%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET818-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:30:58 AM UTC 2026
% Result : Unsatisfiable 22.23s 7.69s
% Output : Refutation 23.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 1168
% Syntax : Number of formulae : 2337 ( 387 unt; 0 typ; 0 def)
% Number of atoms : 4385 ( 268 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 13178 (2066 ~;2048 |; 0 &;9064 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 165 ( 163 usr; 11 con; 0-6 aty)
% Number of variables : 3170 ( 0 ^;3170 !; 0 ?;3170 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_x_decl,type,
v_x: $i > $i ).
thf(tc_IntDef_Oint_decl,type,
tc_IntDef_Oint: $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_Wellfounded__Recursion_Owf_decl,type,
c_Wellfounded__Recursion_Owf: $i > $i > $o ).
thf(c_Wellfounded__Relations_Oless__than_decl,type,
c_Wellfounded__Relations_Oless__than: $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_append_decl,type,
c_append: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(c_List_Olistrel_decl,type,
c_List_Olistrel: $i > $i > $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_Datatype__Universe_OIn1_decl,type,
c_Datatype__Universe_OIn1: $i > $i > $i > $i ).
thf(c_Datatype__Universe_OIn0_decl,type,
c_Datatype__Universe_OIn0: $i > $i > $i > $i ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_SetInterval_OlessThan_decl,type,
c_SetInterval_OlessThan: $i > $i > $i ).
thf(c_Wellfounded__Recursion_Oacyclic_decl,type,
c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).
thf(c_Relation_Oconverse_decl,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_Nat_Osize_decl,type,
c_Nat_Osize: $i > $i > $i ).
thf(c_SetInterval_OgreaterThan_decl,type,
c_SetInterval_OgreaterThan: $i > $i > $i ).
thf(c_List_Olex_decl,type,
c_List_Olex: $i > $i > $i ).
thf(c_Datatype__Universe_Odprod_decl,type,
c_Datatype__Universe_Odprod: $i > $i > $i > $i > $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(tc_Datatype__Universe_Onode_decl,type,
tc_Datatype__Universe_Onode: $i > $i > $i ).
thf(c_Datatype__Universe_OScons_decl,type,
c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__1_decl,type,
c_Main_OdprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__2_decl,type,
c_Main_OdprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__3_decl,type,
c_Main_OdprodE__3: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__4_decl,type,
c_Main_OdprodE__4: $i > $i > $i > $i > $i > $i ).
thf(class_Ring__and__Field_Osemiring__0_decl,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(class_HOL_Otimes_decl,type,
class_HOL_Otimes: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_decl,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_decl,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_decl,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__comm__semiring_decl,type,
class_Ring__and__Field_Opordered__cancel__comm__semiring: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Osemiring_decl,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__add_decl,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__abs_decl,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1__cancel_decl,type,
class_Ring__and__Field_Ocomm__semiring__1__cancel: $i > $o ).
thf(class_Ring__and__Field_Opordered__comm__semiring_decl,type,
class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).
thf(class_HOL_Oplus_decl,type,
class_HOL_Oplus: $i > $o ).
thf(class_OrderedGroup_Osemigroup__add_decl,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
thf(class_Ring__and__Field_Oring__1_decl,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(class_Ring__and__Field_Olordered__ring_decl,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(c_List_Olists_decl,type,
c_List_Olists: $i > $i > $i ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring__1_decl,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Opordered__ring_decl,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(class_OrderedGroup_Ocancel__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Oordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_uminus_decl,type,
c_uminus: $i > $i > $i ).
thf(class_Power_Orecpower_decl,type,
class_Power_Orecpower: $i > $o ).
thf(class_Ring__and__Field_Osemiring__1__cancel_decl,type,
class_Ring__and__Field_Osemiring__1__cancel: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__0_decl,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
thf(c_Finite__Set_OFinites_decl,type,
c_Finite__Set_OFinites: $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Ocomm__semiring__0__cancel_decl,type,
class_Ring__and__Field_Ocomm__semiring__0__cancel: $i > $o ).
thf(class_Numeral_Onumber__ring_decl,type,
class_Numeral_Onumber__ring: $i > $o ).
thf(class_Ring__and__Field_Osemiring__0__cancel_decl,type,
class_Ring__and__Field_Osemiring__0__cancel: $i > $o ).
