TSTP Solution File: SCT016-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SCT016-1 : 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 : n017.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 14:10:45 EDT 2023
% Result : Unsatisfiable 2.00s 2.14s
% Output : CNFRefutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 181
% Syntax : Number of formulae : 303 ( 95 unt; 138 typ; 0 def)
% Number of atoms : 238 ( 133 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 152 ( 79 ~; 73 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 259 ( 120 >; 139 *; 0 +; 0 <<)
% Number of predicates : 44 ( 42 usr; 1 prp; 0-9 aty)
% Number of functors : 96 ( 96 usr; 18 con; 0-5 aty)
% Number of variables : 327 ( 116 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_23,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_24,type,
c_lessequals: $i > $i ).
tff(decl_25,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_26,type,
hBOOL: $i > $o ).
tff(decl_27,type,
c_Orderings_Oorder__class_Ostrict__mono: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
c_HOL_Oord__class_Oless: $i > $i ).
tff(decl_29,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_30,type,
c_Finite__Set_Osetsum: ( $i * $i ) > $i ).
tff(decl_31,type,
tc_bool: $i ).
tff(decl_32,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_33,type,
c_HOL_Ominus__class_Ominus: $i > $i ).
tff(decl_34,type,
c_Set_Oinsert: $i > $i ).
tff(decl_35,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_36,type,
c_in: $i > $i ).
tff(decl_37,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(decl_38,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_39,type,
c_Set_Oimage: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i ).
tff(decl_41,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_42,type,
c_Hilbert__Choice_Oinv__into: ( $i * $i * $i * $i ) > $i ).
tff(decl_43,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_44,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
tff(decl_45,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_46,type,
c_Relation_Oconverse: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
c_Transitive__Closure_Otrancl: ( $i * $i ) > $i ).
tff(decl_48,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
tff(decl_49,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(decl_51,type,
c_Relation_OImage: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
c_COMBB: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
c_Relation_OId: $i > $i ).
tff(decl_55,type,
c_Relation_Oantisym: ( $i * $i ) > $i ).
tff(decl_56,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
tff(decl_57,type,
c_Relation_ORange: ( $i * $i * $i ) > $i ).
tff(decl_58,type,
c_Relation_ODomain: ( $i * $i * $i ) > $i ).
tff(decl_59,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_60,type,
c_Relation_Otrans: ( $i * $i ) > $i ).
tff(decl_61,type,
c_Transitive__Closure_Ortrancl: ( $i * $i ) > $i ).
tff(decl_62,type,
c_Relation_Orel__comp: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_63,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(decl_64,type,
c_Product__Type_OSigma: ( $i * $i * $i * $i ) > $i ).
tff(decl_65,type,
c_Relation_Osingle__valued: ( $i * $i * $i ) > $i ).
tff(decl_66,type,
class_Lattices_Olattice: $i > $o ).
tff(decl_67,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(decl_68,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
tff(decl_69,type,
c_fequal: $i > $i ).
tff(decl_70,type,
c_Predicate_Oconversep: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_72,type,
c_Orderings_Oorder_Ostrict__mono: ( $i * $i * $i ) > $i ).
tff(decl_73,type,
c_Orderings_Oorder: ( $i * $i * $i ) > $o ).
tff(decl_74,type,
c_Orderings_Oorder_Omono: ( $i * $i * $i ) > $i ).
tff(decl_75,type,
c_Fun_Othe__inv__into: ( $i * $i * $i * $i ) > $i ).
tff(decl_76,type,
c_Set_Ovimage: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
c_List_Olistsp: ( $i * $i * $i ) > $i ).
tff(decl_78,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_79,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_80,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_81,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_82,type,
c_COMBS: ( $i * $i * $i ) > $i ).
tff(decl_83,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_84,type,
c_Finite__Set_Olattice_OInf__fin: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
c_Complete__Lattice_Ocomplete__lattice: ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_86,type,
c_Predicate_Opred__comp: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_87,type,
c_Orderings_Oorder__class_Omono: ( $i * $i * $i ) > $i ).
tff(decl_88,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_89,type,
c_Predicate_ODomainP: ( $i * $i * $i * $i ) > $i ).
tff(decl_90,type,
c_Hilbert__Choice_OEps: ( $i * $i ) > $i ).
tff(decl_91,type,
c_Lattices_Oboolean__algebra: ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_92,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_93,type,
c_Relation_Osym: ( $i * $i ) > $i ).
