TSTP Solution File: LCL837-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL837-1 : 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 : n028.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 06:59:54 EDT 2023
% Result : Unsatisfiable 0.17s 0.77s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 104
% Syntax : Number of formulae : 114 ( 13 unt; 98 typ; 0 def)
% Number of atoms : 19 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 135 ( 82 >; 53 *; 0 +; 0 <<)
% Number of predicates : 49 ( 47 usr; 1 prp; 0-3 aty)
% Number of functors : 51 ( 51 usr; 16 con; 0-6 aty)
% Number of variables : 28 ( 3 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
tc_nat: $i ).
tff(decl_23,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_24,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_25,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(decl_26,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(decl_27,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_28,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
c_Suc: $i > $i ).
tff(decl_30,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
tff(decl_31,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_32,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_33,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(decl_35,type,
c_Lambda_Olift: $i ).
tff(decl_36,type,
c_Lambda_Osubst: $i ).
tff(decl_37,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(decl_38,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(decl_39,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(decl_40,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_41,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_43,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_45,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_46,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_47,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_48,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_49,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_50,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_51,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_52,type,
class_Power_Opower: $i > $o ).
tff(decl_53,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_54,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_55,type,
class_Ring__and__Field_Odvd: $i > $o ).
tff(decl_56,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_57,type,
c_List_Olist_ONil: $i > $i ).
tff(decl_58,type,
c_List_Olistsp: ( $i * $i * $i ) > $o ).
tff(decl_59,type,
c_Lambda_OdB_OdB__size: $i > $i ).
tff(decl_60,type,
c_Lambda_OdB_OAbs: $i > $i ).
tff(decl_61,type,
c_Lambda_Osubstn: ( $i * $i * $i ) > $i ).
tff(decl_62,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(decl_63,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_64,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_65,type,
tc_Lambda_OdB: $i ).
tff(decl_66,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(decl_67,type,
c_Lambda_Oliftn: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(decl_69,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(decl_70,type,
tc_Type_Otype: $i ).
tff(decl_71,type,
c_Type_Oshift: ( $i * $i * $i * $i ) > $i ).
tff(decl_72,type,
c_Lambda_Obeta: ( $i * $i ) > $o ).
tff(decl_73,type,
hBOOL: $i > $o ).
tff(decl_74,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_75,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_76,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_77,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_78,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_79,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(decl_80,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_81,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_82,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_83,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_84,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_85,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_86,type,
v_sko__List__Xlexn__Xinduct__1: $i > $i ).
tff(decl_87,type,
c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1: $i > $i ).
tff(decl_88,type,
c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1: $i > $i ).
tff(decl_89,type,
v_sko__List__Xreplicate__Xinduct__1: $i > $i ).
tff(decl_90,type,
v_sko__Nat__Xnat__Xinducts__1: $i > $i ).
tff(decl_91,type,
v_sko__Nat__Xnat__Xinduct__1: $i > $i ).
tff(decl_92,type,
v_sko__List__Xupt__Xinduct__1: $i > $i ).
tff(decl_93,type,
c_Lambda_OdB_OApp: $i ).
tff(decl_94,type,
c_List_Omap: ( $i * $i * $i * $i ) > $i ).
tff(decl_95,type,
c_List_Ofoldl: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_96,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
tff(decl_97,type,
c_SetInterval_Oord__class_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
c_Finite__Set_Osetsum: ( $i * $i * $i * $i ) > $i ).
tff(decl_99,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_100,type,
v_e____: $i ).
tff(decl_101,type,
v_u____: $i ).
tff(decl_102,type,
v_T____: $i ).
tff(decl_103,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_104,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(decl_105,type,
c_InductTermi_OIT: $i ).
tff(decl_106,type,
v_ua______: $i ).
tff(decl_107,type,
v_a____: $i ).
tff(decl_108,type,
v_i____: $i ).
tff(decl_109,type,
v_r____: $i ).
tff(decl_110,type,
v_as____: $i ).
tff(decl_111,type,
v_T_H____: $i ).
tff(decl_112,type,
c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1: $i > $i ).
tff(decl_113,type,
c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1: $i > $i ).
tff(decl_114,type,
c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1: $i > $i ).
tff(decl_115,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_116,type,
c_COMBC: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_117,type,
c_Type_Otypings: ( $i * $i * $i ) > $o ).
tff(decl_118,type,
c_COMBB: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_119,type,
c_fequal: ( $i * $i * $i ) > $o ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),hAPP(hAPP(c_Lambda_Olift,v_u____),c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(v_i____))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_Suc__eq__plus1_0,axiom,
c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
cnf(cls_subst__subst_0,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),X3)),c_Suc(X4))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4)
| ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__subst_0) ).
cnf(cls_zero__less__Suc_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
cnf(cls_subst__map_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X3,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__map_0) ).
cnf(cls_CHAINED_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,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)),v_u____),v_i____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(c_0_6,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),hAPP(hAPP(c_Lambda_Olift,v_u____),c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(v_i____))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
cls_conjecture_0 ).
cnf(c_0_7,axiom,
c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
cls_Suc__eq__plus1_0 ).
cnf(c_0_8,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),X3)),c_Suc(X4))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4)
| ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
cls_subst__subst_0 ).
cnf(c_0_9,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
cls_zero__less__Suc_0 ).
cnf(c_0_10,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),hAPP(hAPP(c_Lambda_Olift,v_u____),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_i____),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4)
| ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(rw,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_12,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X3,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
cls_subst__map_0 ).
cnf(c_0_13,axiom,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,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)),v_u____),v_i____))),
cls_CHAINED_0 ).
cnf(c_0_14,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(rw,[status(thm)],[c_0_9,c_0_7]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL837-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32 % Computer : n028.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Aug 24 17:26:05 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.17/0.55 start to proof: theBenchmark
% 0.17/0.77 % Version : CSE_E---1.5
% 0.17/0.77 % Problem : theBenchmark.p
% 0.17/0.77 % Proof found
% 0.17/0.77 % SZS status Theorem for theBenchmark.p
% 0.17/0.77 % SZS output start Proof
% See solution above
% 0.17/0.77 % Total time : 0.195000 s
% 0.17/0.77 % SZS output end Proof
% 0.17/0.77 % Total time : 0.214000 s
%------------------------------------------------------------------------------