thf(class_Ring__and__Field_Oordered__ring__strict_decl,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(c_SetInterval_OatLeastAtMost_decl,type,
c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__join_decl,type,
class_OrderedGroup_Olordered__ab__group__join: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_HOL_Ominus_decl,type,
class_HOL_Ominus: $i > $o ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__meet_decl,type,
class_OrderedGroup_Olordered__ab__group__meet: $i > $o ).
thf(class_LOrder_Ojoin__semilorder_decl,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_decl,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(c_SetInterval_OgreaterThanAtMost_decl,type,
c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Osemigroup__mult_decl,type,
class_OrderedGroup_Osemigroup__mult: $i > $o ).
thf(c_Divides_Oop_Advd_decl,type,
c_Divides_Oop_Advd: $i > $i > $i > $o ).
thf(c_GCD_Ogcd_decl,type,
c_GCD_Ogcd: $i > $i ).
thf(class_HOL_Ozero_decl,type,
class_HOL_Ozero: $i > $o ).
thf(class_Ring__and__Field_Oring_decl,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(class_LOrder_Omeet__semilorder_decl,type,
class_LOrder_Omeet__semilorder: $i > $o ).
thf(class_Ring__and__Field_Oaxclass__no__zero__divisors_decl,type,
class_Ring__and__Field_Oaxclass__no__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Oidom_decl,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring_decl,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(class_LOrder_Olorder_decl,type,
class_LOrder_Olorder: $i > $o ).
thf(c_SetInterval_OatLeastLessThan_decl,type,
c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_times_decl,type,
c_times: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oaxclass__0__neq__1_decl,type,
class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).
thf(class_HOL_Oone_decl,type,
class_HOL_Oone: $i > $o ).
thf(c_SetInterval_OatLeast_decl,type,
c_SetInterval_OatLeast: $i > $i > $i ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Ocomm__ring_decl,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
thf(class_Ring__and__Field_Osemiring__1_decl,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_decl,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(c_Pow_decl,type,
c_Pow: $i > $i > $i ).
thf(class_Ring__and__Field_Opordered__semiring_decl,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_Nat_Opower_decl,type,
class_Nat_Opower: $i > $o ).
thf(c_Relation_Orel__comp_decl,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_OatMost_decl,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(c_UNIV_decl,type,
c_UNIV: $i ).
thf(class_OrderedGroup_Olordered__ab__group_decl,type,
class_OrderedGroup_Olordered__ab__group: $i > $o ).
thf(c_Datatype__Universe_Odsum_decl,type,
c_Datatype__Universe_Odsum: $i > $i > $i > $i > $i ).
thf(c_List_Oset_decl,type,
c_List_Oset: $i > $i > $i ).
thf(class_Ring__and__Field_Oaxclass__abs__if_decl,type,
class_Ring__and__Field_Oaxclass__abs__if: $i > $o ).
thf(c_Relation_OId_decl,type,
c_Relation_OId: $i ).
thf(c_Relation_OImage_decl,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Sum__Type_OInr_decl,type,
c_Sum__Type_OInr: $i > $i > $i > $i ).
thf(c_Sum__Type_OInl_decl,type,
c_Sum__Type_OInl: $i > $i > $i > $i ).
thf(c_inter_decl,type,
c_inter: $i > $i > $i > $i ).
thf(class_Parity_Oeven__odd_decl,type,
class_Parity_Oeven__odd: $i > $o ).
thf(class_Numeral_Onumber_decl,type,
class_Numeral_Onumber: $i > $o ).
thf(c_Transitive__Closure_Otrancl_decl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_decl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_IntDef_Oint_decl,type,
c_IntDef_Oint: $i > $i ).
thf(c_Main_OImageE__1_decl,type,
c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Relation_Odiag_decl,type,
c_Relation_Odiag: $i > $i > $i ).
thf(c_Sum__Type_OPlus_decl,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(tc_sum_decl,type,
tc_sum: $i > $i > $i ).
thf(c_Main_OPlusE__1_decl,type,
c_Main_OPlusE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OPlusE__2_decl,type,
c_Main_OPlusE__2: $i > $i > $i > $i > $i ).
thf(c_Datatype__Universe_Ouprod_decl,type,
c_Datatype__Universe_Ouprod: $i > $i > $i > $i > $i ).
thf(c_SetInterval_OgreaterThanLessThan_decl,type,
c_SetInterval_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(c_Datatype_Ooption_OSome_decl,type,
c_Datatype_Ooption_OSome: $i > $i > $i ).
