TSTP Solution File: SCT030-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SCT030-1 : 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 : n010.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 14:10:48 EDT 2023
% Result : Unsatisfiable 4.58s 4.65s
% Output : CNFRefutation 4.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 158
% Syntax : Number of formulae : 357 ( 157 unt; 92 typ; 0 def)
% Number of atoms : 410 ( 172 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 304 ( 159 ~; 145 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 230 ( 84 >; 146 *; 0 +; 0 <<)
% Number of predicates : 31 ( 29 usr; 1 prp; 0-9 aty)
% Number of functors : 63 ( 63 usr; 8 con; 0-5 aty)
% Number of variables : 582 ( 174 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
tc_bool: $i ).
tff(decl_23,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_24,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i ) > $i ).
tff(decl_26,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_27,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_28,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(decl_29,type,
c_Set_Oimage: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_31,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i ) > $i ).
tff(decl_32,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(decl_33,type,
class_Orderings_Otop: $i > $o ).
tff(decl_34,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(decl_35,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(decl_36,type,
class_Lattices_Olattice: $i > $o ).
tff(decl_37,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_38,type,
c_Fun_Ofun__upd: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_39,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: ( $i * $i * $i * $i ) > $i ).
tff(decl_40,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: ( $i * $i * $i * $i ) > $i ).
tff(decl_41,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_42,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_43,type,
class_HOL_Oord: $i > $o ).
tff(decl_44,type,
c_HOL_Ominus__class_Ominus: ( $i * $i ) > $i ).
tff(decl_45,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(decl_46,type,
hBOOL: $i > $o ).
tff(decl_47,type,
c_Finite__Set_Ofold__graph: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_48,type,
c_Set_Oinsert: ( $i * $i ) > $i ).
tff(decl_49,type,
class_Orderings_Obot: $i > $o ).
tff(decl_50,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
tff(decl_51,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_52,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_53,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_54,type,
c_in: $i > $i ).
tff(decl_55,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
tff(decl_56,type,
c_COMBC: ( $i * $i * $i * $i ) > $i ).
tff(decl_57,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_58,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_59,type,
c_Not: $i ).
tff(decl_60,type,
c_Collect: ( $i * $i ) > $i ).
tff(decl_61,type,
c_Set_Ovimage: ( $i * $i * $i ) > $i ).
tff(decl_62,type,
c_Nitpick_Ofold__graph_H: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_63,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_64,type,
c_Finite__Set_Osetsum: ( $i * $i * $i * $i ) > $i ).
tff(decl_65,type,
c_ATP__Linkup_Osko__Set__Xbex__Un__1__3: ( $i * $i * $i * $i ) > $i ).
tff(decl_66,type,
c_fequal: $i > $i ).
tff(decl_67,type,
c_Typedef_Otype__definition: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_68,type,
c_Complete__Lattice_Ocomplete__lattice: ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_69,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(decl_70,type,
c_FuncSet_OPi: ( $i * $i * $i * $i ) > $i ).
tff(decl_71,type,
c_FuncSet_Osko__FuncSet__XfuncsetI__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_72,type,
c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_73,type,
c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_74,type,
c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_75,type,
tc_nat: $i ).
tff(decl_76,type,
c_ATP__Linkup_Osko__Set__Xset__insert__1__1: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
v_sko__Arrow__Order__Mirabelle__Xdictator__def__1: ( $i * $i ) > $i ).
tff(decl_78,type,
c_Arrow__Order__Mirabelle_Odictator: ( $i * $i ) > $o ).
tff(decl_79,type,
c_Fun_Ooverride__on: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_80,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_81,type,
c_ATP__Linkup_Osko__Set__Xbspec__1__1: ( $i * $i * $i ) > $i ).
tff(decl_82,type,
c_ATP__Linkup_Osko__Set__XbexCI__1__1: ( $i * $i * $i ) > $i ).
tff(decl_83,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
c_SetInterval_Oord_OatLeastLessThan: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_85,type,
c_SetInterval_Oord_OatLeastAtMost: ( $i * $i * $i * $i ) > $i ).