tff(decl_94,type,
class_OrderedGroup_Olordered__ab__group__add__meet: $i > $o ).
tff(decl_95,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_96,type,
c_Finite__Set_Olattice_OSup__fin: ( $i * $i * $i ) > $i ).
tff(decl_97,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(decl_98,type,
c_COMBC: ( $i * $i * $i ) > $i ).
tff(decl_99,type,
c_Lattices_Odistrib__lattice: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_100,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_101,type,
t_b: $i ).
tff(decl_102,type,
class_HOL_Ouminus: $i > $o ).
tff(decl_103,type,
t_a: $i ).
tff(decl_104,type,
v_A: $i ).
tff(decl_105,type,
v_x: $i ).
tff(decl_106,type,
v_r: $i ).
tff(decl_107,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(decl_108,type,
c_Relation_OField: ( $i * $i ) > $i ).
tff(decl_109,type,
c_Finite__Set_Olattice__class_OSup__fin: ( $i * $i ) > $i ).
tff(decl_110,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_111,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_112,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_113,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_114,type,
c_Finite__Set_Olattice__class_OInf__fin: ( $i * $i ) > $i ).
tff(decl_115,type,
class_HOL_Ominus: $i > $o ).
tff(decl_116,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
tff(decl_117,type,
c_Relation_Ototal__on: ( $i * $i * $i ) > $i ).
tff(decl_118,type,
c_The: ( $i * $i ) > $i ).
tff(decl_119,type,
c_Finite__Set_Olinorder__class_OMin: ( $i * $i ) > $i ).
tff(decl_120,type,
c_Predicate_ORangeP: ( $i * $i * $i * $i ) > $i ).
tff(decl_121,type,
c_Finite__Set_Olinorder__class_OMax: ( $i * $i ) > $i ).
tff(decl_122,type,
c_Wellfounded_Oaccp: ( $i * $i * $i ) > $i ).
tff(decl_123,type,
c_Pair: ( $i * $i ) > $i ).
tff(decl_124,type,
c_Relation_Oirrefl: ( $i * $i ) > $i ).
tff(decl_125,type,
c_Collect: $i > $i ).
tff(decl_126,type,
c_HOL_Oundefined: $i > $i ).
tff(decl_127,type,
c_FuncSet_Oextensional: ( $i * $i * $i ) > $i ).
tff(decl_128,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(decl_129,type,
class_Orderings_Obot: $i > $o ).
tff(decl_130,type,
v_f: $i ).
tff(decl_131,type,
c_and: $i ).
tff(decl_132,type,
c_Not: $i ).
tff(decl_133,type,
v_y: $i ).
tff(decl_134,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(decl_135,type,
c_Arrow__Order__Mirabelle_Omkbot: ( $i * $i ) > $i ).
tff(decl_136,type,
c_Arrow__Order__Mirabelle_Omktop: ( $i * $i ) > $i ).
tff(decl_137,type,
c_Wellfounded_Oacc: ( $i * $i ) > $i ).
tff(decl_138,type,
c_or: $i ).
tff(decl_139,type,
c_Zorn_OChain: ( $i * $i ) > $i ).
tff(decl_140,type,
c_All: $i > $i ).
tff(decl_141,type,
c_implies: $i ).
tff(decl_142,type,
c_Ex: $i > $i ).
tff(decl_143,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bounded__ex__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_144,type,
class_OrderedGroup_Olordered__ab__group__add__join: $i > $o ).
tff(decl_145,type,
class_Orderings_Otop: $i > $o ).
tff(decl_146,type,
c_COMBI: $i > $i ).
tff(decl_147,type,
v_s: $i ).
tff(decl_148,type,
t_c: $i ).
tff(decl_149,type,
c_split: ( $i * $i * $i * $i ) > $i ).
tff(decl_150,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_151,type,
c_Finite__Set_Olinorder_OMin: ( $i * $i * $i ) > $i ).
tff(decl_152,type,
c_OrderedGroup_Oordered__ab__semigroup__add: ( $i * $i * $i * $i ) > $o ).
tff(decl_153,type,
c_Finite__Set_Olinorder_OMax: ( $i * $i * $i ) > $i ).
tff(decl_154,type,
class_OrderedGroup_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_155,type,
v_L: $i ).
tff(decl_156,type,
v_a: $i ).
tff(decl_157,type,
v_b: $i ).
