TSTP Solution File: SCT006-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SCT006-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n014.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 14:10:43 EDT 2023
% Result : Unsatisfiable 55.85s 55.83s
% Output : CNFRefutation 55.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 129
% Syntax : Number of formulae : 276 ( 100 unt; 90 typ; 0 def)
% Number of atoms : 291 ( 123 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 218 ( 113 ~; 105 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 245 ( 84 >; 161 *; 0 +; 0 <<)
% Number of predicates : 29 ( 27 usr; 1 prp; 0-9 aty)
% Number of functors : 63 ( 63 usr; 6 con; 0-5 aty)
% Number of variables : 461 ( 153 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(decl_23,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_24,type,
c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).
tff(decl_25,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_26,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_27,type,
tc_bool: $i ).
tff(decl_28,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_29,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(decl_31,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(decl_32,type,
class_Lattices_Olattice: $i > $o ).
tff(decl_33,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_34,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_35,type,
c_Fun_Ofun__upd: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_36,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_37,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_38,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_39,type,
class_HOL_Oord: $i > $o ).
tff(decl_40,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(decl_42,type,
hBOOL: $i > $o ).
tff(decl_43,type,
c_Relation_OImage: ( $i * $i * $i * $i ) > $i ).
tff(decl_44,type,
c_Finite__Set_Ofold__graph: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_45,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
class_Orderings_Obot: $i > $o ).
tff(decl_47,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
tff(decl_48,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_49,type,
c_Relation_Oconverse: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_51,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_52,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: ( $i * $i * $i * $i ) > $i ).
tff(decl_53,type,
c_in: $i > $i ).
tff(decl_54,type,
c_Equiv__Relations_Oequiv: ( $i * $i * $i ) > $o ).
tff(decl_55,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_56,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_57,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
tff(decl_58,type,
c_COMBC: ( $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
c_Complete__Lattice_OSup__class_OSup: ( $i * $i ) > $i ).
tff(decl_60,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_61,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_62,type,
c_Complete__Lattice_OInf__class_OInf: ( $i * $i ) > $i ).
tff(decl_63,type,
c_Not: $i ).
tff(decl_64,type,
c_Collect: ( $i * $i ) > $i ).
tff(decl_65,type,
c_Set_Ovimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_66,type,
c_Set_OPow: ( $i * $i ) > $i ).
tff(decl_67,type,
c_Equiv__Relations_Oquotient: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
c_Nitpick_Ofold__graph_H: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_69,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_70,type,
c_Finite__Set_Osetsum: ( $i * $i * $i * $i ) > $i ).
tff(decl_71,type,
c_ATP__Linkup_Osko__Set__Xbex__Un__1__3: ( $i * $i * $i * $i ) > $i ).
tff(decl_72,type,
c_fequal: $i > $i ).
tff(decl_73,type,
c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
c_List_Osko__Equiv__Relations__XquotientE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_75,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
c_FuncSet_OPi: ( $i * $i * $i * $i ) > $i ).
tff(decl_77,type,
c_FuncSet_Osko__FuncSet__XfuncsetI__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_78,type,
tc_nat: $i ).
tff(decl_79,type,
c_Typedef_Otype__definition: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_80,type,
c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1: ( $i * $i * $i ) > $i ).
tff(decl_81,type,
c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1: ( $i * $i * $i ) > $i ).
tff(decl_82,type,
c_Complete__Lattice_Ocomplete__lattice: ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_83,type,
c_Fun_Ooverride__on: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_84,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_85,type,
c_ATP__Linkup_Osko__Set__Xbspec__1__1: ( $i * $i * $i ) > $i ).
tff(decl_86,type,
c_ATP__Linkup_Osko__Set__XbexCI__1__1: ( $i * $i * $i ) > $i ).
tff(decl_87,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3: ( $i * $i * $i ) > $i ).
tff(decl_88,type,
c_SetInterval_Oord_OatLeastLessThan: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_89,type,
c_SetInterval_Oord_OatLeastAtMost: ( $i * $i * $i * $i ) > $i ).
tff(decl_90,type,
c_SetInterval_Oord_OgreaterThanLessThan: ( $i * $i * $i * $i ) > $i ).
tff(decl_91,type,
c_SetInterval_Oord_OgreaterThanAtMost: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_92,type,
c_FuncSet_Osko__FuncSet__XextensionalityI__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_93,type,
c_FuncSet_Oextensional: ( $i * $i * $i ) > $i ).
