,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_1341,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_1342,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_1343,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oupper__semilattice(X1)
    | class_Lattices_Oupper__semilattice(X2) ) ).

cnf(i_0_1344,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | class_Lattices_Olower__semilattice(X2) ) ).

cnf(i_0_1345,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_1346,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_1347,axiom,
    ( X1 != X2
    | ~ class_HOL_Ominus(X1)
    | class_HOL_Ominus(X2) ) ).

cnf(i_0_1348,axiom,
    ( X1 != X2
    | ~ class_HOL_Oord(X1)
    | class_HOL_Oord(X2) ) ).

cnf(i_0_1349,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X1,X3)
    | c_Wellfounded_Oacyclic(X2,X3) ) ).

cnf(i_0_1350,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X3,X1)
    | c_Wellfounded_Oacyclic(X3,X2) ) ).

cnf(i_0_1351,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_1352,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_1353,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_1354,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_1355,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_1356,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_1357,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_1358,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_1359,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_1360,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1361,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1362,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oboolean__algebra(X1)
    | class_Lattices_Oboolean__algebra(X2) ) ).

cnf(i_0_1363,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1364,axiom,
    ( X1 != X2
    | ~ class_HOL_Ouminus(X1)
    | class_HOL_Ouminus(X2) ) ).

cnf(i_0_1365,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1366,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_1367,axiom,
    ( X1 != X2
    | ~ c_fequal(X1,X3,X4)
    | c_fequal(X2,X3,X4) ) ).

cnf(i_0_1368,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X1,X4)
    | c_fequal(X3,X2,X4) ) ).

cnf(i_0_1369,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X4,X1)
    | c_fequal(X3,X4,X2) ) ).

cnf(i_0_1370,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_1371,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_1372,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_1373,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_1374,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_1375,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite_Ofinite(X1)
    | class_Finite__Set_Ofinite_Ofinite(X2) ) ).

cnf(i_0_1376,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | class_OrderedGroup_Ogroup__add(X2) ) ).

cnf(i_0_1377,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_1378,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_1379,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_1380,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_1381,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X1,X3,X4)
    | c_Relation_Orefl__on(X2,X3,X4) ) ).

cnf(i_0_1382,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X1,X4)
    | c_Relation_Orefl__on(X3,X2,X4) ) ).

cnf(i_0_1383,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X4,X1)
    | c_Relation_Orefl__on(X3,X4,X2) ) ).

cnf(i_0_1384,axiom,
    ( X1 != X2
    | ~ c_Relation_Osym(X1,X3)
    | c_Relation_Osym(X2,X3) ) ).

cnf(i_0_1385,axiom,
    ( X1 != X2
    | ~ c_Relation_Osym(X3,X1)
    | c_Relation_Osym(X3,X2) ) ).

cnf(i_0_1386,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X1,X3,X4)
    | c_Relation_Osingle__valued(X2,X3,X4) ) ).

cnf(i_0_1387,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X1,X4)
    | c_Relation_Osingle__valued(X3,X2,X4) ) ).

cnf(i_0_1388,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X4,X1)
    | c_Relation_Osingle__valued(X3,X4,X2) ) ).

cnf(i_0_1389,axiom,
    ( X1 != X2
    | ~ c_Relation_Oantisym(X1,X3)
    | c_Relation_Oantisym(X2,X3) ) ).

cnf(i_0_1390,axiom,
    ( X1 != X2
    | ~ c_Relation_Oantisym(X3,X1)
    | c_Relation_Oantisym(X3,X2) ) ).

cnf(i_0_1391,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | c_Finite__Set_Ofinite(X2,X3) ) ).

cnf(i_0_1392,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | c_Finite__Set_Ofinite(X3,X2) ) ).

cnf(i_0_1269_001,axiom,
    X1 = X1 ).

cnf(i_0_1270_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1271_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1272_004,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1273_005,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1274_006,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).

cnf(i_0_1275_007,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).