tff(decl_158,type,
c_Arrow__Order__Mirabelle_Obelow: ( $i * $i * $i ) > $i ).
tff(decl_159,type,
c_Arrow__Order__Mirabelle_Oabove: ( $i * $i * $i ) > $i ).
cnf(cls_vimage__Collect__eq_0,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Collect(X3),X4)) = hAPP(c_Collect(X2),hAPP(hAPP(c_COMBB(X3,tc_bool,X2),X4),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Collect__eq_0) ).
cnf(cls_Collect__def_0,axiom,
hAPP(c_Collect(X1),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
cnf(cls_Collect__mem__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
cnf(cls_Collect__neg__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__neg__eq_0) ).
cnf(cls_vimage__const_0,axiom,
( hAPP(c_Set_Ovimage(c_COMBK(X1,X2,X3),X3,X2),X4) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X1),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_sup__Un__eq_0,axiom,
hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(hAPP(c_COMBC(t_a,tc_fun(t_a,tc_bool),tc_bool),c_in(t_a)),X1)),hAPP(hAPP(c_COMBC(t_a,tc_fun(t_a,tc_bool),tc_bool),c_in(t_a)),X2)),v_x) = hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__Un__eq_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_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_Un__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
cnf(cls_bot__fun__eq_0,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_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_vimage__ident_0,axiom,
hAPP(c_Set_Ovimage(c_COMBI(X1),X1,X1),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__ident_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
cnf(cls_exE__some_0,axiom,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X1,X3)))
| ~ hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exE__some_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_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_COMBI__def_0,axiom,
hAPP(c_COMBI(X1),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
cnf(cls_empty__not__insert_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
cnf(cls_insert__image_0,axiom,
( hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X2,X4,X1),X5)) = hAPP(c_Set_Oimage(X2,X4,X1),X5)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X3),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
cnf(cls_fun__Compl__def_0,axiom,
( hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(t_a,X1)),X2),v_x) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(X2,v_x))
| ~ class_HOL_Ouminus(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__Compl__def_0) ).
cnf(clsarity_bool__HOL_Ouminus,axiom,
class_HOL_Ouminus(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).
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(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_mem__def_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
cnf(cls_total__on__empty_0,axiom,
hBOOL(c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).
cnf(cls_Compl__eq__Compl__iff_0,axiom,
( X2 = X3
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
cnf(cls_sup__compl__top_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__compl__top_0) ).
cnf(cls_sup__bot__right_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__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_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_vimageE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),hAPP(c_Set_Ovimage(X2,X5,X1),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_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__ident_0,axiom,
hAPP(c_Set_Oimage(c_COMBI(X1),X1,X1),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__ident_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_sup__top__left_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
cnf(cls_insert__absorb_0,axiom,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
cnf(cls_RangeP_Ointros_0,axiom,
( hBOOL(c_Predicate_ORangeP(X1,X2,X3,X4))
| ~ hBOOL(hAPP(hAPP(X1,X5),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeP_Ointros_0) ).
cnf(cls_order_Oless__le_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ c_Orderings_Oorder(X3,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Oless__le_1) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
cnf(cls_dual__order_0,axiom,
( c_Orderings_Oorder(hAPP(c_COMBC(X1,X1,tc_bool),c_lessequals(X1)),hAPP(c_COMBC(X1,X1,tc_bool),c_HOL_Oord__class_Oless(X1)),X1)
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dual__order_0) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(c_0_43,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Collect(X3),X4)) = hAPP(c_Collect(X2),hAPP(hAPP(c_COMBB(X3,tc_bool,X2),X4),X1)),
cls_vimage__Collect__eq_0 ).
cnf(c_0_44,axiom,
hAPP(c_Collect(X1),X2) = X2,
cls_Collect__def_0 ).
cnf(c_0_45,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2)) = X2,
cls_Collect__mem__eq_0 ).
cnf(c_0_46,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2)),
cls_Collect__neg__eq_0 ).
cnf(c_0_47,axiom,
( hAPP(c_Set_Ovimage(c_COMBK(X1,X2,X3),X3,X2),X4) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X1),X4)) ),
cls_vimage__const_0 ).
cnf(c_0_48,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),X4) = hAPP(hAPP(c_COMBB(X3,tc_bool,X2),X4),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_44]) ).
cnf(c_0_49,axiom,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_50,plain,
hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_45,c_0_44]) ).