tff(decl_94,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_95,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_96,type,
c_ATP__Linkup_Osko__Set__XbexI__1__1: ( $i * $i * $i ) > $i ).
tff(decl_97,type,
c_ATP__Linkup_Osko__Set__XbexE__1__1: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_99,type,
c_ATP__Linkup_Osko__Set__XballE__1__1: ( $i * $i * $i ) > $i ).
tff(decl_100,type,
c_SetInterval_Oord_OatMost: ( $i * $i * $i ) > $i ).
tff(decl_101,type,
c_SetInterval_Oord_OgreaterThan: ( $i * $i * $i ) > $i ).
tff(decl_102,type,
c_SetInterval_Oord_OlessThan: ( $i * $i * $i ) > $i ).
tff(decl_103,type,
c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1: ( $i * $i * $i ) > $i ).
tff(decl_104,type,
c_FuncSet_Osko__FuncSet__XPi__I__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_105,type,
c_FuncSet_Osko__FuncSet__XPi__I_H__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_106,type,
c_HOL_Oundefined: $i > $i ).
tff(decl_107,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(decl_108,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
tff(decl_109,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(decl_110,type,
v_sko__CHAINED__1: $i ).
tff(decl_111,type,
c_Order__Relation_Owell__order__on: ( $i * $i * $i ) > $o ).
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/sandbox2/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
cnf(cls_Collect__def_0,axiom,
c_Collect(X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_insert__def_0,axiom,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3),X2,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__def_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_Pi__I_H_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_H__1__1(X4,X5,X3,X1,X2)),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pi__I_H_0) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
cnf(cls_singleton__conv2_0,axiom,
c_Collect(hAPP(c_fequal(X1),X2),X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
cnf(cls_funcset__image_0,axiom,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X1),c_FuncSet_OPi(X2,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funcset__image_0) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_vimage__Collect__eq_0,axiom,
c_Set_Ovimage(X1,c_Collect(X2,X3),X4,X3) = c_Collect(c_COMBB(X2,X1,X3,tc_bool,X4),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Collect__eq_0) ).
cnf(cls_CollectD_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectD_0) ).
cnf(cls_image__constant__conv_1,axiom,
( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
cnf(cls_Un__empty__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
cnf(cls_vimage__Compl_0,axiom,
c_Set_Ovimage(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X4,X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_Set_Ovimage(X1,X3,X4,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Collect__neg__eq_0) ).
cnf(cls_Pow__top_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Set_OPow(X2,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pow__top_0) ).
cnf(cls_subset__Compl__self__eq_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).
cnf(cls_Int__absorb_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
cnf(cls_vimage__const_1,axiom,
( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X1),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__const_1) ).
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/sandbox2/benchmark/theBenchmark.p',cls_double__complement_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
cnf(cls_empty__subsetI_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_bot__least_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_ComplD_0) ).
cnf(cls_order__antisym__conv_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
cnf(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/sandbox2/benchmark/theBenchmark.p',cls_ComplI_0) ).
cnf(cls_ord_OlessThan__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OlessThan(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(X3,X2),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OlessThan__iff_1) ).
cnf(cls_Pow__bottom_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Set_OPow(X2,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pow__bottom_0) ).
cnf(cls_Diff__eq_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__eq_0) ).
cnf(cls_Diff__cancel_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
cnf(c_0_39,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_40,axiom,
c_Collect(X1,X2) = X1,
cls_Collect__def_0 ).
cnf(c_0_41,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_42,plain,
hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2) = X2,
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,axiom,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3),X2,tc_fun(X3,tc_bool)),
cls_insert__def_0 ).
cnf(c_0_44,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)),
cls_conjecture_0 ).
cnf(c_0_45,plain,
hAPP(hAPP(c_in(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,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_H__1__1(X4,X5,X3,X1,X2)),X4)) ),
cls_Pi__I_H_0 ).
cnf(c_0_47,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
cls_disjoint__iff__not__equal_0 ).
cnf(c_0_48,axiom,
c_Collect(hAPP(c_fequal(X1),X2),X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
cls_singleton__conv2_0 ).
cnf(c_0_49,plain,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X2,tc_fun(X3,tc_bool)),
inference(rw,[status(thm)],[c_0_43,c_0_40]) ).