thf(class_Divides_Odiv_decl,type,
class_Divides_Odiv: $i > $o ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(c_Union_decl,type,
c_Union: $i > $i > $i ).
thf(c_Main_OUnionE__1_decl,type,
c_Main_OUnionE__1: $i > $i > $i > $i ).
thf(c_Relation_ORange_decl,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Main_ORangeE__1_decl,type,
c_Main_ORangeE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Main_OconverseE__1_decl,type,
c_Main_OconverseE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OconverseE__2_decl,type,
c_Main_OconverseE__2: $i > $i > $i > $i > $i ).
thf(c_Main_Oin__listsI__1_decl,type,
c_Main_Oin__listsI__1: $i > $i > $i > $i ).
thf(c_Inter_decl,type,
c_Inter: $i > $i > $i ).
thf(c_Main_OInterI__1_decl,type,
c_Main_OInterI__1: $i > $i > $i > $i ).
thf(c_Main_OuprodE__1_decl,type,
c_Main_OuprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OuprodE__2_decl,type,
c_Main_OuprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Datatype_Oo2s_decl,type,
c_Datatype_Oo2s: $i > $i > $i ).
thf(c_Infinite__Set_Oatmost__one_decl,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_Main_Orel__compE__1_decl,type,
c_Main_Orel__compE__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_Orel__compE__3_decl,type,
c_Main_Orel__compE__3: $i > $i > $i > $i > $i > $i > $i ).
thf(c_1_decl,type,
c_1: $i ).
thf(c_Main_Ofinite__Union__1_decl,type,
c_Main_Ofinite__Union__1: $i > $i > $i ).
thf(c_Main_OdiagE__1_decl,type,
c_Main_OdiagE__1: $i > $i > $i > $i ).
thf(c_Main_Orel__compE__2_decl,type,
c_Main_Orel__compE__2: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_OIdE__1_decl,type,
c_Main_OIdE__1: $i > $i > $i ).
thf(c_Divides_Oop_Amod_decl,type,
c_Divides_Oop_Amod: $i > $i > $i > $i ).
thf(c_Main_Omod__eq__0D__dest__1_decl,type,
c_Main_Omod__eq__0D__dest__1: $i > $i > $i ).
thf(c_Main_Ozmod__eq__0D__dest__1_decl,type,
c_Main_Ozmod__eq__0D__dest__1: $i > $i > $i ).
thf(c_Relation_ODomain_decl,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Main_ODomainE__1_decl,type,
c_Main_ODomainE__1: $i > $i > $i > $i > $i ).
thf(509,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
thf(2199,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(455,axiom,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).
thf(2094,plain,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(444,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).
thf(2072,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(405,axiom,
tc_nat @ class_HOL_Otimes,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_11) ).
thf(1995,plain,
tc_nat @ class_HOL_Otimes,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(270,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).
thf(1729,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(994,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_3) ).
thf(3167,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(872,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_5) ).
thf(2921,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(1132,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).
thf(3397,plain,
tc_IntDef_Oint @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(57,axiom,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_27) ).
thf(1315,plain,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(681,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_1) ).
thf(2544,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(315,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
thf(1818,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(385,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
thf(1956,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(180,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
thf(1554,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(534,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).
thf(2250,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(197,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).
thf(1586,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(152,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).
thf(1501,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(638,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
thf(2452,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(714,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
thf(2612,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(136,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_11) ).
thf(1469,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(85,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
thf(1369,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(318,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
thf(1823,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(558,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).
thf(2295,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(564,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
thf(2306,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(1103,axiom,
tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
thf(3345,plain,
tc_IntDef_Oint @ class_LOrder_Omeet__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(581,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(2341,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(220,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).
thf(1633,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(797,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).
thf(2778,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(849,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
thf(2876,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).
thf(1237,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(652,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_12) ).
thf(2480,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(398,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).
thf(1982,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(334,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
thf(1855,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(281,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).
thf(1750,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).
thf(1211,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(665,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).
thf(2512,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(368,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) ).
thf(1924,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(658,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).
thf(2495,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(608,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
thf(2395,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(918,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff2_0) ).
thf(3012,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(458,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
thf(2099,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(601,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).
thf(2380,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(252,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff1_0) ).
thf(1692,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(1123,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff2_0) ).
thf(3382,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(4,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).
thf(1173,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(202,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
thf(1596,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(461,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).
