TSTP Solution File: SWV829-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV829-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n016.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 : Thu Aug 31 21:48:19 EDT 2023
% Result : Unsatisfiable 219.29s 219.42s
% Output : CNFRefutation 219.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 136
% Syntax : Number of formulae : 221 ( 52 unt; 109 typ; 0 def)
% Number of atoms : 179 ( 30 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 115 ( 48 ~; 67 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 201 ( 94 >; 107 *; 0 +; 0 <<)
% Number of predicates : 55 ( 53 usr; 1 prp; 0-9 aty)
% Number of functors : 56 ( 56 usr; 15 con; 0-5 aty)
% Number of variables : 390 ( 130 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_23,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
tff(decl_24,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_25,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_26,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_27,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_28,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_29,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_30,type,
tc_bool: $i ).
tff(decl_31,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_32,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_33,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(decl_34,type,
c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
c_Set_Ovimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_36,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(decl_37,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(decl_38,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_39,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_40,type,
class_OrderedGroup_Olordered__ab__group__add__join: $i > $o ).
tff(decl_41,type,
c_HOL_Otimes__class_Otimes: $i > $i ).
tff(decl_42,type,
hBOOL: $i > $o ).
tff(decl_43,type,
c_Collect: ( $i * $i ) > $i ).
tff(decl_44,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
c_in: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(decl_47,type,
class_Lattices_Olattice: $i > $o ).
tff(decl_48,type,
t_a: $i ).
tff(decl_49,type,
v_x: $i ).
tff(decl_50,type,
c_Finite__Set_Ofold__graph: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_51,type,
c_HOL_Ominus__class_Ominus: $i > $i ).
tff(decl_52,type,
c_Finite__Set_Ocard: ( $i * $i ) > $i ).
tff(decl_53,type,
tc_nat: $i ).
tff(decl_54,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_55,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_56,type,
c_SetInterval_Oord__class_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(decl_57,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_58,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_59,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_60,type,
c_Complete__Lattice_Ocomplete__lattice: ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_61,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_62,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
tff(decl_63,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_64,type,
c_Finite__Set_Osetsum: ( $i * $i * $i * $i ) > $i ).
tff(decl_65,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_66,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
tff(decl_67,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
c_Complete__Lattice_OSup__class_OSup: ( $i * $i ) > $i ).
tff(decl_69,type,
class_HOL_Oord: $i > $o ).
tff(decl_70,type,
c_SetInterval_Oord__class_OlessThan: ( $i * $i ) > $i ).
tff(decl_71,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(decl_72,type,
c_Inductive_Ocomplete__lattice__class_Ogfp: ( $i * $i ) > $i ).
tff(decl_73,type,
c_Orderings_Oorder__class_Omono: ( $i * $i * $i ) > $o ).
tff(decl_74,type,
c_COMBC: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_75,type,
class_OrderedGroup_Olordered__ab__group__add__meet: $i > $o ).
tff(decl_76,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_77,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_78,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(decl_79,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_80,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(decl_81,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_82,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_83,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_84,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
tff(decl_85,type,
c_Fun_Ofun__upd: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_86,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_87,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: ( $i * $i * $i * $i ) > $i ).
tff(decl_88,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(decl_89,type,
c_OrderedGroup_Oab__semigroup__mult: ( $i * $i ) > $o ).
tff(decl_90,type,
tc_Option_Ooption: $i > $i ).
tff(decl_91,type,
c_Map_Orestrict__map: ( $i * $i * $i * $i ) > $i ).
tff(decl_92,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_93,type,
class_Orderings_Otop: $i > $o ).
tff(decl_94,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_95,type,
c_Finite__Set_Olinorder__class_OMin: ( $i * $i ) > $i ).
tff(decl_96,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_97,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_98,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_99,type,
c_Hoare__Mirabelle_Ohoare__derivs: ( $i * $i * $i ) > $o ).
tff(decl_100,type,
class_HOL_Ouminus: $i > $o ).
tff(decl_101,type,
c_fequal: ( $i * $i ) > $i ).
tff(decl_102,type,
c_The: ( $i * $i ) > $i ).
tff(decl_103,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(decl_104,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_105,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(decl_106,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: ( $i * $i * $i * $i ) > $i ).
tff(decl_107,type,
class_Orderings_Obot: $i > $o ).
