TSTP Solution File: LCL776-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL776-1 : 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 : 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 06:59:32 EDT 2023
% Result : Unsatisfiable 0.59s 1.17s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 105
% Syntax : Number of formulae : 113 ( 10 unt; 100 typ; 0 def)
% Number of atoms : 19 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 9 ~; 6 |; 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 : 158 ( 89 >; 69 *; 0 +; 0 <<)
% Number of predicates : 47 ( 45 usr; 1 prp; 0-4 aty)
% Number of functors : 55 ( 55 usr; 11 con; 0-5 aty)
% Number of variables : 16 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(decl_23,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(decl_24,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_25,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(decl_26,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_27,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_28,type,
tc_List_Olist: $i > $i ).
tff(decl_29,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(decl_30,type,
c_Suc: $i > $i ).
tff(decl_31,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_33,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
tff(decl_34,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_36,type,
tc_nat: $i ).
tff(decl_37,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
c_List_Otl: ( $i * $i ) > $i ).
tff(decl_39,type,
c_List_Odrop: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_41,type,
c_List_Onth: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
c_HOL_Oord__class_Oless: $i > $i ).
tff(decl_43,type,
hBOOL: $i > $o ).
tff(decl_44,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_45,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(decl_46,type,
c_List_Olist__update: ( $i * $i * $i * $i ) > $i ).
tff(decl_47,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_48,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_49,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_52,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_53,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_54,type,
c_List_Oappend: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
c_List_Ohd: ( $i * $i ) > $i ).
tff(decl_56,type,
c_List_Olist_ONil: $i > $i ).
tff(decl_57,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_58,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_59,type,
class_Power_Opower: $i > $o ).
tff(decl_60,type,
c_List_Orev: ( $i * $i ) > $i ).
tff(decl_61,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_62,type,
class_Int_Onumber: $i > $o ).
tff(decl_63,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_64,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(decl_65,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_66,type,
c_List_Otake: ( $i * $i * $i ) > $i ).
tff(decl_67,type,
c_List_Olast: ( $i * $i ) > $i ).
tff(decl_68,type,
c_List_Obutlast: ( $i * $i ) > $i ).
tff(decl_69,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_70,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_71,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_72,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_73,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_74,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(decl_75,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_76,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_77,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_78,type,
c_List_Oreplicate: ( $i * $i * $i ) > $i ).
tff(decl_79,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_80,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_81,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_82,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(decl_83,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_84,type,
c_HOL_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(decl_85,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_86,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_87,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_88,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_89,type,
class_Ring__and__Field_Osgn__if: $i > $o ).
tff(decl_90,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_91,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
tff(decl_92,type,
c_List_Ofoldl: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_93,type,
c_Ring__and__Field_Oordered__semidom__axioms: ( $i * $i * $i * $i ) > $o ).
tff(decl_94,type,
c_ListOrder_Ostep1: ( $i * $i ) > $i ).
tff(decl_95,type,
c_Wellfounded_Oaccp: ( $i * $i ) > $i ).
tff(decl_96,type,
c_List_Orotate1: ( $i * $i ) > $i ).
tff(decl_97,type,
c_List_Olistsp: ( $i * $i * $i ) > $o ).
tff(decl_98,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(decl_99,type,
c_Lambda_Osubst: ( $i * $i * $i ) > $i ).
tff(decl_100,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(decl_101,type,
c_Lambda_Obeta: $i ).
tff(decl_102,type,
tc_Lambda_OdB: $i ).
tff(decl_103,type,
c_Transitive__Closure_Ortranclp: ( $i * $i ) > $i ).
tff(decl_104,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: ( $i * $i * $i ) > $i ).
tff(decl_105,type,
c_Lambda_OdB_OApp: $i ).
tff(decl_106,type,
c_Lambda_OdB_OAbs: $i > $i ).
tff(decl_107,type,
c_Predicate_Oconversep: ( $i * $i * $i ) > $i ).
tff(decl_108,type,
c_fequal: $i > $i ).
tff(decl_109,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(decl_110,type,
c_InductTermi_OIT: $i ).
tff(decl_111,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_112,type,
c_List_Osko__List__Xappend__eq__Cons__conv__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_113,type,
c_List_Osko__List__XCons__eq__append__conv__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_114,type,
c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_115,type,
v_r: $i ).
tff(decl_116,type,
v_s: $i ).
tff(decl_117,type,
v_ss: $i ).
tff(decl_118,type,
v_i: $i ).
tff(decl_119,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_120,type,
tc_bool: $i ).
tff(decl_121,type,
tc_Int_Oint: $i ).
cnf(cls_Beta_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).
cnf(cls_app__last_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__last_0) ).
cnf(cls_conjecture_4,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_conjecture_1,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_2,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(c_0_5,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
cls_Beta_0 ).
cnf(c_0_6,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
cls_app__last_0 ).
cnf(c_0_7,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
cls_conjecture_4 ).
cnf(c_0_8,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_6]) ).
cnf(c_0_9,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,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_10,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
cls_conjecture_2 ).
cnf(c_0_11,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_12,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]),c_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL776-1 : 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
% 0.13/0.35 % Computer : n014.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 : Fri Aug 25 00:36:03 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.59/1.17 % Version : CSE_E---1.5
% 0.59/1.17 % Problem : theBenchmark.p
% 0.59/1.17 % Proof found
% 0.59/1.17 % SZS status Theorem for theBenchmark.p
% 0.59/1.17 % SZS output start Proof
% See solution above
% 0.59/1.18 % Total time : 0.559000 s
% 0.59/1.18 % SZS output end Proof
% 0.59/1.18 % Total time : 0.585000 s
%------------------------------------------------------------------------------