cnf(c_0_50,axiom,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X1),c_FuncSet_OPi(X2,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4))) ),
cls_funcset__image_0 ).
cnf(c_0_51,negated_conjecture,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X1)),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,plain,
( hBOOL(hAPP(X1,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X1,X2,X3,X4,X5)))
| hBOOL(hAPP(c_FuncSet_OPi(X1,X2,X4,X5),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_45]),c_0_45]) ).
cnf(c_0_53,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X2,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_45]),c_0_45]) ).
cnf(c_0_54,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
cls_ATP__Linkup_Oequal__imp__fequal_0 ).
cnf(c_0_55,axiom,
c_Set_Ovimage(X1,c_Collect(X2,X3),X4,X3) = c_Collect(c_COMBB(X2,X1,X3,tc_bool,X4),X4),
cls_vimage__Collect__eq_0 ).
cnf(c_0_56,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3))) ),
cls_CollectD_0 ).
cnf(c_0_57,axiom,
( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_image__constant__conv_1 ).
cnf(c_0_58,plain,
hAPP(c_fequal(X1),X2) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_40]),c_0_49]) ).
cnf(c_0_59,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
cls_Un__empty__right_0 ).
cnf(c_0_60,plain,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(c_FuncSet_OPi(X2,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4),X1)) ),
inference(rw,[status(thm)],[c_0_50,c_0_45]) ).
cnf(c_0_61,negated_conjecture,
hBOOL(hAPP(c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OLin,X1,X2,X3),X4)),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_62,plain,
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_fequal(X1),X2),X3,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_63,axiom,
c_Set_Ovimage(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X4,X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_Set_Ovimage(X1,X3,X4,X2)),
cls_vimage__Compl_0 ).
cnf(c_0_64,plain,
c_Set_Ovimage(X1,X2,X4,X3) = c_COMBB(X2,X1,X3,tc_bool,X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_40]),c_0_40]) ).
cnf(c_0_65,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_66,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
inference(rw,[status(thm)],[c_0_56,c_0_40]) ).
cnf(c_0_67,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),X2),c_Set_OPow(X2,X1))),
cls_Pow__top_0 ).
cnf(c_0_68,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
inference(rw,[status(thm)],[c_0_57,c_0_49]) ).
cnf(c_0_69,plain,
hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2) = hAPP(c_fequal(X1),X2),
inference(rw,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_70,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool)) ),
cls_subset__Compl__self__eq_0 ).
cnf(c_0_71,negated_conjecture,
c_lessequals(c_Set_Oimage(X1,c_Arrow__Order__Mirabelle_OLin,X2,X3),X4,tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_72,plain,
c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_fequal(X1),X2),hAPP(c_fequal(X3),X2),tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
inference(spm,[status(thm)],[c_0_62,c_0_54]) ).
cnf(c_0_73,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
cls_Int__absorb_0 ).
cnf(c_0_74,axiom,
( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = 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,
c_COMBB(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X1,X2,tc_bool,X4) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_COMBB(X3,X1,X2,tc_bool,X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64]),c_0_64]) ).
cnf(c_0_76,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_65,c_0_40]),c_0_40]) ).
cnf(c_0_77,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_78,plain,
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_in(X1),X2),X3,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X5,X2))
| ~ hBOOL(hAPP(X3,X5)) ),
inference(spm,[status(thm)],[c_0_53,c_0_45]) ).
cnf(c_0_79,plain,
hBOOL(hAPP(c_Set_OPow(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_80,plain,
( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = hAPP(c_fequal(X2),X1)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69]),c_0_59]) ).
cnf(c_0_81,negated_conjecture,
c_Set_Oimage(X1,c_Arrow__Order__Mirabelle_OLin,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_82,plain,
hAPP(c_fequal(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_83,plain,
( c_COMBB(X4,c_COMBK(X1,X2,X3),X2,tc_bool,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X1),X4)) ),
inference(rw,[status(thm)],[c_0_74,c_0_64]) ).
cnf(c_0_84,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_COMBB__def_0 ).
cnf(c_0_85,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_75,c_0_76]),c_0_77]) ).
cnf(c_0_86,plain,
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_in(X1),X2),X3,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X3,c_Set_OPow(X2,X5))) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_87,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_88,negated_conjecture,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Arrow__Order__Mirabelle_OLin,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_89,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_83,c_0_45]) ).