cnf(c_0_51,axiom,
hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(hAPP(c_COMBC(t_a,tc_fun(t_a,tc_bool),tc_bool),c_in(t_a)),X1)),hAPP(hAPP(c_COMBC(t_a,tc_fun(t_a,tc_bool),tc_bool),c_in(t_a)),X2)),v_x) = hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X1),X2)),
cls_sup__Un__eq_0 ).
cnf(c_0_52,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_53,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_44]),c_0_44]) ).
cnf(c_0_54,plain,
( hAPP(hAPP(c_COMBB(X1,tc_bool,X2),X3),c_COMBK(X4,X1,X2)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3)) ),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,plain,
hAPP(hAPP(c_in(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,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_57,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_58,plain,
hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X1),X2)) = hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X1),X2),v_x),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_50]),c_0_50]) ).
cnf(c_0_59,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
cls_Un__empty__right_0 ).
cnf(c_0_60,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__fun__eq_0 ).
cnf(c_0_61,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_62,axiom,
hAPP(c_Set_Ovimage(c_COMBI(X1),X1,X1),X2) = X2,
cls_vimage__ident_0 ).
cnf(c_0_63,plain,
hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53]),c_0_53]) ).
cnf(c_0_64,plain,
( hAPP(hAPP(c_COMBB(X1,tc_bool,X2),X3),c_COMBK(X4,X1,X2)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(X3,X4)) ),
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_65,plain,
hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[c_0_56,c_0_53]) ).
cnf(c_0_66,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(rw,[status(thm)],[c_0_57,c_0_53]) ).
cnf(c_0_67,plain,
hAPP(hAPP(c_in(t_a),v_x),X1) = hAPP(X1,v_x),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_68,axiom,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
cls_COMBB__def_0 ).
cnf(c_0_69,axiom,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X1,X3)))
| ~ hBOOL(hAPP(X1,X2)) ),
cls_exE__some_0 ).
cnf(c_0_70,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_71,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0 ).
cnf(c_0_72,plain,
hAPP(hAPP(c_COMBB(X1,tc_bool,X1),X2),c_COMBI(X1)) = X2,
inference(rw,[status(thm)],[c_0_62,c_0_48]) ).
cnf(c_0_73,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_74,plain,
( c_COMBK(X1,tc_bool,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(c_Not,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).
cnf(c_0_75,plain,
( hBOOL(hAPP(c_Not,hAPP(X1,v_x)))
| hBOOL(hAPP(X1,v_x)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_67]) ).
cnf(c_0_76,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_77,axiom,
hAPP(c_COMBI(X1),X2) = X2,
cls_COMBI__def_0 ).
cnf(c_0_78,plain,
c_COMBI(tc_bool) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not),
inference(spm,[status(thm)],[c_0_63,c_0_72]) ).
cnf(c_0_79,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2) = X3
| ~ hBOOL(hAPP(c_Not,X3)) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_80,plain,
hBOOL(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_70]),c_0_76]) ).
cnf(c_0_81,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
cls_empty__not__insert_0 ).
cnf(c_0_82,axiom,
( hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X2,X4,X1),X5)) = hAPP(c_Set_Oimage(X2,X4,X1),X5)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X3),X5)) ),
cls_insert__image_0 ).
cnf(c_0_83,plain,
hAPP(c_Not,hAPP(c_Not,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_68]) ).
cnf(c_0_84,axiom,
( hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(t_a,X1)),X2),v_x) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(X2,v_x))
| ~ class_HOL_Ouminus(X1) ),
cls_fun__Compl__def_0 ).
cnf(c_0_85,axiom,
class_HOL_Ouminus(tc_bool),
clsarity_bool__HOL_Ouminus ).
cnf(c_0_86,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_87,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra ).
cnf(c_0_88,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_79,c_0_80]) ).
cnf(c_0_89,plain,
( hAPP(c_Set_Oimage(X1,X2,X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X5),X4)) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_90,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
cls_mem__def_1 ).
cnf(c_0_91,plain,
( hBOOL(hAPP(c_Not,c_Hilbert__Choice_OEps(c_Not,X1)))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_69,c_0_83]) ).
cnf(c_0_92,axiom,
hBOOL(c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1)),
cls_total__on__empty_0 ).
cnf(c_0_93,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(X1,v_x)) = hAPP(c_Not,hAPP(X1,v_x)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_53]),c_0_68]) ).