tff(decl_86,type,
c_SetInterval_Oord_OgreaterThanLessThan: ( $i * $i * $i * $i ) > $i ).
tff(decl_87,type,
c_SetInterval_Oord_OgreaterThanAtMost: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_88,type,
c_FuncSet_Osko__FuncSet__XextensionalityI__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_89,type,
c_FuncSet_Oextensional: ( $i * $i * $i ) > $i ).
tff(decl_90,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_91,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_92,type,
c_ATP__Linkup_Osko__Set__XbexI__1__1: ( $i * $i * $i ) > $i ).
tff(decl_93,type,
c_ATP__Linkup_Osko__Set__XbexE__1__1: ( $i * $i * $i ) > $i ).
tff(decl_94,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_95,type,
c_ATP__Linkup_Osko__Set__XballE__1__1: ( $i * $i * $i ) > $i ).
tff(decl_96,type,
c_SetInterval_Oord_OatMost: ( $i * $i * $i ) > $i ).
tff(decl_97,type,
c_SetInterval_Oord_OgreaterThan: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
c_SetInterval_Oord_OlessThan: ( $i * $i * $i ) > $i ).
tff(decl_99,type,
c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1: ( $i * $i * $i ) > $i ).
tff(decl_100,type,
c_FuncSet_Osko__FuncSet__XPi__I__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_101,type,
c_FuncSet_Osko__FuncSet__XPi__I_H__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_102,type,
c_HOL_Oundefined: $i > $i ).
tff(decl_103,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
tff(decl_104,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
tff(decl_105,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(decl_106,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_107,type,
v_sko__Arrow__Order__Mirabelle__XIIA__def__2: $i > $i ).
tff(decl_108,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
tff(decl_109,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
tff(decl_110,type,
v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2: $i > $i ).
tff(decl_111,type,
v_sko__Arrow__Order__Mirabelle__XIIA__def__3: $i > $i ).
tff(decl_112,type,
v_P____: $i ).
tff(decl_113,type,
v_Q____: $i ).
cnf(cls_Collect__neg__eq_0,axiom,
c_Collect(c_COMBB(c_Not,X1,tc_bool,tc_bool,X2),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Collect(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__neg__eq_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_Collect__mem__eq_0,axiom,
c_Collect(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
cnf(cls_vimage__Collect__eq_0,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),c_Collect(X4,X3)) = c_Collect(c_COMBB(X4,X1,X3,tc_bool,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Collect__eq_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(cls_COMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_vimage__const_1,axiom,
( hAPP(c_Set_Ovimage(c_COMBK(X1,X2,X3),X3,X2),X4) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X1),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_1) ).
cnf(cls_vimage__Compl_0,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X4)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Compl_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_bot__least_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
cnf(cls_le__funD_0,axiom,
( c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1)
| ~ class_HOL_Oord(X1)
| ~ c_lessequals(X2,X4,tc_fun(X5,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
cnf(cls_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(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
cnf(cls_ComplD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplD_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_order__antisym__conv_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(cls_le__infE_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
cnf(cls_DiffE_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X1,tc_bool)),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
cnf(cls_Diff__Compl_0,axiom,
hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Compl_0) ).
cnf(cls_CollectD_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectD_0) ).
cnf(cls_Int__commute_0,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X2,tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
cnf(cls_image__vimage__eq_0,axiom,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Ovimage(X1,X2,X3),X4)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).
cnf(cls_Compl__empty__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).
cnf(cls_CHAINED_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_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/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
cnf(cls_top__greatest_0,axiom,
( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
| ~ class_Orderings_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X1,tc_bool)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_CollectI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Collect(X3,X1)))
| ~ hBOOL(hAPP(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectI_0) ).
cnf(cls_xt1_I11_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
cnf(cls_UNIV__I_0,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
cnf(cls_Int__UNIV__left_0,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
cnf(cls_rangeI_0,axiom,
hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X2,X4,X1),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).
cnf(cls_le__supE_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X1),X2),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(cls_Diff__eq_0,axiom,
hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),X3) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__eq_0) ).
cnf(cls_xt1_I7_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
cnf(cls_Pi__I_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2)))
| hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X4,X5,X3,X1,X2)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_0) ).