tff(decl_108,type,
c_Nitpick_Osko__Nitpick__XEx1__def__1__3: ( $i * $i ) > $i ).
tff(decl_109,type,
c_Finite__Set_Ofold1Set: ( $i * $i * $i * $i ) > $o ).
tff(decl_110,type,
c_Nitpick_Ofold__graph_H: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_111,type,
c_COMBS: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_112,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
tff(decl_113,type,
class_HOL_Ominus: $i > $o ).
tff(decl_114,type,
c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_115,type,
c_ATP__Linkup_Osko__Inductive__Xgfp__least__1__1: ( $i * $i * $i ) > $i ).
tff(decl_116,type,
c_ATP__Linkup_Osko__Inductive__Xgfp__mono__1__1: ( $i * $i * $i ) > $i ).
tff(decl_117,type,
v_P: $i ).
tff(decl_118,type,
v_Q: $i ).
tff(decl_119,type,
t_b: $i ).
tff(decl_120,type,
t_c: $i ).
tff(decl_121,type,
v_R: $i ).
tff(decl_122,type,
c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_123,type,
c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_124,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i ).
tff(decl_125,type,
c_Com_Ocom_OBODY: $i ).
tff(decl_126,type,
v_pn: $i ).
tff(decl_127,type,
v_Procs: $i ).
tff(decl_128,type,
tc_Com_Opname: $i ).
tff(decl_129,type,
tc_Com_Ostate: $i ).
tff(decl_130,type,
tc_Com_Ocom: $i ).
cnf(cls_CollectD_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,c_Collect(X1,X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectD_0) ).
cnf(cls_Collect__def_0,axiom,
c_Collect(X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
cnf(cls_ComplI_0,axiom,
( hBOOL(c_in(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X2))
| hBOOL(c_in(X1,X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).
cnf(cls_double__complement_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).
cnf(cls_CollectI_0,axiom,
( hBOOL(c_in(X1,c_Collect(X2,X3),X3))
| ~ hBOOL(hAPP(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectI_0) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
cnf(cls_insert__mono_0,axiom,
( c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
cnf(cls_empty__subsetI_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
cnf(cls_insert__absorb_0,axiom,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_lessequals(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_pn)),hAPP(c_Com_Ocom_OBODY,v_pn)),hAPP(v_Q,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_subset__Un__eq_1,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
cnf(cls_insert__is__Un_0,axiom,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
cnf(cls_insert__subset_2,axiom,
( c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
cnf(cls_insert__code_2,axiom,
( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
cnf(cls_insert__subset_1,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X4,X1,X3),X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
cnf(cls_rev__predicate1D_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
cnf(cls_image__insert_0,axiom,
c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
cnf(cls_conjecture_0,negated_conjecture,
hBOOL(c_in(v_pn,v_Procs,tc_Com_Opname)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
cnf(cls_subset__image__iff_2,axiom,
( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
cnf(cls_subset__insertI_0,axiom,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
cnf(cls_insert__commute_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
cnf(cls_subset__trans_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
cnf(cls_ComplD_0,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplD_0) ).
cnf(cls_insert__subset_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
cnf(cls_COMBS__def_0,axiom,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBS__def_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
cnf(c_0_27,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,c_Collect(X1,X3),X3)) ),
cls_CollectD_0 ).
cnf(c_0_28,axiom,
c_Collect(X1,X2) = X1,
cls_Collect__def_0 ).
cnf(c_0_29,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,X1,X3)) ),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,axiom,
( hBOOL(c_in(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X2))
| hBOOL(c_in(X1,X3,X2)) ),
cls_ComplI_0 ).
cnf(c_0_31,plain,
( hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(c_in(X3,X2,X1)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
cls_double__complement_0 ).
cnf(c_0_33,axiom,
( hBOOL(c_in(X1,c_Collect(X2,X3),X3))
| ~ hBOOL(hAPP(X2,X1)) ),
cls_CollectI_0 ).
cnf(c_0_34,plain,
( hBOOL(c_in(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X2))
| hBOOL(hAPP(X3,X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(rw,[status(thm)],[c_0_33,c_0_28]) ).
cnf(c_0_36,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
cls_insert__code_1 ).
cnf(c_0_37,plain,
( hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(X2,X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_34]) ).
cnf(c_0_38,axiom,
( c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
cls_insert__mono_0 ).