cnf(c_0_94,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_86,c_0_87]) ).
cnf(c_0_95,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| ~ hBOOL(hAPP(c_Not,X1)) ),
inference(rw,[status(thm)],[c_0_79,c_0_88]) ).
cnf(c_0_96,plain,
( hBOOL(hAPP(c_Not,X1))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_75,c_0_73]) ).
cnf(c_0_97,axiom,
( X2 = X3
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3) ),
cls_Compl__eq__Compl__iff_0 ).
cnf(c_0_98,plain,
( hAPP(c_Set_Oimage(X1,X2,X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X4,X5)) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_99,plain,
hBOOL(hAPP(c_Not,c_Hilbert__Choice_OEps(c_Not,X1))),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_100,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_sup__compl__top_0 ).
cnf(c_0_101,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) = hAPP(c_Not,X1),
inference(spm,[status(thm)],[c_0_93,c_0_73]) ).
cnf(c_0_102,plain,
c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_70]),c_0_94]) ).
cnf(c_0_103,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_104,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__bot__right_0 ).
cnf(c_0_105,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_106,plain,
( X1 = X2
| hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X3),c_Not),X1) != hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X3),c_Not),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_53]),c_0_53]) ).
cnf(c_0_107,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_108,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),hAPP(c_Set_Ovimage(X2,X5,X1),X4))) ),
cls_vimageE_0 ).
cnf(c_0_109,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
cnf(c_0_110,plain,
hAPP(c_Set_Oimage(X1,X2,X3),c_Not) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_111,axiom,
hAPP(c_Set_Oimage(c_COMBI(X1),X1,X1),X2) = X2,
cls_image__ident_0 ).
cnf(c_0_112,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),hAPP(c_Not,X1)) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_87]),c_0_101]),c_0_102]) ).
cnf(c_0_113,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Not,X1)
| c_Orderings_Obot__class_Obot(tc_bool) = X1 ),
inference(spm,[status(thm)],[c_0_95,c_0_103]) ).
cnf(c_0_114,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),c_Orderings_Obot__class_Obot(tc_bool)) = X1,
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_115,plain,
( hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not) = X1
| hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),X1) != c_Not ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_72]),c_0_78]) ).
cnf(c_0_116,plain,
hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[c_0_107,c_0_53]) ).
cnf(c_0_117,plain,
( hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),hAPP(hAPP(c_COMBB(X1,tc_bool,X5),X4),X2))) ),
inference(rw,[status(thm)],[c_0_108,c_0_48]) ).
cnf(c_0_118,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_119,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(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_98,c_0_109]) ).
cnf(c_0_120,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Not,
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_121,plain,
( X1 = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))
| c_Orderings_Obot__class_Obot(tc_bool) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114]) ).
cnf(c_0_122,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not)
| c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)) != c_Not ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_123,plain,
hBOOL(hAPP(hAPP(c_in(tc_bool),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),c_Not)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_116]),c_0_118])]) ).
cnf(c_0_124,plain,
( hAPP(c_Set_Oimage(X1,X2,X3),c_COMBI(X4)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(X5) ),
inference(spm,[status(thm)],[c_0_98,c_0_77]) ).
cnf(c_0_125,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_119,c_0_111]) ).
cnf(c_0_126,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool)
| hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) != c_Not ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_127,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not)
| c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool)
| hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) != c_Not ),
inference(spm,[status(thm)],[c_0_122,c_0_121]) ).
cnf(c_0_128,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__top__left_0 ).
cnf(c_0_129,axiom,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
cls_insert__absorb_0 ).
cnf(c_0_130,plain,
hBOOL(hAPP(hAPP(c_in(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Not)),
inference(spm,[status(thm)],[c_0_123,c_0_70]) ).
cnf(c_0_131,plain,
( c_COMBI(X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_124,c_0_111]) ).
cnf(c_0_132,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_bool)
| hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) != c_Not ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_133,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not)
| c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Not ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_121])]) ).
cnf(c_0_134,axiom,
( hBOOL(c_Predicate_ORangeP(X1,X2,X3,X4))
| ~ hBOOL(hAPP(hAPP(X1,X5),X2)) ),
cls_RangeP_Ointros_0 ).
cnf(c_0_135,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X1) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_128,c_0_105]) ).
cnf(c_0_136,plain,
( hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) != c_Not
| c_Orderings_Obot__class_Obot(tc_bool) != c_Not ),
inference(spm,[status(thm)],[c_0_120,c_0_126]) ).