cnf(i_0_1276_008,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4) ) ).

cnf(i_0_1277_009,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X4) ) ).

cnf(i_0_1278_010,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2) ) ).

cnf(i_0_1279_011,axiom,
    ( X1 != X2
    | c_Relation_Oconverse(X1,X3,X4) = c_Relation_Oconverse(X2,X3,X4) ) ).

cnf(i_0_1280_012,axiom,
    ( X1 != X2
    | c_Relation_Oconverse(X3,X1,X4) = c_Relation_Oconverse(X3,X2,X4) ) ).

cnf(i_0_1281_013,axiom,
    ( X1 != X2
    | c_Relation_Oconverse(X3,X4,X1) = c_Relation_Oconverse(X3,X4,X2) ) ).

cnf(i_0_1282_014,axiom,
    ( X1 != X2
    | c_Product__Type_OSigma(X1,X3,X4,X5) = c_Product__Type_OSigma(X2,X3,X4,X5) ) ).

cnf(i_0_1283_015,axiom,
    ( X1 != X2
    | c_Product__Type_OSigma(X3,X1,X4,X5) = c_Product__Type_OSigma(X3,X2,X4,X5) ) ).

cnf(i_0_1284_016,axiom,
    ( X1 != X2
    | c_Product__Type_OSigma(X3,X4,X1,X5) = c_Product__Type_OSigma(X3,X4,X2,X5) ) ).

cnf(i_0_1285_017,axiom,
    ( X1 != X2
    | c_Product__Type_OSigma(X3,X4,X5,X1) = c_Product__Type_OSigma(X3,X4,X5,X2) ) ).

cnf(i_0_1286_018,axiom,
    ( X1 != X2
    | c_Relation_ODomain(X1,X3,X4) = c_Relation_ODomain(X2,X3,X4) ) ).

cnf(i_0_1287_019,axiom,
    ( X1 != X2
    | c_Relation_ODomain(X3,X1,X4) = c_Relation_ODomain(X3,X2,X4) ) ).

cnf(i_0_1288_020,axiom,
    ( X1 != X2
    | c_Relation_ODomain(X3,X4,X1) = c_Relation_ODomain(X3,X4,X2) ) ).

cnf(i_0_1289_021,axiom,
    ( X1 != X2
    | c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).

cnf(i_0_1290_022,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).

cnf(i_0_1291_023,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).

cnf(i_0_1292_024,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).

cnf(i_0_1293_025,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_1294_026,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_1295_027,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_1296_028,axiom,
    ( X1 != X2
    | c_in(X1,X3,X4) = c_in(X2,X3,X4) ) ).

cnf(i_0_1297_029,axiom,
    ( X1 != X2
    | c_in(X3,X1,X4) = c_in(X3,X2,X4) ) ).

cnf(i_0_1298_030,axiom,
    ( X1 != X2
    | c_in(X3,X4,X1) = c_in(X3,X4,X2) ) ).

cnf(i_0_1299_031,axiom,
    ( X1 != X2
    | c_Relation_OImage(X1,X3,X4,X5) = c_Relation_OImage(X2,X3,X4,X5) ) ).

cnf(i_0_1300_032,axiom,
    ( X1 != X2
    | c_Relation_OImage(X3,X1,X4,X5) = c_Relation_OImage(X3,X2,X4,X5) ) ).

cnf(i_0_1301_033,axiom,
    ( X1 != X2
    | c_Relation_OImage(X3,X4,X1,X5) = c_Relation_OImage(X3,X4,X2,X5) ) ).

cnf(i_0_1302_034,axiom,
    ( X1 != X2
    | c_Relation_OImage(X3,X4,X5,X1) = c_Relation_OImage(X3,X4,X5,X2) ) ).

cnf(i_0_1303_035,axiom,
    ( X1 != X2
    | c_HOL_Ouminus__class_Ouminus(X1,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3) ) ).