cnf(cls_Compl__UNIV__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__UNIV__eq_0) ).
cnf(cls_ComplI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).
cnf(cls_compl__top__eq_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).
cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
cnf(cls_insert__absorb_0,axiom,
( hAPP(c_Set_Oinsert(X1,X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X2),X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
cnf(cls_compl__bot__eq_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).
cnf(cls_sup__top__right_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(cls_ball__conj__distrib_9,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X4,X1,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4))
| ~ hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X4,X5,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__conj__distrib_9) ).
cnf(cls_rev__bexI_1,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3)))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__bexI_1) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
cnf(cls_double__compl_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(cls_empty__Diff_0,axiom,
hAPP(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
cnf(cls_compl__inf__bot_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
cnf(cls_le__iff__inf_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
cnf(cls_sup__idem_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
cnf(cls_vimage__UNIV_0,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
cnf(cls_image__insert_0,axiom,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oinsert(X4,X2),X5)) = hAPP(c_Set_Oinsert(hAPP(X1,X4),X3),hAPP(c_Set_Oimage(X1,X2,X3),X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
cnf(cls_image__constant__conv_1,axiom,
( hAPP(c_Set_Oimage(c_COMBK(X1,X2,X3),X3,X2),X4) = hAPP(c_Set_Oinsert(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
cnf(cls_singleton__conv2_0,axiom,
c_Collect(hAPP(c_fequal(X1),X2),X1) = hAPP(c_Set_Oinsert(X2,X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
cnf(c_0_66,axiom,
c_Collect(c_COMBB(c_Not,X1,tc_bool,tc_bool,X2),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Collect(X1,X2)),
cls_Collect__neg__eq_0 ).
cnf(c_0_67,axiom,
c_Collect(X1,X2) = X1,
cls_Collect__def_0 ).
cnf(c_0_68,axiom,
c_Collect(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),X1) = X2,
cls_Collect__mem__eq_0 ).
cnf(c_0_69,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),c_Collect(X4,X3)) = c_Collect(c_COMBB(X4,X1,X3,tc_bool,X2),X2),
cls_vimage__Collect__eq_0 ).
cnf(c_0_70,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_COMBB__def_0 ).
cnf(c_0_71,plain,
c_COMBB(c_Not,X1,tc_bool,tc_bool,X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67]),c_0_67]) ).
cnf(c_0_72,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_73,plain,
hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2) = X2,
inference(rw,[status(thm)],[c_0_68,c_0_67]) ).
cnf(c_0_74,axiom,
( hAPP(c_Set_Ovimage(c_COMBK(X1,X2,X3),X3,X2),X4) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X1),X4)) ),
cls_vimage__const_1 ).
cnf(c_0_75,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),X4) = c_COMBB(X4,X1,X3,tc_bool,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_67]),c_0_67]) ).
cnf(c_0_76,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X4)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),
cls_vimage__Compl_0 ).
cnf(c_0_77,plain,
hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3) = hAPP(c_Not,hAPP(X2,X3)),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_78,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_79,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__least_0 ).
cnf(c_0_80,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_81,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 ).
cnf(c_0_82,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_83,axiom,
class_HOL_Oord(tc_bool),
clsarity_bool__HOL_Oord ).
cnf(c_0_84,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
cls_ComplD_0 ).
cnf(c_0_85,plain,
hAPP(hAPP(c_in(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_86,plain,
( c_COMBB(X1,c_COMBK(X2,X3,X4),X3,tc_bool,X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
inference(rw,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_87,plain,
c_COMBB(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3,X1,tc_bool,X4) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_COMBB(X2,X3,X1,tc_bool,X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_75]),c_0_75]) ).
cnf(c_0_88,plain,
hAPP(c_Not,hAPP(c_Not,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_77]) ).
cnf(c_0_89,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_90,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_order__antisym__conv_0 ).
cnf(c_0_91,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_92,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_93,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4),X1) ),
cls_le__infE_0 ).
cnf(c_0_94,plain,
c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),hAPP(X3,X2),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83])]) ).
cnf(c_0_95,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice ).