cnf(c_0_137,plain,
( X1 = X2
| hBOOL(X1)
| hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_103,c_0_103]) ).
cnf(c_0_138,plain,
hAPP(hAPP(c_Set_Oinsert(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Not) = c_Not,
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_139,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not)
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_131,c_0_78]) ).
cnf(c_0_140,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not)
| c_Orderings_Obot__class_Obot(tc_bool) = c_Not ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_121]) ).
cnf(c_0_141,plain,
( hBOOL(c_Predicate_ORangeP(c_Not,X1,X2,X3))
| ~ hBOOL(hAPP(X4,X1)) ),
inference(spm,[status(thm)],[c_0_134,c_0_83]) ).
cnf(c_0_142,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),X1) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_135,c_0_102]),c_0_102]) ).
cnf(c_0_143,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Not,X1)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_83]) ).
cnf(c_0_144,plain,
( hBOOL(c_Not)
| hAPP(c_Not,c_Not) != c_Not ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_76])]) ).
cnf(c_0_145,plain,
( hAPP(c_Set_Oinsert(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool)
| hAPP(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),c_Not) = c_Not ),
inference(spm,[status(thm)],[c_0_138,c_0_121]) ).
cnf(c_0_146,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = c_Not
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_147,plain,
hBOOL(c_Predicate_ORangeP(c_Not,X1,X2,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_80])]) ).
cnf(c_0_148,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Not,c_Not)
| hAPP(c_Not,c_Not) != c_Not ),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_149,plain,
hAPP(hAPP(c_Set_Oinsert(tc_bool),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),c_Not) = c_Not,
inference(spm,[status(thm)],[c_0_129,c_0_123]) ).
cnf(c_0_150,plain,
( hAPP(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),c_Not) = c_Not
| hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Not) = c_Not ),
inference(spm,[status(thm)],[c_0_138,c_0_145]) ).
cnf(c_0_151,plain,
c_Orderings_Obot__class_Obot(tc_bool) = c_Not,
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_152,plain,
hAPP(c_Not,c_Not) != c_Not,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_148]),c_0_83])]) ).
cnf(c_0_153,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ c_Orderings_Oorder(X3,X1,X4) ),
cls_order_Oless__le_1 ).
cnf(c_0_154,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
cls_insert__code_1 ).
cnf(c_0_155,plain,
( hAPP(hAPP(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Not) = c_Not
| c_Set_Oinsert(tc_bool) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_121]),c_0_88]) ).
cnf(c_0_156,plain,
hAPP(hAPP(c_Not,c_Not),c_Not) = c_Not,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_151]),c_0_151]),c_0_152]) ).
cnf(c_0_157,plain,
~ c_Orderings_Oorder(X1,hAPP(c_Set_Oinsert(X2),X3),X4),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_158,plain,
c_Set_Oinsert(tc_bool) = c_Not,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_151]),c_0_151]),c_0_151]),c_0_156]),c_0_152]) ).
cnf(c_0_159,plain,
~ c_Orderings_Oorder(X1,hAPP(c_Not,X2),X3),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_160,plain,
~ c_Orderings_Oorder(X1,X2,X3),
inference(spm,[status(thm)],[c_0_159,c_0_83]) ).
cnf(c_0_161,axiom,
( c_Orderings_Oorder(hAPP(c_COMBC(X1,X1,tc_bool),c_lessequals(X1)),hAPP(c_COMBC(X1,X1,tc_bool),c_HOL_Oord__class_Oless(X1)),X1)
| ~ class_Orderings_Oorder(X1) ),
cls_dual__order_0 ).
cnf(c_0_162,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_163,plain,
~ class_Orderings_Oorder(X1),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_164,plain,
$false,
inference(sr,[status(thm)],[c_0_162,c_0_163]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT016-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 14:58:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 2.00/2.14 % Version : CSE_E---1.5
% 2.00/2.14 % Problem : theBenchmark.p
% 2.00/2.14 % Proof found
% 2.00/2.14 % SZS status Theorem for theBenchmark.p
% 2.00/2.14 % SZS output start Proof
% See solution above
% 2.00/2.15 % Total time : 1.499000 s
% 2.00/2.15 % SZS output end Proof
% 2.00/2.15 % Total time : 1.555000 s
%------------------------------------------------------------------------------