TSTP Solution File: LCL754-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL754-1 : 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 : n018.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 06:59:25 EDT 2023
% Result : Unsatisfiable 56.79s 56.88s
% Output : CNFRefutation 56.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 107
% Syntax : Number of formulae : 167 ( 56 unt; 81 typ; 0 def)
% Number of atoms : 116 ( 50 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 69 ( 39 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 105 ( 77 >; 28 *; 0 +; 0 <<)
% Number of predicates : 59 ( 57 usr; 1 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 4 con; 0-3 aty)
% Number of variables : 131 ( 28 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_23,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_24,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_25,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_26,type,
tc_nat: $i ).
tff(decl_27,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(decl_28,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_30,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(decl_32,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_33,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_35,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_36,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_38,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_40,type,
c_Suc: $i > $i ).
tff(decl_41,type,
c_Lambda_Oliftn: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
c_Lambda_Olift: ( $i * $i ) > $i ).
tff(decl_43,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(decl_44,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(decl_45,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_46,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_47,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(decl_48,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_49,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(decl_50,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(decl_51,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_52,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_53,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_54,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_55,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_56,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(decl_57,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_58,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(decl_59,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(decl_60,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_61,type,
c_Lambda_OdB_OAbs: $i > $i ).
tff(decl_62,type,
c_Lambda_Osubstn: ( $i * $i * $i ) > $i ).
tff(decl_63,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_64,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_65,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_66,type,
class_Power_Opower: $i > $o ).
tff(decl_67,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_68,type,
c_Lambda_Osubst: ( $i * $i * $i ) > $i ).
tff(decl_69,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_70,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_71,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(decl_72,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_73,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_74,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_75,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_76,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_77,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_78,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_79,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_80,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_81,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(decl_82,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(decl_83,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(decl_84,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(decl_85,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(decl_86,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(decl_87,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_88,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(decl_89,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_90,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_91,type,
c_Lambda_OdB_OApp: ( $i * $i ) > $i ).
tff(decl_92,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(decl_93,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(decl_94,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_95,type,
c_Lambda_Osko__Lambda__Xbeta__cases__2__1: ( $i * $i ) > $i ).
tff(decl_96,type,
c_Lambda_Obeta: ( $i * $i ) > $o ).
tff(decl_97,type,
c_List_Oupt: ( $i * $i ) > $i ).
tff(decl_98,type,
c_List_Olast: ( $i * $i ) > $i ).
tff(decl_99,type,
c_InductTermi_OIT: $i > $o ).
tff(decl_100,type,
v_ra: $i ).
tff(decl_101,type,
v_ia: $i ).
tff(decl_102,type,
v_ja: $i ).
cnf(cls_less__Suc__eq__le_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
cnf(cls_Suc__eq__plus1_0,axiom,
c_Suc(X1) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
cnf(cls_class__semiring_Oadd__0_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
cnf(cls_diff__self__eq__0_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
cnf(cls_mod__less__eq__dividend_0,axiom,
c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).
cnf(cls_mod__1_0,axiom,
c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).
cnf(cls_minus__nat_Odiff__0_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
cnf(cls_gr__implies__not0_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
cnf(cls_mod__if_1,axiom,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_1) ).
cnf(cls_nat__less__le_1,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
cnf(cls_plus__nat_Oadd__0_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
cnf(cls_mod__if_0,axiom,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).
cnf(cls_mod__by__0_0,axiom,
( c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
cnf(clsarity_nat__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
cnf(cls_natgb_Oadd__r0__iff_1,axiom,
X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
cnf(cls_not__less__eq_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
cnf(cls_mod__mult__self1__is__0_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
cnf(cls_trans__less__add2_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
cnf(cls_subst__Abs_0,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Abs_0) ).
cnf(cls_mod__mult__self2__is__0_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
cnf(cls_Lambda_0,axiom,
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
| ~ c_InductTermi_OIT(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_lift_Osimps_I1_J_1,axiom,
( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(v_ia),v_ja)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(c_0_26,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_less__Suc__eq__le_1 ).
cnf(c_0_27,axiom,
c_Suc(X1) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
cls_Suc__eq__plus1_0 ).
cnf(c_0_28,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__0_0 ).
cnf(c_0_30,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_diff__self__eq__0_0 ).
cnf(c_0_31,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
clsarity_nat__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_32,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_lessequals(X1,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),tc_nat) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_33,axiom,
c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
cls_mod__less__eq__dividend_0 ).
cnf(c_0_34,axiom,
c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_mod__1_0 ).
cnf(c_0_35,axiom,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
cls_minus__nat_Odiff__0_0 ).
cnf(c_0_36,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_gr__implies__not0_0 ).
cnf(c_0_37,plain,
c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,axiom,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_mod__if_1 ).
cnf(c_0_39,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
cls_nat__less__le_1 ).
cnf(c_0_40,plain,
c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(rw,[status(thm)],[c_0_34,c_0_27]) ).
cnf(c_0_41,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
cls_plus__nat_Oadd__0_0 ).