cnf(c_0_39,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
cls_empty__subsetI_0 ).
cnf(c_0_40,axiom,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
cls_insert__absorb_0 ).
cnf(c_0_41,plain,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X4)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
( hBOOL(c_in(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X4))
| hBOOL(hAPP(X3,X1)) ),
inference(spm,[status(thm)],[c_0_35,c_0_37]) ).
cnf(c_0_43,plain,
c_lessequals(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),c_Set_Oinsert(X1,X3,X2),tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X4) = c_Set_Oinsert(X1,X2,X3),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
( hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(c_in(X3,X2,X4)) ),
inference(spm,[status(thm)],[c_0_42,c_0_32]) ).
cnf(c_0_46,plain,
c_lessequals(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),c_Set_Oinsert(X1,X3,X4),tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,plain,
( c_Set_Oinsert(X1,X2,X3) = X2
| hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X2),X1)) ),
inference(spm,[status(thm)],[c_0_40,c_0_45]) ).
cnf(c_0_48,negated_conjecture,
~ c_lessequals(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_pn)),hAPP(c_Com_Ocom_OBODY,v_pn)),hAPP(v_Q,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),
cls_conjecture_1 ).
cnf(c_0_49,plain,
( c_lessequals(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3,tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X3),X1)) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,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 ).
cnf(c_0_51,axiom,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,tc_fun(X3,tc_bool)),
cls_insert__is__Un_0 ).
cnf(c_0_52,negated_conjecture,
hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_pn)),hAPP(c_Com_Ocom_OBODY,v_pn)),hAPP(v_Q,v_pn)))),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
( c_lessequals(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3,tc_fun(X2,tc_bool))
| c_Set_Oinsert(X1,X3,X2) != X3 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
( c_Set_Oinsert(X1,X2,X3) = X2
| hBOOL(c_in(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X2),X5)) ),
inference(spm,[status(thm)],[c_0_35,c_0_47]) ).
cnf(c_0_55,axiom,
( c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X3)) ),
cls_insert__subset_2 ).
cnf(c_0_56,negated_conjecture,
hBOOL(c_in(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_pn)),hAPP(c_Com_Ocom_OBODY,v_pn)),hAPP(v_Q,v_pn)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),X2)),
inference(spm,[status(thm)],[c_0_35,c_0_52]) ).
cnf(c_0_57,plain,
( c_lessequals(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3,tc_fun(X2,tc_bool))
| hBOOL(c_in(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X3),X5)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,negated_conjecture,
( c_lessequals(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_pn)),hAPP(c_Com_Ocom_OBODY,v_pn)),hAPP(v_Q,v_pn)),X1,X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),tc_fun(X2,tc_bool)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_59,plain,
( c_lessequals(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X4),tc_fun(X2,tc_bool))
| hBOOL(c_in(X1,X4,X5)) ),
inference(spm,[status(thm)],[c_0_57,c_0_32]) ).
cnf(c_0_60,negated_conjecture,
( c_lessequals(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_pn)),hAPP(c_Com_Ocom_OBODY,v_pn)),hAPP(v_Q,v_pn)),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),tc_fun(X2,tc_bool))
| hBOOL(c_in(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),X4)) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_61,axiom,
( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
cls_insert__code_2 ).
cnf(c_0_62,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X4,X1,X3),X2,tc_fun(X3,tc_bool)) ),
cls_insert__subset_1 ).
cnf(c_0_63,negated_conjecture,
( c_Set_Oinsert(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),X2) = c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))
| c_lessequals(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_pn)),hAPP(c_Com_Ocom_OBODY,v_pn)),hAPP(v_Q,v_pn)),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),tc_fun(X3,tc_bool)) ),
inference(spm,[status(thm)],[c_0_40,c_0_60]) ).
cnf(c_0_64,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X5),X2)),
inference(spm,[status(thm)],[c_0_61,c_0_36]) ).
cnf(c_0_65,negated_conjecture,
( c_Set_Oinsert(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),X2) = c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))
| c_lessequals(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),tc_fun(X3,tc_bool)) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_66,axiom,
( hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X3,X2)) ),
cls_rev__predicate1D_0 ).