cnf(c_0_90,plain,
hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(tc_bool,tc_bool)),c_Not),hAPP(X1,X2)) = hAPP(X1,X2),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_91,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_92,plain,
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_in(X1),X2),hAPP(c_in(X3),X4),tc_fun(X5,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(hAPP(c_Set_OPow(X2,X6),X4)) ),
inference(spm,[status(thm)],[c_0_86,c_0_45]) ).
cnf(c_0_93,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__least_0 ).
cnf(c_0_94,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_95,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_96,plain,
c_lessequals(c_Arrow__Order__Mirabelle_OLin,X1,tc_fun(X2,tc_bool)),
inference(rw,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_97,axiom,
class_HOL_Oord(tc_bool),
clsarity_bool__HOL_Oord ).
cnf(c_0_98,plain,
( c_COMBB(X1,c_COMBK(X2,X3,X4),X3,tc_bool,X4) = c_Arrow__Order__Mirabelle_OLin
| hBOOL(hAPP(X1,X2)) ),
inference(rw,[status(thm)],[c_0_89,c_0_88]) ).
cnf(c_0_99,plain,
hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(tc_bool,tc_bool)),c_Not),X1) = X1,
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_100,plain,
c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_in(X1),X2),hAPP(c_in(X3),X2),tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
inference(spm,[status(thm)],[c_0_92,c_0_79]) ).
cnf(c_0_101,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_102,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_103,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_104,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_105,plain,
c_lessequals(hAPP(c_Arrow__Order__Mirabelle_OLin,X1),hAPP(X2,X1),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97])]) ).
cnf(c_0_106,plain,
( c_COMBK(X1,tc_bool,X2) = c_Arrow__Order__Mirabelle_OLin
| hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_98]),c_0_99]) ).
cnf(c_0_107,plain,
hAPP(c_in(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_100,c_0_73]) ).
cnf(c_0_108,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_101,c_0_45]),c_0_45]) ).
cnf(c_0_109,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_102,c_0_103]),c_0_104])]) ).
cnf(c_0_110,plain,
c_lessequals(hAPP(c_Arrow__Order__Mirabelle_OLin,X1),X2,tc_bool),
inference(spm,[status(thm)],[c_0_105,c_0_91]) ).
cnf(c_0_111,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0 ).
cnf(c_0_112,plain,
( hAPP(c_Arrow__Order__Mirabelle_OLin,X1) = X2
| hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_91,c_0_106]) ).
cnf(c_0_113,plain,
hAPP(c_in(X1),X2) != c_Arrow__Order__Mirabelle_OLin,
inference(rw,[status(thm)],[c_0_107,c_0_88]) ).
cnf(c_0_114,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(tc_bool,tc_bool)),c_Not)),X2))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_108,c_0_99]) ).
cnf(c_0_115,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,X1) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_116,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| ~ hBOOL(hAPP(hAPP(c_Arrow__Order__Mirabelle_OLin,X1),X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_88]) ).
cnf(c_0_117,plain,
( hBOOL(hAPP(c_in(X1),X2))
| hAPP(c_Arrow__Order__Mirabelle_OLin,X3) != c_Arrow__Order__Mirabelle_OLin ),
inference(spm,[status(thm)],[c_0_113,c_0_112]) ).
cnf(c_0_118,plain,
( ~ hBOOL(hAPP(c_Not,X1))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_77]) ).
cnf(c_0_119,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_115,c_0_112]) ).
cnf(c_0_120,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| hBOOL(X1)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(spm,[status(thm)],[c_0_116,c_0_112]) ).
cnf(c_0_121,plain,
( hBOOL(hAPP(c_in(X1),X2))
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_112])]) ).
cnf(c_0_122,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_123,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra ).
cnf(c_0_124,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_84,c_0_76]) ).
cnf(c_0_125,plain,
( hAPP(c_Not,X1) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_126,plain,
( hBOOL(c_in(X1))
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_127,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_128,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_122,c_0_123]) ).
cnf(c_0_129,plain,
hAPP(c_Not,hAPP(c_Not,X1)) = X1,
inference(rw,[status(thm)],[c_0_99,c_0_124]) ).
cnf(c_0_130,plain,
( hAPP(c_Not,c_in(X1)) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_131,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_127,c_0_45]),c_0_45]) ).
cnf(c_0_132,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(tc_bool),X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X3)))
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_53,c_0_128]) ).