cnf(c_0_42,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),tc_nat) = X1,
inference(rw,[status(thm)],[c_0_35,c_0_30]) ).
cnf(c_0_43,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),
inference(rw,[status(thm)],[c_0_30,c_0_30]) ).
cnf(c_0_44,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),tc_nat),
inference(rw,[status(thm)],[c_0_36,c_0_30]) ).
cnf(c_0_45,axiom,
( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_mod__if_0 ).
cnf(c_0_46,plain,
c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_47,plain,
c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_30]) ).
cnf(c_0_48,axiom,
( c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__by__0_0 ).
cnf(c_0_49,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X2,tc_nat),tc_nat) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,axiom,
class_Divides_Osemiring__div(tc_nat),
clsarity_nat__Divides_Osemiring__div ).
cnf(c_0_51,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X2,tc_nat),tc_nat),
inference(spm,[status(thm)],[c_0_44,c_0_43]) ).
cnf(c_0_52,axiom,
X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_natgb_Oadd__r0__iff_1 ).
cnf(c_0_53,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),X1,tc_nat) = X1,
inference(rw,[status(thm)],[c_0_41,c_0_30]) ).
cnf(c_0_54,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ominus__class_Ominus(X2,X2,tc_nat),
inference(spm,[status(thm)],[c_0_43,c_0_43]) ).
cnf(c_0_55,plain,
c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat) = c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_56,plain,
c_Divides_Odiv__class_Omod(X1,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),tc_nat) = X1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_38]),c_0_30]),c_0_30]),c_0_49]),c_0_30]),c_0_50])]),c_0_51]) ).
cnf(c_0_57,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),tc_nat) = X1,
inference(rw,[status(thm)],[c_0_52,c_0_30]) ).
cnf(c_0_58,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
cls_not__less__eq_1 ).
cnf(c_0_59,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),X2,tc_nat) = X2,
inference(spm,[status(thm)],[c_0_53,c_0_43]) ).
cnf(c_0_60,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__self1__is__0_0 ).
cnf(c_0_62,plain,
c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),tc_nat) = X1,
inference(rw,[status(thm)],[c_0_56,c_0_55]) ).
cnf(c_0_63,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X2,tc_nat),tc_nat) = X1,
inference(spm,[status(thm)],[c_0_57,c_0_43]) ).
cnf(c_0_64,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(rw,[status(thm)],[c_0_58,c_0_27]) ).
cnf(c_0_65,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_trans__less__add2_0 ).
cnf(c_0_66,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I3_J_0 ).
cnf(c_0_67,plain,
c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),X1,tc_nat) = X1,
inference(rw,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_68,plain,
c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_30]),c_0_60]),c_0_50])]) ).
cnf(c_0_69,plain,
c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),tc_nat) = X1,
inference(rw,[status(thm)],[c_0_63,c_0_60]) ).
cnf(c_0_70,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
cls_subst__Abs_0 ).
cnf(c_0_71,plain,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_72,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
cls_mod__mult__self2__is__0_0 ).
cnf(c_0_73,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_69]),c_0_31])]) ).
cnf(c_0_74,axiom,
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
| ~ c_InductTermi_OIT(X1) ),
cls_Lambda_0 ).
cnf(c_0_75,plain,
c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat)),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) = c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3),
inference(rw,[status(thm)],[c_0_70,c_0_30]) ).
cnf(c_0_76,negated_conjecture,
c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X1),X2)),
cls_conjecture_1 ).
cnf(c_0_77,axiom,
( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_lift_Osimps_I1_J_1 ).
cnf(c_0_78,plain,
~ c_HOL_Oord__class_Oless(X1,c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),tc_nat),
inference(spm,[status(thm)],[c_0_71,c_0_46]) ).
cnf(c_0_79,plain,
c_Divides_Odiv__class_Omod(X1,X1,tc_nat) = c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_30]),c_0_60]),c_0_50])]) ).
cnf(c_0_80,plain,
( c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3))
| ~ c_InductTermi_OIT(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_Divides_Odiv__class_Omod(tc_nat,tc_nat,tc_nat)),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_60]) ).
cnf(c_0_81,negated_conjecture,
( c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2),X3))
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_82,plain,
~ c_HOL_Oord__class_Oless(X1,c_Divides_Odiv__class_Omod(X2,X2,tc_nat),tc_nat),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_83,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(v_ia),v_ja)),
cls_conjecture_2 ).
cnf(c_0_84,negated_conjecture,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(X1),X2)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_85,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL754-1 : 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 : n018.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 06:59:28 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 56.79/56.88 % Version : CSE_E---1.5
% 56.79/56.88 % Problem : theBenchmark.p
% 56.79/56.88 % Proof found
% 56.79/56.88 % SZS status Theorem for theBenchmark.p
% 56.79/56.88 % SZS output start Proof
% See solution above
% 56.79/56.89 % Total time : 56.276000 s
% 56.79/56.89 % SZS output end Proof
% 56.79/56.89 % Total time : 56.298000 s
%------------------------------------------------------------------------------