cnf(c_0_96,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X1,tc_bool)),X3))) ),
cls_DiffE_1 ).
cnf(c_0_97,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85]),c_0_85]) ).
cnf(c_0_98,plain,
( c_COMBB(X1,c_COMBK(X2,X3,X4),X3,tc_bool,X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| hBOOL(hAPP(X1,X2)) ),
inference(rw,[status(thm)],[c_0_86,c_0_85]) ).
cnf(c_0_99,plain,
c_COMBB(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(tc_bool,tc_bool)),c_Not),X1,tc_bool,tc_bool,X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_71]),c_0_78]) ).
cnf(c_0_100,plain,
hAPP(c_Not,hAPP(c_Not,X1)) = X1,
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_101,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92])]) ).
cnf(c_0_102,plain,
c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),X3,tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95])]) ).
cnf(c_0_103,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(X3,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_85]),c_0_85]) ).
cnf(c_0_104,axiom,
hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3),
cls_Diff__Compl_0 ).
cnf(c_0_105,plain,
( ~ hBOOL(hAPP(c_Not,hAPP(X1,X2)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(rw,[status(thm)],[c_0_97,c_0_77]) ).
cnf(c_0_106,plain,
( c_COMBK(X1,tc_bool,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_77]),c_0_100]) ).
cnf(c_0_107,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_108,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3))) ),
cls_CollectD_0 ).
cnf(c_0_109,plain,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X4)) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_110,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X2,tc_bool)),X1),
cls_Int__commute_0 ).
cnf(c_0_111,axiom,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Ovimage(X1,X2,X3),X4)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)))),
cls_image__vimage__eq_0 ).
cnf(c_0_112,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
cls_Compl__empty__eq_0 ).
cnf(c_0_113,plain,
( ~ hBOOL(hAPP(c_Not,X1))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_105,c_0_89]) ).
cnf(c_0_114,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_106]),c_0_107]) ).
cnf(c_0_115,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
inference(rw,[status(thm)],[c_0_108,c_0_67]) ).
cnf(c_0_116,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
cls_CHAINED_0 ).
cnf(c_0_117,plain,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),X4)) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_118,plain,
hAPP(c_Set_Oimage(X1,X2,X3),c_COMBB(X4,X1,X3,tc_bool,X2)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X3,tc_bool)),hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)))),
inference(rw,[status(thm)],[c_0_111,c_0_75]) ).
cnf(c_0_119,axiom,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
cls_subset__UNIV_0 ).
cnf(c_0_120,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2) = hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
inference(spm,[status(thm)],[c_0_77,c_0_112]) ).
cnf(c_0_121,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Not,X1)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_122,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_123,axiom,
( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
| ~ class_Orderings_Otop(X1) ),
cls_top__greatest_0 ).
cnf(c_0_124,axiom,
class_Orderings_Otop(tc_bool),
clsarity_bool__Orderings_Otop ).
cnf(c_0_125,plain,
( ~ hBOOL(hAPP(hAPP(c_Set_Oimage(X1,X2,X3),c_COMBB(X4,X1,X3,tc_bool,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X4),X5)) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_126,plain,
c_lessequals(hAPP(X1,X2),hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2)),tc_bool),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_119]),c_0_83])]),c_0_120]) ).
cnf(c_0_127,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X1,tc_bool)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
cls_disjoint__iff__not__equal_0 ).
cnf(c_0_128,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
cls_conjecture_0 ).
cnf(c_0_129,plain,
c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_130,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Collect(X3,X1)))
| ~ hBOOL(hAPP(X3,X2)) ),
cls_CollectI_0 ).
cnf(c_0_131,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_xt1_I11_J_0 ).
cnf(c_0_132,plain,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_bool),tc_bool),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_133,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))),
cls_UNIV__I_0 ).
cnf(c_0_134,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X2) = X2,
cls_Int__UNIV__left_0 ).
cnf(c_0_135,plain,
( ~ hBOOL(hAPP(hAPP(c_Set_Oimage(X1,X2,tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(tc_bool,tc_bool)),c_Not),X3)) ),
inference(spm,[status(thm)],[c_0_125,c_0_71]) ).
