TSTP Solution File: LCL834-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL834-1 : 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 : n023.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 06:59:53 EDT 2023
% Result : Unsatisfiable 0.54s 0.64s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 110
% Syntax : Number of formulae : 114 ( 5 unt; 107 typ; 0 def)
% Number of atoms : 9 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 179 ( 85 >; 94 *; 0 +; 0 <<)
% Number of predicates : 36 ( 35 usr; 1 prp; 0-3 aty)
% Number of functors : 72 ( 72 usr; 22 con; 0-5 aty)
% Number of variables : 10 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
c_Lambda_OdB_OApp: $i ).
tff(decl_23,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_24,type,
tc_Lambda_OdB: $i ).
tff(decl_25,type,
c_List_Ofoldl: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_26,type,
c_List_Olist_ONil: $i > $i ).
tff(decl_27,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
c_List_Oappend: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
c_ListOrder_Ostep1: ( $i * $i ) > $i ).
tff(decl_30,type,
tc_List_Olist: $i > $i ).
tff(decl_31,type,
c_Wellfounded_Oaccp: ( $i * $i ) > $i ).
tff(decl_32,type,
hBOOL: $i > $o ).
tff(decl_33,type,
c_List_Olistsp: ( $i * $i * $i ) > $o ).
tff(decl_34,type,
c_List_Oreplicate: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
c_List_Orev: ( $i * $i ) > $i ).
tff(decl_36,type,
tc_nat: $i ).
tff(decl_37,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
tff(decl_38,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_39,type,
c_List_Omap: ( $i * $i * $i * $i ) > $i ).
tff(decl_40,type,
c_List_Orotate1: ( $i * $i ) > $i ).
tff(decl_41,type,
c_List_Otake: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
c_InductTermi_OIT: $i ).
tff(decl_43,type,
v_ua______: $i ).
tff(decl_44,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_45,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_46,type,
c_List_Olast: ( $i * $i ) > $i ).
tff(decl_47,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_48,type,
v_u____: $i ).
tff(decl_49,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(decl_50,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: ( $i * $i * $i * $i ) > $i ).
tff(decl_51,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(decl_52,type,
c_Lambda_Osubstn: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_54,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_55,type,
c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_56,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_57,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_58,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_59,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(decl_60,type,
c_Type_Oshift: ( $i * $i * $i * $i ) > $i ).
tff(decl_61,type,
c_ATP__Linkup_Osko__Nat__Xex__least__nat__less__1__1: ( $i * $i ) > $i ).
tff(decl_62,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_63,type,
c_Type_Otype_OFun: ( $i * $i ) > $i ).
tff(decl_64,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_65,type,
c_List_Obutlast: ( $i * $i ) > $i ).
tff(decl_66,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_67,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(decl_68,type,
c_List_Osko__List__Xappend__eq__Cons__conv__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_69,type,
c_List_Osko__List__XCons__eq__append__conv__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_70,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(decl_71,type,
c_Lambda_Osubst: $i ).
tff(decl_72,type,
c_Lambda_Olift: $i ).
tff(decl_73,type,
c_Lambda_Oliftn: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
c_Lambda_OdB_OAbs: $i > $i ).
tff(decl_75,type,
tc_Type_Otype: $i ).
tff(decl_76,type,
v_e____: $i ).
tff(decl_77,type,
v_T____: $i ).
tff(decl_78,type,
v_ea______: $i ).
tff(decl_79,type,
c_COMBC: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_80,type,
c_Type_Otypings: ( $i * $i * $i ) > $o ).
tff(decl_81,type,
c_ListBeta_Osko__ListBeta__Xapps__betasE__1__4: ( $i * $i * $i ) > $i ).
tff(decl_82,type,
c_ListBeta_Osko__ListBeta__Xapps__betasE__1__5: ( $i * $i * $i ) > $i ).
tff(decl_83,type,
c_ListBeta_Osko__ListBeta__Xapps__betasE__1__2: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
c_ListBeta_Osko__ListBeta__Xapps__betasE__1__1: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
c_Lambda_Obeta: $i ).
tff(decl_86,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_87,type,
c_Transitive__Closure_Ortranclp: ( $i * $i ) > $i ).
tff(decl_88,type,
c_Predicate_Oconversep: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_90,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_91,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_92,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_93,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_94,type,
c_OrderedGroup_Omonoid__add: ( $i * $i * $i ) > $o ).
tff(decl_95,type,
c_ListBeta_Osko__ListBeta__Xapps__betasE__1__3: ( $i * $i * $i ) > $i ).
tff(decl_96,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_97,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_98,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_99,type,
class_Power_Opower: $i > $o ).
tff(decl_100,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_101,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_102,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_103,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_104,type,
t_a: $i ).
tff(decl_105,type,
c_Lambda_OdB_OdB__case: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_106,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_107,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_108,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_109,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(decl_110,type,
c_fequal: $i > $i ).
tff(decl_111,type,
c_Lambda_OdB_OdB__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_112,type,
c_OrderedGroup_Osemigroup__add: ( $i * $i ) > $o ).
tff(decl_113,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
tff(decl_114,type,
v_a____: $i ).
tff(decl_115,type,
c_Lambda_Osko__Lambda__Xbeta__cases__3__3: ( $i * $i * $i ) > $i ).
tff(decl_116,type,
c_Lambda_Osko__Lambda__Xbeta__cases__3__2: ( $i * $i * $i ) > $i ).
tff(decl_117,type,
c_Lambda_Osko__Lambda__Xbeta__cases__3__1: ( $i * $i * $i ) > $i ).
tff(decl_118,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: ( $i * $i * $i ) > $i ).
tff(decl_119,type,
c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2: $i > $i ).
tff(decl_120,type,
c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1: $i > $i ).
tff(decl_121,type,
v_ia______: $i ).
tff(decl_122,type,
v_r____: $i ).
tff(decl_123,type,
v_as____: $i ).
tff(decl_124,type,
v_T_Ha______: $i ).
tff(decl_125,type,
v_i____: $i ).
tff(decl_126,type,
v_T_H____: $i ).
tff(decl_127,type,
c_Lambda_Osko__Lambda__Xbeta__cases__2__1: ( $i * $i ) > $i ).
tff(decl_128,type,
tc_bool: $i ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_apps__preserves__beta_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
cnf(cls_beta_0,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).
cnf(c_0_3,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
cls_conjecture_0 ).
cnf(c_0_4,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)) ),
cls_apps__preserves__beta_0 ).
cnf(c_0_5,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)))),
cls_beta_0 ).
cnf(c_0_6,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4]),c_0_5])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL834-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Aug 25 04:29:12 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.54/0.64 % Version : CSE_E---1.5
% 0.54/0.64 % Problem : theBenchmark.p
% 0.54/0.64 % Proof found
% 0.54/0.64 % SZS status Theorem for theBenchmark.p
% 0.54/0.64 % SZS output start Proof
% See solution above
% 0.54/0.64 % Total time : 0.058000 s
% 0.54/0.64 % SZS output end Proof
% 0.54/0.64 % Total time : 0.073000 s
%------------------------------------------------------------------------------