cnf(c_0_67,negated_conjecture,
( c_lessequals(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),tc_fun(X2,tc_bool))
| hBOOL(hAPP(c_Set_Oinsert(X4,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),X5),X1)) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_68,axiom,
c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
cls_image__insert_0 ).
cnf(c_0_69,negated_conjecture,
hBOOL(c_in(v_pn,v_Procs,tc_Com_Opname)),
cls_conjecture_0 ).
cnf(c_0_70,plain,
( hBOOL(hAPP(X1,X2))
| ~ c_lessequals(c_Set_Oinsert(X2,X3,X4),X1,tc_fun(X5,tc_bool)) ),
inference(spm,[status(thm)],[c_0_66,c_0_36]) ).
cnf(c_0_71,negated_conjecture,
( c_lessequals(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),tc_fun(X2,tc_bool))
| hBOOL(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(X4,v_Procs,tc_Com_Opname),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),X1)) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_72,negated_conjecture,
hBOOL(hAPP(v_Procs,v_pn)),
inference(spm,[status(thm)],[c_0_29,c_0_69]) ).
cnf(c_0_73,negated_conjecture,
( hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),X2))
| hBOOL(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(X3,v_Procs,tc_Com_Opname),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),X2)) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_74,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 ).
cnf(c_0_75,negated_conjecture,
hBOOL(c_in(v_pn,v_Procs,X1)),
inference(spm,[status(thm)],[c_0_35,c_0_72]) ).
cnf(c_0_76,negated_conjecture,
( hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),X2))
| hBOOL(c_in(X2,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(X3,v_Procs,tc_Com_Opname),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),X4)) ),
inference(spm,[status(thm)],[c_0_35,c_0_73]) ).
cnf(c_0_77,negated_conjecture,
hBOOL(c_in(hAPP(X1,v_pn),c_Set_Oimage(X1,v_Procs,X2,X3),X3)),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_78,negated_conjecture,
( c_Set_Oinsert(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(X2,v_Procs,tc_Com_Opname),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),X3) = c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(X2,v_Procs,tc_Com_Opname),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))
| hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),X1)) ),
inference(spm,[status(thm)],[c_0_40,c_0_76]) ).
cnf(c_0_79,plain,
hBOOL(c_in(X1,c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X5),X6)),
inference(spm,[status(thm)],[c_0_35,c_0_64]) ).
cnf(c_0_80,negated_conjecture,
hBOOL(hAPP(c_Set_Oimage(X1,v_Procs,X2,X3),hAPP(X1,v_pn))),
inference(spm,[status(thm)],[c_0_29,c_0_77]) ).
cnf(c_0_81,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 ).
cnf(c_0_82,axiom,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
cls_subset__insertI_0 ).
cnf(c_0_83,negated_conjecture,
( c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(X1,c_Set_Oinsert(X2,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)) = c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(X2,v_Procs,tc_Com_Opname),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))
| hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),hAPP(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),X1))) ),
inference(spm,[status(thm)],[c_0_68,c_0_78]) ).
cnf(c_0_84,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
cls_insert__commute_0 ).
cnf(c_0_85,plain,
c_lessequals(c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),c_Set_Oinsert(X1,c_Set_Oinsert(X2,X4,X5),X3),tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_38,c_0_46]) ).
cnf(c_0_86,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X5),X6) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X5),
inference(spm,[status(thm)],[c_0_40,c_0_79]) ).
cnf(c_0_87,negated_conjecture,
hBOOL(c_in(hAPP(X1,v_pn),c_Set_Oimage(X1,v_Procs,X2,X3),X4)),
inference(spm,[status(thm)],[c_0_35,c_0_80]) ).
cnf(c_0_88,plain,
c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,c_Set_Oinsert(X5,X2,X3),X3,X4),tc_fun(X4,tc_bool)),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_89,negated_conjecture,
( c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(X1,c_Set_Oinsert(X2,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)) = c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(X1,v_Procs,tc_Com_Opname),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))
| hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),hAPP(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),X2))) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_90,plain,
c_lessequals(c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),c_Set_Oinsert(X2,c_Set_Oinsert(X1,X4,X5),X6),tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_91,negated_conjecture,
c_Set_Oinsert(hAPP(X1,v_pn),c_Set_Oimage(X1,v_Procs,X2,X3),X4) = c_Set_Oimage(X1,v_Procs,X2,X3),
inference(spm,[status(thm)],[c_0_40,c_0_87]) ).