cnf(i_0_1304_036,axiom,
    ( X1 != X2
    | c_HOL_Ouminus__class_Ouminus(X3,X1) = c_HOL_Ouminus__class_Ouminus(X3,X2) ) ).

cnf(i_0_1305_037,axiom,
    ( X1 != X2
    | c_Order__Relation_Owell__order__on(X1,X3,X4) = c_Order__Relation_Owell__order__on(X2,X3,X4) ) ).

cnf(i_0_1306_038,axiom,
    ( X1 != X2
    | c_Order__Relation_Owell__order__on(X3,X1,X4) = c_Order__Relation_Owell__order__on(X3,X2,X4) ) ).

cnf(i_0_1307_039,axiom,
    ( X1 != X2
    | c_Order__Relation_Owell__order__on(X3,X4,X1) = c_Order__Relation_Owell__order__on(X3,X4,X2) ) ).

cnf(i_0_1308_040,axiom,
    ( X1 != X2
    | c_Order__Relation_Olinear__order__on(X1,X3,X4) = c_Order__Relation_Olinear__order__on(X2,X3,X4) ) ).

cnf(i_0_1309_041,axiom,
    ( X1 != X2
    | c_Order__Relation_Olinear__order__on(X3,X1,X4) = c_Order__Relation_Olinear__order__on(X3,X2,X4) ) ).

cnf(i_0_1310_042,axiom,
    ( X1 != X2
    | c_Order__Relation_Olinear__order__on(X3,X4,X1) = c_Order__Relation_Olinear__order__on(X3,X4,X2) ) ).

cnf(i_0_1311_043,axiom,
    ( X1 != X2
    | c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X3,X4,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X3,X4,X5) ) ).

cnf(i_0_1312_044,axiom,
    ( X1 != X2
    | c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X1,X4,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X2,X4,X5) ) ).

cnf(i_0_1313_045,axiom,
    ( X1 != X2
    | c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X4,X1,X5) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X4,X2,X5) ) ).

cnf(i_0_1314_046,axiom,
    ( X1 != X2
    | c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X4,X5,X1) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,X4,X5,X2) ) ).

cnf(i_0_1315_047,axiom,
    ( X1 != X2
    | c_Order__Relation_Ostrict__linear__order__on(X1,X3) = c_Order__Relation_Ostrict__linear__order__on(X2,X3) ) ).

cnf(i_0_1316_048,axiom,
    ( X1 != X2
    | c_Order__Relation_Ostrict__linear__order__on(X3,X1) = c_Order__Relation_Ostrict__linear__order__on(X3,X2) ) ).

cnf(i_0_1317_049,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X1,X3,X4,X5) = c_Set_Ovimage(X2,X3,X4,X5) ) ).

cnf(i_0_1318_050,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X1,X4,X5) = c_Set_Ovimage(X3,X2,X4,X5) ) ).

cnf(i_0_1319_051,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X1,X5) = c_Set_Ovimage(X3,X4,X2,X5) ) ).

cnf(i_0_1320_052,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X5,X1) = c_Set_Ovimage(X3,X4,X5,X2) ) ).

cnf(i_0_1321_053,axiom,
    ( X1 != X2
    | c_and(X1,X3) = c_and(X2,X3) ) ).

cnf(i_0_1322_054,axiom,
    ( X1 != X2
    | c_and(X3,X1) = c_and(X3,X2) ) ).

cnf(i_0_1323_055,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_1324_056,axiom,
    ( X1 != X2
    | c_Relation_Oinv__image(X1,X3,X4,X5) = c_Relation_Oinv__image(X2,X3,X4,X5) ) ).

cnf(i_0_1325_057,axiom,
    ( X1 != X2
    | c_Relation_Oinv__image(X3,X1,X4,X5) = c_Relation_Oinv__image(X3,X2,X4,X5) ) ).