cnf(c_0_133,plain,
( hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = c_in(X1)
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_134,plain,
( hBOOL(hAPP(c_Not,X1))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_131,c_0_99]) ).
cnf(c_0_135,plain,
( c_HOL_Ouminus__class_Ouminus(tc_bool) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_73]),c_0_128])]) ).
cnf(c_0_136,plain,
( hAPP(c_Not,X1) = c_Orderings_Obot__class_Obot(tc_bool)
| X1 = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_125,c_0_119]) ).
cnf(c_0_137,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| hAPP(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),X1) != c_Arrow__Order__Mirabelle_OLin ),
inference(spm,[status(thm)],[c_0_113,c_0_133]) ).
cnf(c_0_138,plain,
( hBOOL(c_Not)
| hBOOL(c_Arrow__Order__Mirabelle_OLin)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_134]) ).
cnf(c_0_139,plain,
( hBOOL(c_in(X1))
| hAPP(c_Orderings_Obot__class_Obot(tc_bool),X2) != c_Arrow__Order__Mirabelle_OLin ),
inference(spm,[status(thm)],[c_0_113,c_0_119]) ).
cnf(c_0_140,plain,
( c_HOL_Ouminus__class_Ouminus(tc_bool) != c_Arrow__Order__Mirabelle_OLin
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_135,c_0_88]) ).
cnf(c_0_141,plain,
( hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = X1
| X1 = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_129,c_0_136]) ).
cnf(c_0_142,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OLin)
| hAPP(X1,X2) != c_Arrow__Order__Mirabelle_OLin
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_125]),c_0_129]) ).
cnf(c_0_143,plain,
( hBOOL(c_Not)
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(ef,[status(thm)],[c_0_138]) ).
cnf(c_0_144,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OlessThan(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(X3,X2),X4)) ),
cls_ord_OlessThan__iff_1 ).
cnf(c_0_145,plain,
( hBOOL(c_in(X1))
| hAPP(hAPP(c_Not,X2),X3) != c_Arrow__Order__Mirabelle_OLin
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_139,c_0_125]) ).
cnf(c_0_146,plain,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) != c_Arrow__Order__Mirabelle_OLin
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_147,plain,
hBOOL(c_Arrow__Order__Mirabelle_OLin),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_129])]),c_0_143]) ).
cnf(c_0_148,plain,
( hBOOL(hAPP(c_SetInterval_Oord_OlessThan(X1,X2,X3),X4))
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(rw,[status(thm)],[c_0_144,c_0_45]) ).
cnf(c_0_149,plain,
( hBOOL(c_in(X1))
| hAPP(X2,X3) != c_Arrow__Order__Mirabelle_OLin
| ~ hBOOL(hAPP(c_Not,X2)) ),
inference(spm,[status(thm)],[c_0_145,c_0_129]) ).
cnf(c_0_150,plain,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin)
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_125]),c_0_129])]),c_0_147])]) ).
cnf(c_0_151,plain,
hBOOL(hAPP(c_SetInterval_Oord_OlessThan(c_fequal(X1),X2,X3),X2)),
inference(spm,[status(thm)],[c_0_148,c_0_54]) ).
cnf(c_0_152,plain,
( hBOOL(c_in(X1))
| ~ class_Lattices_Oboolean__algebra(X2)
| ~ hBOOL(hAPP(c_Not,c_HOL_Ouminus__class_Ouminus(X2))) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_122])]) ).
cnf(c_0_153,plain,
c_HOL_Ouminus__class_Ouminus(tc_bool) = hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_154,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Set_OPow(X2,X1))),
cls_Pow__bottom_0 ).
cnf(c_0_155,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X1)),X2)) ),
inference(spm,[status(thm)],[c_0_108,c_0_131]) ).
cnf(c_0_156,plain,
hBOOL(c_in(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_123]),c_0_129]),c_0_147])]) ).
cnf(c_0_157,plain,
hBOOL(hAPP(c_Set_OPow(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),
inference(rw,[status(thm)],[c_0_154,c_0_45]) ).
cnf(c_0_158,plain,
( hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X2),X3)) ),
inference(spm,[status(thm)],[c_0_155,c_0_77]) ).
cnf(c_0_159,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_OPow(X1,X2),X3,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X3,X1)) ),
inference(spm,[status(thm)],[c_0_53,c_0_79]) ).