thf(2104,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
thf(1290,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(347,axiom,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).
thf(1882,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(813,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) ).
thf(2808,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(163,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
thf(1522,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(796,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_15) ).
thf(2776,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(310,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
thf(1808,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(737,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_2) ).
thf(2659,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(1146,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
thf(3417,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(932,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_13) ).
thf(3040,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(987,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
thf(3153,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(703,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).
thf(2590,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_2) ).
thf(1401,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(112,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_4) ).
thf(1422,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(885,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
thf(2947,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(188,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
thf(1569,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(376,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).
thf(1939,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(533,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).
thf(2248,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(743,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_12) ).
thf(2671,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(175,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).
thf(1544,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(746,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).
thf(2676,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(415,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).
thf(2014,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(466,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_5) ).
thf(2114,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(829,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).
thf(2837,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(1135,axiom,
tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
thf(3402,plain,
tc_IntDef_Oint @ class_LOrder_Ojoin__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(169,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_30) ).
thf(1533,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(150,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_9) ).
thf(1497,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(1159,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).
thf(3439,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(969,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(3120,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(751,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_4) ).
thf(2686,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(914,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Olordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).
thf(3004,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Olordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(998,axiom,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(3175,plain,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
thf(1327,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(833,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
thf(2844,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(696,axiom,
tc_nat @ class_LOrder_Olorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).
thf(2575,plain,
tc_nat @ class_LOrder_Olorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(300,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_5) ).
thf(1788,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(114,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) ).
thf(1426,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(1022,axiom,
tc_IntDef_Oint @ class_Numeral_Onumber__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).
thf(3217,plain,
tc_IntDef_Oint @ class_Numeral_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(284,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
thf(1756,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(54,axiom,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).
thf(1310,plain,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(934,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
thf(3044,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(273,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).
thf(1735,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(569,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).
thf(2316,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(1164,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
thf(3446,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(636,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).
thf(2448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(1097,axiom,
tc_IntDef_Oint @ class_HOL_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(3338,plain,
tc_IntDef_Oint @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(878,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
thf(2933,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(629,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
thf(2434,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(342,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_12) ).
thf(1872,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(763,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
thf(2712,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(650,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
thf(2476,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(721,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) ).
thf(2627,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(493,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
thf(2168,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff1_0) ).
thf(1260,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1044,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
thf(3253,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(401,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_35) ).
thf(1988,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(1144,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
thf(3414,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_5) ).
thf(1342,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(970,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).
thf(3121,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
thf(1354,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(482,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
thf(2146,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(155,axiom,
! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_4) ).
thf(1507,plain,
! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).
thf(1222,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(591,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
thf(2360,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_1) ).
thf(1835,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(517,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).
thf(2216,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(899,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
!= ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).
thf(2972,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
!= ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(1042,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(3249,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(418,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).
thf(2020,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(210,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) ).
thf(1613,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(229,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
thf(1650,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(854,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
thf(2886,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(449,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
thf(2082,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(980,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
thf(3140,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_5) ).
thf(1366,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(667,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
thf(2516,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(819,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_11) ).
thf(2819,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(279,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).
thf(1746,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(961,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).
thf(3103,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(585,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).
thf(2348,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(769,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).
thf(2723,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(628,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff1_0) ).
thf(2432,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(363,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).
thf(1914,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(656,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).
thf(2491,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(683,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
thf(2548,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(297,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).
thf(1782,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(523,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
thf(2227,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
thf(1391,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(192,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).
thf(1576,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(1077,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).
thf(3308,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(413,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).
thf(2010,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(611,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).
thf(2400,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(442,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).
thf(2067,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff1_0) ).
thf(1529,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(477,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).
thf(2136,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(358,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
thf(1904,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(161,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_9) ).
thf(1518,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).
thf(1228,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(215,axiom,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).
thf(1623,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(1025,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
thf(3221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(575,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
thf(2328,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(927,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_2) ).
thf(3029,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(741,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).
thf(2667,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(785,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).
thf(2755,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(941,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).
thf(3061,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(761,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_3) ).
thf(2708,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(634,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).
thf(2444,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).
thf(1313,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(954,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
thf(3089,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(1108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
thf(3353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(758,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_3) ).
thf(2703,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(1041,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__abs__if,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
thf(3248,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__abs__if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(1161,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).
thf(3442,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(1151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
thf(3425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(302,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_0) ).
thf(1792,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(116,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
thf(1430,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(756,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).