cnf(i_0_1326_058,axiom,
    ( X1 != X2
    | c_Relation_Oinv__image(X3,X4,X1,X5) = c_Relation_Oinv__image(X3,X4,X2,X5) ) ).

cnf(i_0_1327_059,axiom,
    ( X1 != X2
    | c_Relation_Oinv__image(X3,X4,X5,X1) = c_Relation_Oinv__image(X3,X4,X5,X2) ) ).

cnf(i_0_1328_060,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).

cnf(i_0_1329_061,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).

cnf(i_0_1330_062,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_1331_063,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4) ) ).

cnf(i_0_1332_064,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X4) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) ) ).

cnf(i_0_1333_065,axiom,
    ( X1 != X2
    | c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2) ) ).

cnf(i_0_1334_066,axiom,
    ( X1 != X2
    | c_Relation_Orel__comp(X1,X3,X4,X5,X6) = c_Relation_Orel__comp(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1335_067,axiom,
    ( X1 != X2
    | c_Relation_Orel__comp(X3,X1,X4,X5,X6) = c_Relation_Orel__comp(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1336_068,axiom,
    ( X1 != X2
    | c_Relation_Orel__comp(X3,X4,X1,X5,X6) = c_Relation_Orel__comp(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1337_069,axiom,
    ( X1 != X2
    | c_Relation_Orel__comp(X3,X4,X5,X1,X6) = c_Relation_Orel__comp(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1338_070,axiom,
    ( X1 != X2
    | c_Relation_Orel__comp(X3,X4,X5,X6,X1) = c_Relation_Orel__comp(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1339_071,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1340_072,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_1341_073,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_1342_074,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_1343_075,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oupper__semilattice(X1)
    | class_Lattices_Oupper__semilattice(X2) ) ).

cnf(i_0_1344_076,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | class_Lattices_Olower__semilattice(X2) ) ).

cnf(i_0_1345_077,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_1346_078,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_1347_079,axiom,
    ( X1 != X2
    | ~ class_HOL_Ominus(X1)
    | class_HOL_Ominus(X2) ) ).

cnf(i_0_1348_080,axiom,
    ( X1 != X2
    | ~ class_HOL_Oord(X1)
    | class_HOL_Oord(X2) ) ).

cnf(i_0_1349_081,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X1,X3)
    | c_Wellfounded_Oacyclic(X2,X3) ) ).

cnf(i_0_1350_082,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X3,X1)
    | c_Wellfounded_Oacyclic(X3,X2) ) ).

cnf(i_0_1351_083,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_1352_084,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_1353_085,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_1354_086,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_1355_087,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_1356_088,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_1357_089,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_1358_090,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_1359_091,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_1360_092,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1361_093,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1362_094,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oboolean__algebra(X1)
    | class_Lattices_Oboolean__algebra(X2) ) ).

cnf(i_0_1363_095,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1364_096,axiom,
    ( X1 != X2
    | ~ class_HOL_Ouminus(X1)
    | class_HOL_Ouminus(X2) ) ).

cnf(i_0_1365_097,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1366_098,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_1367_099,axiom,
    ( X1 != X2
    | ~ c_fequal(X1,X3,X4)
    | c_fequal(X2,X3,X4) ) ).

cnf(i_0_1368_100,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X1,X4)
    | c_fequal(X3,X2,X4) ) ).

cnf(i_0_1369_101,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X4,X1)
    | c_fequal(X3,X4,X2) ) ).

cnf(i_0_1370_102,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_1371_103,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_1372_104,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_1373_105,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_1374_106,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_1375_107,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite_Ofinite(X1)
    | class_Finite__Set_Ofinite_Ofinite(X2) ) ).

cnf(i_0_1376_108,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | class_OrderedGroup_Ogroup__add(X2) ) ).

cnf(i_0_1377_109,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_1378_110,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_1379_111,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_1380_112,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_1381_113,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X1,X3,X4)
    | c_Relation_Orefl__on(X2,X3,X4) ) ).

