TSTP Solution File: LCL778-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL778-1 : 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 : n011.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 06:59:33 EDT 2023
% Result : Unsatisfiable 0.69s 0.75s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 107
% Syntax : Number of formulae : 110 ( 5 unt; 105 typ; 0 def)
% Number of atoms : 5 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 172 ( 90 >; 82 *; 0 +; 0 <<)
% Number of predicates : 42 ( 41 usr; 1 prp; 0-6 aty)
% Number of functors : 64 ( 64 usr; 15 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_23,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_24,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(decl_25,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_26,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_28,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
class_Power_Opower: $i > $o ).
tff(decl_30,type,
tc_nat: $i ).
tff(decl_31,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_32,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(decl_33,type,
tc_Type_Otype: $i ).
tff(decl_34,type,
c_Type_Oshift: ( $i * $i * $i * $i ) > $i ).
tff(decl_35,type,
c_Lambda_Osubst: $i ).
tff(decl_36,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_37,type,
c_Lambda_Olift: $i ).
tff(decl_38,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
tff(decl_39,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(decl_40,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_41,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(decl_42,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_43,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_44,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_45,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_46,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_47,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_48,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_49,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_50,type,
c_Groebner__Basis_Ogb__semiring: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_51,type,
c_Orderings_Oord__class_Omax: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_53,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(decl_54,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_55,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_56,type,
c_Lambda_OdB_OAbs: $i > $i ).
tff(decl_57,type,
c_Lambda_Oliftn: ( $i * $i * $i ) > $i ).
tff(decl_58,type,
c_Lambda_Osubstn: ( $i * $i * $i ) > $i ).
tff(decl_59,type,
tc_Lambda_OdB: $i ).
tff(decl_60,type,
c_COMBC: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_61,type,
c_List_Omap: ( $i * $i * $i * $i ) > $i ).
tff(decl_62,type,
c_Type_Otypings: ( $i * $i * $i ) > $o ).
tff(decl_63,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_64,type,
hBOOL: $i > $o ).
tff(decl_65,type,
c_Lambda_OdB_OApp: $i ).
tff(decl_66,type,
c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3: $i > $i ).
tff(decl_67,type,
c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4: $i > $i ).
tff(decl_68,type,
c_List_Ofoldl: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_69,type,
c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1: $i > $i ).
tff(decl_70,type,
c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2: $i > $i ).
tff(decl_71,type,
c_ListApplication_Osko__ListApplication__Xlem__1__3: $i > $i ).
tff(decl_72,type,
c_ListApplication_Osko__ListApplication__Xlem__1__4: $i > $i ).
tff(decl_73,type,
c_ListApplication_Osko__ListApplication__Xlem__1__1: $i > $i ).
tff(decl_74,type,
c_ListApplication_Osko__ListApplication__Xlem__1__2: $i > $i ).
tff(decl_75,type,
v_sko__InductTermi__XIT__Xcases__4: $i > $i ).
tff(decl_76,type,
v_sko__InductTermi__XIT__Xcases__5: $i > $i ).
tff(decl_77,type,
v_sko__InductTermi__XIT__Xcases__6: $i > $i ).
tff(decl_78,type,
v_sko__InductTermi__XIT__Xcases__3: $i > $i ).
tff(decl_79,type,
c_InductTermi_OIT: $i ).
tff(decl_80,type,
v_sko__InductTermi__XIT__Xcases__1: $i > $i ).
tff(decl_81,type,
c_List_Olistsp: ( $i * $i * $i ) > $o ).
tff(decl_82,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(decl_83,type,
c_Lambda_Obeta: $i ).
tff(decl_84,type,
c_Transitive__Closure_Ortranclp: ( $i * $i ) > $i ).
tff(decl_85,type,
c_List_Oappend: ( $i * $i * $i ) > $i ).
tff(decl_86,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_87,type,
c_List_Olist_ONil: $i > $i ).
tff(decl_88,type,
c_List_Olistsum: ( $i * $i ) > $i ).
tff(decl_89,type,
c_ListOrder_Ostep1: ( $i * $i * $i * $i ) > $o ).
tff(decl_90,type,
c_Predicate_Oconversep: ( $i * $i * $i ) > $i ).
tff(decl_91,type,
c_List_Ofoldr: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_92,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_93,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_94,type,
c_Lambda_OdB_OdB__case: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_95,type,
c_List_Oreplicate: ( $i * $i * $i ) > $i ).
tff(decl_96,type,
c_Wellfounded_Oaccp: ( $i * $i * $i ) > $o ).
tff(decl_97,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(decl_98,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_99,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_100,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_101,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_102,type,
v_sko__InductTermi__XIT__Xcases__2: $i > $i ).
tff(decl_103,type,
c_OrderedGroup_Omonoid__add: ( $i * $i * $i ) > $o ).
tff(decl_104,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_105,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_106,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_107,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_108,type,
c_fequal: $i > $i ).
tff(decl_109,type,
c_OrderedGroup_Osemigroup__add: ( $i * $i ) > $o ).
tff(decl_110,type,
c_Lambda_OdB_OdB__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_111,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
tff(decl_112,type,
t_a: $i ).
tff(decl_113,type,
tc_String_Ochar: $i ).
tff(decl_114,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(decl_115,type,
c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_116,type,
c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2: $i > $i ).
tff(decl_117,type,
c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1: $i > $i ).
tff(decl_118,type,
c_Type_Osko__Type__Xvar__app__typesE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_119,type,
c_Type_Osko__Type__Xvar__app__types__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_120,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: ( $i * $i * $i ) > $i ).
tff(decl_121,type,
c_Lambda_OdB_OdB__size: $i > $i ).
tff(decl_122,type,
v_r: $i ).
tff(decl_123,type,
v_s: $i ).
tff(decl_124,type,
v_ss: $i ).
tff(decl_125,type,
v_i: $i ).
tff(decl_126,type,
tc_bool: $i ).
cnf(cls_conjecture_1,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_4,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(c_0_2,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
cls_conjecture_1 ).
cnf(c_0_3,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
cls_conjecture_4 ).
cnf(c_0_4,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_2,c_0_3]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL778-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n011.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 : Fri Aug 25 04:44:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.69/0.75 % Version : CSE_E---1.5
% 0.69/0.75 % Problem : theBenchmark.p
% 0.69/0.75 % Proof found
% 0.69/0.75 % SZS status Theorem for theBenchmark.p
% 0.69/0.75 % SZS output start Proof
% See solution above
% 0.69/0.75 % Total time : 0.149000 s
% 0.69/0.75 % SZS output end Proof
% 0.69/0.75 % Total time : 0.166000 s
%------------------------------------------------------------------------------