TSTP Solution File: SWV885-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV885-1 : 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 : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 21:48:30 EDT 2023
% Result : Unsatisfiable 0.87s 0.99s
% Output : CNFRefutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 132
% Syntax : Number of formulae : 170 ( 41 unt; 113 typ; 0 def)
% Number of atoms : 82 ( 48 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 22 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 186 ( 104 >; 82 *; 0 +; 0 <<)
% Number of predicates : 68 ( 66 usr; 1 prp; 0-4 aty)
% Number of functors : 47 ( 47 usr; 9 con; 0-5 aty)
% Number of variables : 76 ( 7 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
tc_nat: $i ).
tff(decl_23,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_24,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_26,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_28,type,
c_Suc: $i > $i ).
tff(decl_29,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_30,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
tc_bool: $i ).
tff(decl_33,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_34,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_36,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_38,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(decl_39,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_40,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
c_Set_Ovimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_42,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(decl_43,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(decl_44,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_45,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_46,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_47,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_48,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_49,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_50,type,
class_OrderedGroup_Olordered__ab__group__add__meet: $i > $o ).
tff(decl_51,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_52,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(decl_53,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(decl_54,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_55,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_56,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_57,type,
class_Ring__and__Field_Odvd: $i > $o ).
tff(decl_58,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_59,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_60,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(decl_61,type,
c_in: ( $i * $i * $i ) > $o ).
tff(decl_62,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_63,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(decl_64,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_65,type,
c_Hilbert__Choice_Oinv__into: ( $i * $i * $i * $i ) > $i ).
tff(decl_66,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_67,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_68,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(decl_69,type,
c_Finite__Set_Ocard: ( $i * $i ) > $i ).
tff(decl_70,type,
c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(decl_72,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(decl_73,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(decl_74,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_75,type,
c_Finite__Set_Olinorder__class_OMax: ( $i * $i ) > $i ).
tff(decl_76,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(decl_77,type,
class_Lattices_Olattice: $i > $o ).
tff(decl_78,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(decl_79,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(decl_80,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_81,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_82,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_83,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_84,type,
hBOOL: $i > $o ).
tff(decl_85,type,
c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1: $i > $i ).
tff(decl_86,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(decl_87,type,
c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2: ( $i * $i * $i ) > $i ).
tff(decl_88,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(decl_89,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_90,type,
c_Fun_Ofun__upd: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_91,type,
c_Finite__Set_Olinorder__class_OMin: ( $i * $i ) > $i ).
tff(decl_92,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_93,type,
c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1: ( $i * $i ) > $i ).
tff(decl_94,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(decl_95,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_96,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_97,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_98,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
tff(decl_99,type,
c_Inductive_Ocomplete__lattice__class_Ogfp: ( $i * $i ) > $i ).
tff(decl_100,type,
class_Orderings_Otop: $i > $o ).
tff(decl_101,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_102,type,
c_SetInterval_Oord__class_OatLeast: ( $i * $i ) > $i ).
tff(decl_103,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_104,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(decl_105,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(decl_106,type,
class_Orderings_Obot: $i > $o ).
tff(decl_107,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_108,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(decl_109,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_110,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
tff(decl_111,type,
class_HOL_Oord: $i > $o ).
tff(decl_112,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
tff(decl_113,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_114,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(decl_115,type,
c_ATP__Linkup_Osko__Set__Ximage__cong__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_116,type,
c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1: $i > $i ).
tff(decl_117,type,
c_ATP__Linkup_Osko__Set__XimageE__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_118,type,
c_ATP__Linkup_Osko__Set__Ximage__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_119,type,
c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1: $i > $i ).
tff(decl_120,type,
c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1: ( $i * $i ) > $i ).
tff(decl_121,type,
c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_122,type,
c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1: ( $i * $i ) > $i ).
tff(decl_123,type,
c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_124,type,
c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_125,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_126,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(decl_127,type,
v_U: $i ).
tff(decl_128,type,
tc_Com_Opname: $i ).
tff(decl_129,type,
v_G: $i ).
tff(decl_130,type,
v_mgt__call: $i ).
tff(decl_131,type,
t_a: $i ).
tff(decl_132,type,
v_na: $i ).
tff(decl_133,type,
v_pn: $i ).
tff(decl_134,type,
c_fequal: ( $i * $i * $i ) > $o ).
cnf(cls_le__imp__diff__is__add_0,axiom,
( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).
cnf(cls_nat__add__commute_0,axiom,
c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
cnf(cls_conjecture_3,negated_conjecture,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_Suc__eq__plus1_0,axiom,
c_Suc(X1) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_nat__add__assoc_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
cnf(cls_card__Suc__eq_4,axiom,
( c_in(X1,X2,X3)
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(X2,X3))
| c_Finite__Set_Ocard(X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Suc__eq_4) ).