cnf(c_0_136,axiom,
hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X2,X4,X1),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool))))),
cls_rangeI_0 ).
cnf(c_0_137,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X1),X2),X3,X1) ),
cls_le__supE_1 ).
cnf(c_0_138,plain,
c_lessequals(hAPP(X1,X2),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),
inference(spm,[status(thm)],[c_0_126,c_0_107]) ).
cnf(c_0_139,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_140,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X3,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_85]),c_0_85]) ).
cnf(c_0_141,axiom,
hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),X3) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3)),
cls_Diff__eq_0 ).
cnf(c_0_142,negated_conjecture,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)),
inference(rw,[status(thm)],[c_0_128,c_0_85]) ).
cnf(c_0_143,plain,
( hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) = X1
| hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_114,c_0_129]) ).
cnf(c_0_144,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(rw,[status(thm)],[c_0_130,c_0_67]) ).
cnf(c_0_145,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
cls_xt1_I7_J_0 ).
cnf(c_0_146,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_bool)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_92])]) ).
cnf(c_0_147,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_133]),c_0_134]) ).
cnf(c_0_148,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2)))
| hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X4,X5,X3,X1,X2)),X4)) ),
cls_Pi__I_0 ).
cnf(c_0_149,plain,
( ~ hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X1,tc_bool),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(tc_bool,tc_bool)),c_Not),X3)) ),
inference(spm,[status(thm)],[c_0_135,c_0_78]) ).
cnf(c_0_150,plain,
hBOOL(hAPP(hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))),hAPP(X1,X4))),
inference(rw,[status(thm)],[c_0_136,c_0_85]) ).
cnf(c_0_151,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Compl__UNIV__eq_0 ).
cnf(c_0_152,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
cls_ComplI_0 ).
cnf(c_0_153,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__top__eq_0 ).
cnf(c_0_154,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra ).
cnf(c_0_155,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = X1
| ~ c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),X1,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_132]),c_0_92])]) ).
cnf(c_0_156,plain,
c_lessequals(X1,hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_139])]) ).
cnf(c_0_157,plain,
( hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_158,negated_conjecture,
hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_159,plain,
hBOOL(hAPP(hAPP(c_in(X1),v_P____),c_Arrow__Order__Mirabelle_OProf)),
inference(spm,[status(thm)],[c_0_144,c_0_122]) ).
cnf(c_0_160,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_bool)
| c_HOL_Oord__class_Oless(X2,c_Orderings_Otop__class_Otop(tc_bool),tc_bool)
| ~ c_lessequals(X2,X1,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_92])]) ).
cnf(c_0_161,plain,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2)))
| X4 != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_162,axiom,
( hAPP(c_Set_Oinsert(X1,X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X2),X1),X3)) ),
cls_insert__absorb_0 ).
cnf(c_0_163,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__bot__eq_0 ).
cnf(c_0_164,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(tc_bool,tc_bool)),c_Not),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_151]) ).
cnf(c_0_165,plain,
( hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_85]),c_0_85]) ).
cnf(c_0_166,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_167,plain,
c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_168,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__top__right_0 ).
cnf(c_0_169,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_170,plain,
( hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(c_Not,hAPP(X3,X4)))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(rw,[status(thm)],[c_0_157,c_0_77]) ).
cnf(c_0_171,negated_conjecture,
hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),
inference(spm,[status(thm)],[c_0_100,c_0_158]) ).
cnf(c_0_172,plain,
( hAPP(c_Not,X1) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_129]),c_0_158]) ).
cnf(c_0_173,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____) = X1
| hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_143,c_0_158]) ).
cnf(c_0_174,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Arrow__Order__Mirabelle_OProf,
inference(spm,[status(thm)],[c_0_147,c_0_159]) ).
cnf(c_0_175,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_bool)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Otop__class_Otop(tc_bool),tc_bool) ),
inference(spm,[status(thm)],[c_0_160,c_0_91]) ).
cnf(c_0_176,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X4,X1,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4))
| ~ hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X4,X5,X3))) ),
cls_ball__conj__distrib_9 ).