cnf(c_0_160,plain,
hAPP(c_Not,c_in(X1)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_125,c_0_156]) ).
cnf(c_0_161,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_OPow(X1,X2),X3,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) ),
inference(spm,[status(thm)],[c_0_53,c_0_157]) ).
cnf(c_0_162,plain,
( hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Not),X2))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_158,c_0_99]) ).
cnf(c_0_163,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_OPow(X1,X2),c_Set_OPow(X1,X3),tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
inference(spm,[status(thm)],[c_0_159,c_0_79]) ).
cnf(c_0_164,plain,
hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = c_in(X1),
inference(spm,[status(thm)],[c_0_129,c_0_160]) ).
cnf(c_0_165,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_OPow(X1,X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Not),tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) ),
inference(spm,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_166,plain,
c_Set_OPow(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_163,c_0_73]) ).
cnf(c_0_167,plain,
hAPP(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),X1) != c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_113,c_0_164]) ).
cnf(c_0_168,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_OPow(X1,X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Not),tc_fun(X4,tc_bool)) != c_Arrow__Order__Mirabelle_OLin
| ~ hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_165,c_0_88]),c_0_88]) ).
cnf(c_0_169,plain,
c_Set_OPow(X1,X2) != c_Arrow__Order__Mirabelle_OLin,
inference(rw,[status(thm)],[c_0_166,c_0_88]) ).
cnf(c_0_170,plain,
( hAPP(X1,X2) != c_Arrow__Order__Mirabelle_OLin
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_125]),c_0_129]) ).
cnf(c_0_171,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_OPow(X1,X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Not),tc_fun(X4,tc_bool)) != c_Arrow__Order__Mirabelle_OLin,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_168,c_0_147])]) ).
cnf(c_0_172,axiom,
c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),tc_fun(X3,tc_bool)),
cls_Diff__eq_0 ).
cnf(c_0_173,plain,
( c_Set_OPow(X1,X2) = c_Orderings_Obot__class_Obot(tc_bool)
| hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) != c_Arrow__Order__Mirabelle_OLin ),
inference(spm,[status(thm)],[c_0_169,c_0_141]) ).
cnf(c_0_174,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| ~ hBOOL(c_HOL_Ouminus__class_Ouminus(X1)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_122])]) ).
cnf(c_0_175,plain,
~ hBOOL(c_Not),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_129])]) ).
cnf(c_0_176,plain,
( X1 = X2
| hBOOL(X1)
| hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_112,c_0_112]) ).
cnf(c_0_177,plain,
c_HOL_Ominus__class_Ominus(c_Set_OPow(X1,X2),c_Not,tc_fun(X3,tc_bool)) != c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_171,c_0_172]) ).
cnf(c_0_178,plain,
c_Set_OPow(X1,X2) = hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_125]),c_0_129])]),c_0_147])]) ).
cnf(c_0_179,plain,
~ hBOOL(hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_153]),c_0_123])]) ).
cnf(c_0_180,plain,
( X1 = c_Not
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_175,c_0_176]) ).
cnf(c_0_181,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
cls_Diff__cancel_0 ).
cnf(c_0_182,plain,
c_HOL_Ominus__class_Ominus(hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin),c_Not,tc_fun(X1,tc_bool)) != c_Arrow__Order__Mirabelle_OLin,
inference(rw,[status(thm)],[c_0_177,c_0_178]) ).
cnf(c_0_183,plain,
hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin) = c_Not,
inference(spm,[status(thm)],[c_0_179,c_0_180]) ).
cnf(c_0_184,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Arrow__Order__Mirabelle_OLin,
inference(rw,[status(thm)],[c_0_181,c_0_88]) ).
cnf(c_0_185,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_182,c_0_183]),c_0_184])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SCT006-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.35 % Computer : n014.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 24 15:28:48 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.59 start to proof: theBenchmark
% 55.85/55.83 % Version : CSE_E---1.5
% 55.85/55.83 % Problem : theBenchmark.p
% 55.85/55.83 % Proof found
% 55.85/55.83 % SZS status Theorem for theBenchmark.p
% 55.85/55.83 % SZS output start Proof
% See solution above
% 55.85/55.85 % Total time : 55.215000 s
% 55.85/55.85 % SZS output end Proof
% 55.85/55.85 % Total time : 55.239000 s
%------------------------------------------------------------------------------