cnf(cls_card__Suc__eq_5,axiom,
( c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Suc__eq_5) ).
cnf(cls_conjecture_6,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
cnf(cls_diff__add__inverse_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
cnf(cls_Diff__cancel_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
cnf(cls_ex__in__conv_0,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
cnf(cls_card__empty_0,axiom,
c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__empty_0) ).
cnf(cls_card__eq__0__iff_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__eq__0__iff_0) ).
cnf(cls_conjecture_5,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_finite__surj_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__surj_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_natgb_Oadd__r0__iff_1,axiom,
X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
cnf(c_0_19,axiom,
( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_le__imp__diff__is__add_0 ).
cnf(c_0_20,axiom,
c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
cls_nat__add__commute_0 ).
cnf(c_0_21,negated_conjecture,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
cls_conjecture_3 ).
cnf(c_0_22,axiom,
c_Suc(X1) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
cls_Suc__eq__plus1_0 ).
cnf(c_0_23,negated_conjecture,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
cls_conjecture_2 ).
cnf(c_0_24,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
c_lessequals(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
inference(rw,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_27,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
cls_nat__add__assoc_0 ).
cnf(c_0_28,axiom,
( c_in(X1,X2,X3)
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(X2,X3))
| c_Finite__Set_Ocard(X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_card__Suc__eq_4 ).
cnf(c_0_29,axiom,
( c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
cls_card__Suc__eq_5 ).
cnf(c_0_30,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
cls_conjecture_6 ).
cnf(c_0_31,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_32,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
cls_diff__add__inverse_0 ).
cnf(c_0_33,plain,
( c_Finite__Set_Ocard(X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(X2,X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_in(X1,X2,X3) ),
inference(rw,[status(thm)],[c_0_28,c_0_22]) ).
cnf(c_0_34,plain,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
inference(rw,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_35,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_36,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
cls_ex__in__conv_0 ).
cnf(c_0_37,axiom,
c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_card__empty_0 ).
cnf(c_0_38,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
cls_card__eq__0__iff_0 ).
cnf(c_0_39,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_40,plain,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(X2,X3),tc_nat)
| c_Finite__Set_Ocard(X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_in(X1,X2,X3) ),
inference(rw,[status(thm)],[c_0_33,c_0_20]) ).
cnf(c_0_41,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
cls_conjecture_5 ).
cnf(c_0_42,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X4,X5) ),
cls_finite__surj_0 ).
cnf(c_0_43,negated_conjecture,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
cls_conjecture_1 ).
cnf(c_0_44,negated_conjecture,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
cls_conjecture_0 ).
cnf(c_0_45,plain,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_fun(X2,tc_bool)),X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_fun(X2,tc_bool)),X2),tc_nat)
| c_in(X1,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_fun(X2,tc_bool)),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_35]),c_0_20]),c_0_35]) ).
cnf(c_0_46,plain,
~ c_in(X1,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_fun(X2,tc_bool)),X2),
inference(rw,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_47,plain,
c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_fun(X1,tc_bool)),X1) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(rw,[status(thm)],[c_0_37,c_0_35]) ).
cnf(c_0_48,axiom,
X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_natgb_Oadd__r0__iff_1 ).
cnf(c_0_49,plain,
( X1 = c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(rw,[status(thm)],[c_0_38,c_0_35]) ).
cnf(c_0_50,negated_conjecture,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_51,negated_conjecture,
c_Finite__Set_Ofinite(v_G,t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_52,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_fun(X2,tc_bool)),X2),X2) = c_HOL_Oone__class_Oone(tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48]) ).
cnf(c_0_53,negated_conjecture,
c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_fun(t_a,tc_bool)) = v_G,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
cnf(c_0_54,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Oone__class_Oone(tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_50]),c_0_48]) ).
cnf(c_0_55,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oinsert(X1,v_G,t_a),t_a) = c_HOL_Oone__class_Oone(tc_nat),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWV885-1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n021.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 : Tue Aug 29 03:43:14 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.87/0.99 % Version : CSE_E---1.5
% 0.87/0.99 % Problem : theBenchmark.p
% 0.87/0.99 % Proof found
% 0.87/0.99 % SZS status Theorem for theBenchmark.p
% 0.87/0.99 % SZS output start Proof
% See solution above
% 0.87/1.00 % Total time : 0.370000 s
% 0.87/1.00 % SZS output end Proof
% 0.87/1.00 % Total time : 0.401000 s
%------------------------------------------------------------------------------