TSTP Solution File: LCL816-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL816-1 : 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 : n008.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 06:59:47 EDT 2023
% Result : Unsatisfiable 5.27s 5.36s
% Output : CNFRefutation 5.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 100
% Syntax : Number of formulae : 112 ( 14 unt; 94 typ; 0 def)
% Number of atoms : 25 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 153 ( 73 >; 80 *; 0 +; 0 <<)
% Number of predicates : 41 ( 39 usr; 1 prp; 0-4 aty)
% Number of functors : 55 ( 55 usr; 21 con; 0-6 aty)
% Number of variables : 47 ( 6 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(decl_23,type,
c_ListOrder_Ostep1: ( $i * $i * $i * $i ) > $o ).
tff(decl_24,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_25,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_26,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_28,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_29,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_30,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_31,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(decl_32,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
tff(decl_33,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_34,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_35,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_36,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_37,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_38,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(decl_39,type,
tc_nat: $i ).
tff(decl_40,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
c_Suc: $i > $i ).
tff(decl_42,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(decl_43,type,
class_Power_Opower: $i > $o ).
tff(decl_44,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_45,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(decl_46,type,
c_Lambda_Oliftn: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
c_Lambda_Olift: $i ).
tff(decl_48,type,
hBOOL: $i > $o ).
tff(decl_49,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_50,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_51,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_52,type,
c_List_Olist_ONil: $i > $i ).
tff(decl_53,type,
c_List_Oappend: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_55,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_56,type,
c_Lambda_OdB_OApp: $i ).
tff(decl_57,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_58,type,
c_Lambda_Obeta: $i ).
tff(decl_59,type,
tc_Lambda_OdB: $i ).
tff(decl_60,type,
c_List_Ofoldl: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_61,type,
c_Lambda_Osubstn: ( $i * $i * $i ) > $i ).
tff(decl_62,type,
c_Lambda_Osubst: $i ).
tff(decl_63,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_64,type,
c_List_Orev: ( $i * $i ) > $i ).
tff(decl_65,type,
c_List_Olistsp: ( $i * $i * $i ) > $o ).
tff(decl_66,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: ( $i * $i * $i ) > $i ).
tff(decl_67,type,
v_rs____: $i ).
tff(decl_68,type,
v_a____: $i ).
tff(decl_69,type,
v_as____: $i ).
tff(decl_70,type,
c_Lambda_OdB_OAbs: $i > $i ).
tff(decl_71,type,
c_Lambda_OdB_OdB__size: $i > $i ).
tff(decl_72,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(decl_73,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_74,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_75,type,
class_Int_Onumber__ring: $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_Type_Otype_OAtom: $i > $i ).
tff(decl_79,type,
t_a: $i ).
tff(decl_80,type,
c_Type_Otype_Otype__case: ( $i * $i * $i * $i ) > $i ).
tff(decl_81,type,
c_InductTermi_OIT: $i ).
tff(decl_82,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_83,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_84,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_85,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_86,type,
c_List_Omap: ( $i * $i * $i * $i ) > $i ).
tff(decl_87,type,
c_Fun_Ocomp: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_88,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
tff(decl_89,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(decl_90,type,
c_Type_Otype_OFun: $i ).
tff(decl_91,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(decl_92,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_93,type,
c_Type_Otype_Otype__rec: ( $i * $i * $i * $i ) > $i ).
tff(decl_94,type,
c_OrderedGroup_Oab__semigroup__add: ( $i * $i ) > $o ).
tff(decl_95,type,
c_List_Ofoldr: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_96,type,
c_Type_Oshift: ( $i * $i * $i * $i ) > $i ).
tff(decl_97,type,
v_n____: $i ).
tff(decl_98,type,
v_i____: $i ).
tff(decl_99,type,
c_Type_Osko__Type__Xlist__app__typeD__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_100,type,
c_Type_Otypings: ( $i * $i * $i ) > $o ).
tff(decl_101,type,
c_Type_Osko__Type__Xlist__app__typeE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_102,type,
v_e____: $i ).
tff(decl_103,type,
v_T____: $i ).
tff(decl_104,type,
tc_Type_Otype: $i ).
tff(decl_105,type,
v_T_H_H____: $i ).
tff(decl_106,type,
v_u____: $i ).
tff(decl_107,type,
c_Type_Osko__Type__Xtyping__elims__2__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_108,type,
c_Type_Osko__Type__Xvar__app__typesE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_109,type,
c_Type_Osko__Type__Xvar__app__types__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_110,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_111,type,
c_COMBC: ( $i * $i * $i * $i ) > $i ).
tff(decl_112,type,
v_Ts____: $i ).
tff(decl_113,type,
v_T_H____: $i ).
tff(decl_114,type,
c_COMBB: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_115,type,
c_fequal: ( $i * $i * $i ) > $o ).
cnf(cls_list__app__typeI_0,axiom,
( c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otypings(X1,X3,X5)
| ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).
cnf(cls_foldr__foldl_0,axiom,
c_List_Ofoldr(X1,X2,X3,X4,X5) = c_List_Ofoldl(c_COMBC(X1,X4,X5,X5),X3,c_List_Orev(X2,X4),X5,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__foldl_0) ).
cnf(cls_typing_OVar_0,axiom,
c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
cnf(cls_shift__eq_0,axiom,
hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).
cnf(cls_CHAINED_0,axiom,
c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_6,axiom,
( c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otypings(X1,X3,X5)
| ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype)) ),
cls_list__app__typeI_0 ).
cnf(c_0_7,axiom,
c_List_Ofoldr(X1,X2,X3,X4,X5) = c_List_Ofoldl(c_COMBC(X1,X4,X5,X5),X3,c_List_Orev(X2,X4),X5,X4),
cls_foldr__foldl_0 ).
cnf(c_0_8,axiom,
c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
cls_typing_OVar_0 ).
cnf(c_0_9,axiom,
hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
cls_shift__eq_0 ).
cnf(c_0_10,plain,
( c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otypings(X1,X3,X5)
| ~ c_Type_Otyping(X1,X2,c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),X4,c_List_Orev(X5,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype)) ),
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,plain,
c_Type_Otyping(c_Type_Oshift(X1,X2,X3,X4),c_Lambda_OdB_OVar(X2),X3),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,axiom,
c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
cls_CHAINED_0 ).
cnf(c_0_13,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
cls_conjecture_0 ).
cnf(c_0_14,plain,
( c_Type_Otyping(c_Type_Oshift(X1,X2,c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),X3,c_List_Orev(X4,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype),X5),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X6,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ c_Type_Otypings(c_Type_Oshift(X1,X2,c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),X3,c_List_Orev(X4,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype),X5),X6,X4) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(v_Ts____,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(rw,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_16,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(v_Ts____,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(rw,[status(thm)],[c_0_13,c_0_7]) ).
cnf(c_0_17,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL816-1 : 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 : n008.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 01:43:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 5.27/5.36 % Version : CSE_E---1.5
% 5.27/5.36 % Problem : theBenchmark.p
% 5.27/5.36 % Proof found
% 5.27/5.36 % SZS status Theorem for theBenchmark.p
% 5.27/5.36 % SZS output start Proof
% See solution above
% 5.32/5.36 % Total time : 4.755000 s
% 5.32/5.36 % SZS output end Proof
% 5.32/5.36 % Total time : 4.770000 s
%------------------------------------------------------------------------------