cnf(i_0_1382_114,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X1,X4)
    | c_Relation_Orefl__on(X3,X2,X4) ) ).

cnf(i_0_1383_115,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X4,X1)
    | c_Relation_Orefl__on(X3,X4,X2) ) ).

cnf(i_0_1384_116,axiom,
    ( X1 != X2
    | ~ c_Relation_Osym(X1,X3)
    | c_Relation_Osym(X2,X3) ) ).

cnf(i_0_1385_117,axiom,
    ( X1 != X2
    | ~ c_Relation_Osym(X3,X1)
    | c_Relation_Osym(X3,X2) ) ).

cnf(i_0_1386_118,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X1,X3,X4)
    | c_Relation_Osingle__valued(X2,X3,X4) ) ).

cnf(i_0_1387_119,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X1,X4)
    | c_Relation_Osingle__valued(X3,X2,X4) ) ).

cnf(i_0_1388_120,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X4,X1)
    | c_Relation_Osingle__valued(X3,X4,X2) ) ).

cnf(i_0_1389_121,axiom,
    ( X1 != X2
    | ~ c_Relation_Oantisym(X1,X3)
    | c_Relation_Oantisym(X2,X3) ) ).

cnf(i_0_1390_122,axiom,
    ( X1 != X2
    | ~ c_Relation_Oantisym(X3,X1)
    | c_Relation_Oantisym(X3,X2) ) ).

cnf(i_0_1391_123,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | c_Finite__Set_Ofinite(X2,X3) ) ).

cnf(i_0_1392_124,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | c_Finite__Set_Ofinite(X3,X2) ) ).

cnf(i_0_1393,plain,
    ( X1 = X1
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    inference(equality_inference,[],[780]) ).

cnf(i_0_1394,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X3,tc_bool)),X3,X4) ),
    inference(equality_inference,[],[782]) ).

cnf(i_0_1395,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    inference(equality_inference,[],[798]) ).

cnf(i_0_1396,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,X5)
    | ~ hBOOL(c_in(X1,X3,X4))
    | ~ hBOOL(c_in(X1,X3,X4)) ),
    inference(equality_inference,[],[837]) ).

cnf(i_0_1397,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    inference(equality_inference,[],[899]) ).

cnf(i_0_1398,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[1114]) ).

cnf(i_0_1399,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[1115]) ).

cnf(i_0_1400,plain,
    X1 = X1,
    inference(equality_inference,[],[1169]) ).

cnf(i_0_1401,plain,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    inference(equality_inference,[],[1186]) ).

cnf(i_0_1402,plain,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    inference(equality_inference,[],[1187]) ).

cnf(i_0_1403,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ogroup__add(X2) ),
    inference(equality_inference,[],[1228]) ).

cnf(i_0_1404,plain,
    ( X1 = X1
    | ~ class_Lattices_Oboolean__algebra(X2) ),
    inference(equality_inference,[],[1229]) ).

cnf(i_0_1405,plain,
    $false,
    inference(scs_inference,[],[i_0_952,i_0_1102,i_0_734]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SCT007-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.11  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32  % Computer : n029.cluster.edu
% 0.15/0.32  % Model    : x86_64 x86_64
% 0.15/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32  % Memory   : 8042.1875MB
% 0.15/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32  % CPULimit   : 300
% 0.15/0.32  % WCLimit    : 300
% 0.15/0.32  % DateTime   : Tue May  5 01:53:29 EDT 2026
% 0.15/0.32  % CPUTime    : 
% 0.15/0.33  % start to proof: theBenchmark
% 1.03/1.66  % Version  : CSE_E---1.7
% 1.03/1.66  % Problem  : theBenchmark.p
% 1.03/1.66  % SZS status Unsatisfiable for theBenchmark.p
% 1.03/1.66  % SZS output start CNFRefutation
% See solution above
% 1.09/1.72  % Total time : 1.326s
%------------------------------------------------------------------------------