cnf(c_0_92,negated_conjecture,
( c_lessequals(c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(X1,v_Procs,tc_Com_Opname),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(X2,v_Procs,tc_Com_Opname),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),hAPP(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),X1))) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_93,negated_conjecture,
c_Set_Oinsert(v_pn,v_Procs,X1) = v_Procs,
inference(spm,[status(thm)],[c_0_40,c_0_75]) ).
cnf(c_0_94,negated_conjecture,
c_lessequals(c_Set_Oinsert(hAPP(X1,v_pn),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),c_Set_Oinsert(X2,c_Set_Oimage(X1,v_Procs,X4,X5),X6),tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_95,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 ).
cnf(c_0_96,negated_conjecture,
( c_lessequals(c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(X1,v_Procs,tc_Com_Opname),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),hAPP(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),X1))) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_97,negated_conjecture,
c_lessequals(c_Set_Oinsert(X1,c_Set_Oinsert(hAPP(X2,v_pn),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),c_Set_Oinsert(X1,c_Set_Oimage(X2,v_Procs,X4,X5),X6),tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_94,c_0_84]) ).
cnf(c_0_98,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),X3)) ),
cls_ComplD_0 ).
cnf(c_0_99,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
cls_insert__subset_0 ).
cnf(c_0_100,negated_conjecture,
( c_lessequals(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),hAPP(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),X3)))
| ~ c_lessequals(X1,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(X3,v_Procs,tc_Com_Opname),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_101,negated_conjecture,
c_lessequals(c_Set_Oinsert(hAPP(X1,X2),c_Set_Oinsert(hAPP(X1,v_pn),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),c_Set_Oimage(X1,c_Set_Oinsert(X2,v_Procs,X4),X4,X5),tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_97,c_0_68]) ).
cnf(c_0_102,axiom,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),hAPP(X2,X6)),
cls_COMBS__def_0 ).
cnf(c_0_103,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_COMBB__def_0 ).
cnf(c_0_104,negated_conjecture,
~ hBOOL(c_in(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_pn)),hAPP(c_Com_Ocom_OBODY,v_pn)),hAPP(v_Q,v_pn)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)))),X1)),
inference(spm,[status(thm)],[c_0_98,c_0_56]) ).
cnf(c_0_105,plain,
( hBOOL(c_in(X1,X2,X3))
| ~ c_lessequals(c_Set_Oinsert(X1,X4,X5),X2,tc_fun(X3,tc_bool)) ),
inference(spm,[status(thm)],[c_0_99,c_0_44]) ).
cnf(c_0_106,negated_conjecture,
( c_lessequals(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_pn)),hAPP(c_Com_Ocom_OBODY,v_pn)),hAPP(v_Q,v_pn)),c_Set_Oinsert(hAPP(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),hAPP(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]),c_0_102]),c_0_103]),c_0_84]) ).
cnf(c_0_107,negated_conjecture,
~ hBOOL(c_in(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_pn)),hAPP(c_Com_Ocom_OBODY,v_pn)),hAPP(v_Q,v_pn)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),X1)),
inference(spm,[status(thm)],[c_0_104,c_0_32]) ).
cnf(c_0_108,negated_conjecture,
hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),hAPP(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),X2))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]) ).
cnf(c_0_109,negated_conjecture,
~ hBOOL(c_in(hAPP(X1,v_pn),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Set_Oimage(X1,v_Procs,X3,X4)),X2)),
inference(spm,[status(thm)],[c_0_98,c_0_87]) ).
cnf(c_0_110,negated_conjecture,
hBOOL(c_in(hAPP(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a))),X3)),
inference(spm,[status(thm)],[c_0_35,c_0_108]) ).
cnf(c_0_111,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_109,c_0_110]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV829-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 05:38:15 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.55 start to proof: theBenchmark
% 219.29/219.42 % Version : CSE_E---1.5
% 219.29/219.42 % Problem : theBenchmark.p
% 219.29/219.42 % Proof found
% 219.29/219.42 % SZS status Theorem for theBenchmark.p
% 219.29/219.42 % SZS output start Proof
% See solution above
% 219.29/219.43 % Total time : 218.713000 s
% 219.29/219.43 % SZS output end Proof
% 219.29/219.43 % Total time : 218.748000 s
%------------------------------------------------------------------------------