cnf(c_0_177,plain,
( hBOOL(hAPP(c_FuncSet_OPi(X1,X2,X3,X4),X5))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(rw,[status(thm)],[c_0_161,c_0_85]) ).
cnf(c_0_178,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3)))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
cls_rev__bexI_1 ).
cnf(c_0_179,axiom,
hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1)),
cls_insert__code_1 ).
cnf(c_0_180,plain,
( hAPP(c_Set_Oinsert(X1,X2),X3) = X3
| ~ hBOOL(hAPP(X3,X1)) ),
inference(rw,[status(thm)],[c_0_162,c_0_85]) ).
cnf(c_0_181,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_163,c_0_154]) ).
cnf(c_0_182,plain,
hBOOL(hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2))),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_183,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_double__compl_0 ).
cnf(c_0_184,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) = c_Orderings_Obot__class_Obot(tc_bool),
inference(rw,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_185,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_186,negated_conjecture,
( hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),c_Arrow__Order__Mirabelle_OProf) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(X1,v_Q____)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_122])]) ).
cnf(c_0_187,axiom,
hAPP(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_empty__Diff_0 ).
cnf(c_0_188,plain,
( hAPP(c_Not,X1) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____) = X1 ),
inference(spm,[status(thm)],[c_0_172,c_0_173]) ).
cnf(c_0_189,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__inf__bot_0 ).
cnf(c_0_190,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_less__le__not__le_1 ).
cnf(c_0_191,plain,
c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Otop__class_Otop(tc_bool),tc_bool),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_175]) ).
cnf(c_0_192,axiom,
class_Orderings_Opreorder(tc_bool),
clsarity_bool__Orderings_Opreorder ).
cnf(c_0_193,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X1,X2,X3)))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X1,X5,X3)))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_176,c_0_85]),c_0_85]) ).
cnf(c_0_194,plain,
hBOOL(hAPP(c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,X3),X4)),
inference(er,[status(thm)],[c_0_177]) ).
cnf(c_0_195,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Arrow__Order__Mirabelle_OProf,X1,X2)))
| ~ hBOOL(hAPP(X1,v_P____)) ),
inference(spm,[status(thm)],[c_0_178,c_0_159]) ).
cnf(c_0_196,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_Set_Oinsert(X2,X3),X4))),
inference(spm,[status(thm)],[c_0_144,c_0_179]) ).
cnf(c_0_197,plain,
( hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),X1),c_HOL_Ouminus__class_Ouminus(tc_bool)) = c_HOL_Ouminus__class_Ouminus(tc_bool)
| ~ hBOOL(c_Orderings_Otop__class_Otop(tc_bool)) ),
inference(spm,[status(thm)],[c_0_180,c_0_181]) ).
cnf(c_0_198,plain,
hBOOL(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),
inference(spm,[status(thm)],[c_0_182,c_0_107]) ).
cnf(c_0_199,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) = X1,
inference(spm,[status(thm)],[c_0_183,c_0_154]) ).
cnf(c_0_200,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_184,c_0_129]),c_0_100]),c_0_129]),c_0_158]) ).
cnf(c_0_201,plain,
( hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),X1),c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool)
| ~ hBOOL(c_Orderings_Otop__class_Otop(tc_bool)) ),
inference(spm,[status(thm)],[c_0_180,c_0_185]) ).
cnf(c_0_202,negated_conjecture,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),v_Q____)),
inference(spm,[status(thm)],[c_0_186,c_0_187]) ).
cnf(c_0_203,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____) = X1
| hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_188]),c_0_171]) ).
cnf(c_0_204,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) != X2 ),
cls_le__iff__inf_1 ).
cnf(c_0_205,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),tc_bool),X1) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_189,c_0_154]) ).
cnf(c_0_206,plain,
~ c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_192])]) ).
cnf(c_0_207,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X1,X2,X3)))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_208,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf,X1))),
inference(spm,[status(thm)],[c_0_195,c_0_122]) ).
cnf(c_0_209,plain,
hAPP(c_Set_Oinsert(X1,X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
inference(spm,[status(thm)],[c_0_147,c_0_196]) ).
cnf(c_0_210,plain,
hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),X1),c_HOL_Ouminus__class_Ouminus(tc_bool)) = c_HOL_Ouminus__class_Ouminus(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_197,c_0_167]),c_0_198])]) ).
cnf(c_0_211,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_212,plain,
hAPP(c_Set_Oinsert(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),X1),c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_201,c_0_167]),c_0_167]),c_0_198])]) ).
cnf(c_0_213,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)
| ~ hBOOL(hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),v_Q____)) ),
inference(spm,[status(thm)],[c_0_202,c_0_203]) ).
cnf(c_0_214,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__idem_0 ).
cnf(c_0_215,plain,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),X1,tc_bool)
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_205]),c_0_95])]) ).
cnf(c_0_216,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[c_0_181,c_0_167]) ).
cnf(c_0_217,plain,
~ c_lessequals(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_bool),
inference(rw,[status(thm)],[c_0_206,c_0_167]) ).
cnf(c_0_218,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
cls_vimage__UNIV_0 ).
cnf(c_0_219,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0 ).
cnf(c_0_220,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf,X2)))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(c_Arrow__Order__Mirabelle_OProf,X1,X3))) ),
inference(spm,[status(thm)],[c_0_207,c_0_208]) ).
cnf(c_0_221,plain,
c_HOL_Ouminus__class_Ouminus(tc_bool) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_209,c_0_210]) ).
cnf(c_0_222,plain,
( hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)
| c_HOL_Ouminus__class_Ouminus(tc_bool) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) ),
inference(spm,[status(thm)],[c_0_211,c_0_203]) ).
cnf(c_0_223,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_209,c_0_212]) ).
cnf(c_0_224,negated_conjecture,
( hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),v_Q____) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) ),
inference(spm,[status(thm)],[c_0_213,c_0_173]) ).
cnf(c_0_225,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X1) = X1,
inference(spm,[status(thm)],[c_0_214,c_0_139]) ).
cnf(c_0_226,plain,
hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) != c_Orderings_Obot__class_Obot(tc_bool),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_216]),c_0_217]) ).
cnf(c_0_227,plain,
c_COMBB(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,tc_bool,X3) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
inference(rw,[status(thm)],[c_0_218,c_0_75]) ).
cnf(c_0_228,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(c_Arrow__Order__Mirabelle_OProf,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2))),
inference(spm,[status(thm)],[c_0_219,c_0_220]) ).
cnf(c_0_229,plain,
( hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) ),
inference(spm,[status(thm)],[c_0_221,c_0_222]) ).
cnf(c_0_230,negated_conjecture,
( hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),v_Q____) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)
| c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool) != hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) ),
inference(spm,[status(thm)],[c_0_223,c_0_224]) ).
cnf(c_0_231,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)
| hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),X1) = X1 ),
inference(spm,[status(thm)],[c_0_225,c_0_203]) ).
cnf(c_0_232,plain,
hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) != hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_226,c_0_129]),c_0_100]),c_0_129]) ).
cnf(c_0_233,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),hAPP(X4,X2)),
inference(spm,[status(thm)],[c_0_70,c_0_227]) ).
cnf(c_0_234,plain,
hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(c_Arrow__Order__Mirabelle_OProf,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),X3),c_Arrow__Order__Mirabelle_OProf) = c_Arrow__Order__Mirabelle_OProf,
inference(spm,[status(thm)],[c_0_180,c_0_228]) ).
cnf(c_0_235,negated_conjecture,
( hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)
| hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),v_Q____) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____) ),
inference(spm,[status(thm)],[c_0_229,c_0_224]) ).
cnf(c_0_236,negated_conjecture,
( hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),v_Q____) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)
| hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),X1) = X1 ),
inference(spm,[status(thm)],[c_0_230,c_0_231]) ).
cnf(c_0_237,plain,
hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____) != hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),
inference(rw,[status(thm)],[c_0_232,c_0_158]) ).
cnf(c_0_238,axiom,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oinsert(X4,X2),X5)) = hAPP(c_Set_Oinsert(hAPP(X1,X4),X3),hAPP(c_Set_Oimage(X1,X2,X3),X5)),
cls_image__insert_0 ).
cnf(c_0_239,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Arrow__Order__Mirabelle_OProf) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),c_Arrow__Order__Mirabelle_OProf),
inference(spm,[status(thm)],[c_0_233,c_0_234]) ).
cnf(c_0_240,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
cnf(c_0_241,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[c_0_120,c_0_107]) ).
cnf(c_0_242,negated_conjecture,
hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),v_Q____) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_236]),c_0_237]) ).
cnf(c_0_243,plain,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oinsert(X4,X2),X5)) != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),
inference(spm,[status(thm)],[c_0_209,c_0_238]) ).
cnf(c_0_244,plain,
hAPP(c_Set_Oinsert(c_Arrow__Order__Mirabelle_OProf,X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_239]),c_0_240])]) ).
cnf(c_0_245,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_241,c_0_129]),c_0_100]) ).
cnf(c_0_246,negated_conjecture,
( hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____) = X1
| hAPP(X1,v_Q____) = X1 ),
inference(spm,[status(thm)],[c_0_242,c_0_203]) ).
cnf(c_0_247,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)))),
inference(spm,[status(thm)],[c_0_144,c_0_240]) ).
cnf(c_0_248,plain,
hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),
inference(spm,[status(thm)],[c_0_243,c_0_244]) ).
cnf(c_0_249,negated_conjecture,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),
inference(spm,[status(thm)],[c_0_245,c_0_246]) ).
cnf(c_0_250,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_147,c_0_247]) ).
cnf(c_0_251,plain,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
inference(rw,[status(thm)],[c_0_248,c_0_249]) ).
cnf(c_0_252,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),
inference(rw,[status(thm)],[c_0_250,c_0_249]) ).
cnf(c_0_253,plain,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) != hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_203]),c_0_252]) ).
cnf(c_0_254,axiom,
( hAPP(c_Set_Oimage(c_COMBK(X1,X2,X3),X3,X2),X4) = hAPP(c_Set_Oinsert(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_image__constant__conv_1 ).
cnf(c_0_255,axiom,
c_Collect(hAPP(c_fequal(X1),X2),X1) = hAPP(c_Set_Oinsert(X2,X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),
cls_singleton__conv2_0 ).
cnf(c_0_256,plain,
hAPP(c_Set_Oinsert(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) != hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_253,c_0_254]),c_0_252]) ).
cnf(c_0_257,plain,
hAPP(c_fequal(X1),X2) = hAPP(c_Set_Oinsert(X2,X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),
inference(rw,[status(thm)],[c_0_255,c_0_67]) ).
cnf(c_0_258,plain,
hAPP(c_fequal(X1),X2) != hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),
inference(spm,[status(thm)],[c_0_256,c_0_257]) ).
cnf(c_0_259,negated_conjecture,
c_fequal(X1) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_258,c_0_246]),c_0_203]) ).
cnf(c_0_260,plain,
( hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)
| hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____) ),
inference(spm,[status(thm)],[c_0_200,c_0_222]) ).
cnf(c_0_261,plain,
hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),X1) != hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),
inference(rw,[status(thm)],[c_0_258,c_0_259]) ).
cnf(c_0_262,plain,
hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)) = hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____),
inference(sr,[status(thm)],[c_0_260,c_0_261]) ).
cnf(c_0_263,plain,
hAPP(c_Set_Oinsert(X1,X2),hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)) != hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_256,c_0_203]),c_0_252]) ).
cnf(c_0_264,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_262]),c_0_122])]),c_0_263]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SCT030-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 15:20:05 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.59 start to proof: theBenchmark
% 4.58/4.65 % Version : CSE_E---1.5
% 4.58/4.65 % Problem : theBenchmark.p
% 4.58/4.65 % Proof found
% 4.58/4.65 % SZS status Theorem for theBenchmark.p
% 4.58/4.65 % SZS output start Proof
% See solution above
% 4.62/4.67 % Total time : 4.031000 s
% 4.62/4.67 % SZS output end Proof
% 4.62/4.67 % Total time : 4.054000 s
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