thf(2698,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(234,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
thf(1660,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).
thf(1298,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(286,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).
thf(1760,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(975,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_22) ).
thf(3131,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(580,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
thf(2339,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(935,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).
thf(3046,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(1101,axiom,
tc_IntDef_Oint @ class_HOL_Oone,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
thf(3342,plain,
tc_IntDef_Oint @ class_HOL_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(545,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).
thf(2269,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).
thf(1323,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(984,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_29) ).
thf(3148,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(749,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff2_0) ).
thf(2682,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(972,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).
thf(3125,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(1141,axiom,
tc_IntDef_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
thf(3410,plain,
tc_IntDef_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(501,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).
thf(2185,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(129,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).
thf(1455,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1062,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
thf(3280,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(645,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
thf(2466,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(472,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
thf(2126,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(780,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).
thf(2745,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(694,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_22) ).
thf(2571,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(589,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).
thf(2356,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(367,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).
thf(1922,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(839,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
thf(2857,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(159,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_19) ).
thf(1514,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(597,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
thf(2373,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(561,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).
thf(2301,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(80,axiom,
tc_nat @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_23) ).
thf(1362,plain,
tc_nat @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1001,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).
thf(3180,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(295,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).
thf(1778,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(1030,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
thf(3231,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(605,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).
thf(2388,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(330,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).
thf(1847,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(825,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
thf(2829,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(959,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__mult_0) ).
thf(3099,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(306,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_23) ).
thf(1800,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(352,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).
thf(1892,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(90,axiom,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).
thf(1379,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(1117,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).
thf(3374,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(1125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).
thf(3385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(433,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) ).
thf(2049,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(685,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
thf(2552,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(258,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_0) ).
thf(1704,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(351,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
thf(1890,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(141,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).
thf(1479,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(208,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__ring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).
thf(1609,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__ring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(725,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_1) ).
thf(2635,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(876,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
thf(2929,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(1081,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff2_0) ).
thf(3312,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(187,axiom,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
thf(1568,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(919,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).
thf(3014,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(669,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
thf(2520,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(420,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).
thf(2024,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(224,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_39) ).
thf(1641,plain,
tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(1056,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).
thf(3268,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(1048,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
thf(3258,plain,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(640,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
thf(2456,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(1087,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
thf(3322,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(1154,axiom,
tc_IntDef_Oint @ class_Divides_Odiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_61) ).
thf(3431,plain,
tc_IntDef_Oint @ class_Divides_Odiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(573,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).
thf(2324,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(947,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).
thf(3075,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(453,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
thf(2090,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(799,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).
thf(2782,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(992,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_11) ).
thf(3163,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(527,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
thf(2236,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(851,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).
thf(2880,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(7,axiom,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(1183,plain,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(498,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff1_0) ).
thf(2178,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(520,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
thf(2222,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).
thf(1489,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(108,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).
thf(1415,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(716,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
thf(2616,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(134,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) ).
thf(1465,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_2) ).
thf(1302,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(236,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
thf(1664,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_18) ).
thf(1373,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(910,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
thf(2996,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(338,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).
thf(1864,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(470,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).
thf(2122,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(874,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring__1 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).
thf(2925,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring__1 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).
thf(1978,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(556,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).
thf(2291,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_2) ).
thf(1383,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(536,axiom,
tc_nat @ class_Parity_Oeven__odd,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_47) ).
thf(2254,plain,
tc_nat @ class_Parity_Oeven__odd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(243,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_8) ).
thf(1677,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(679,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) ).
thf(2540,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(425,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
thf(2034,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(387,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).
thf(1960,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(1072,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
thf(3300,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(956,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
thf(3093,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(328,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
thf(1843,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(1,negated_conjecture,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ ( A @ v_x @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(1169,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ ( A @ v_x @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(349,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_5) ).
thf(1886,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(596,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).
thf(2371,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(165,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_6) ).
thf(1526,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(74,axiom,
tc_nat @ class_HOL_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(1351,plain,
tc_nat @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(811,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) ).
thf(2804,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(1600,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(1019,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(3211,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(185,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
thf(1564,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(789,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_4) ).
thf(2762,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(1127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).
thf(3389,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(663,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).
thf(2508,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(894,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
thf(2964,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(594,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_2) ).
thf(2367,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(370,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_7) ).
thf(1928,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(943,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
thf(3068,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(89,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).
thf(1377,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(717,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(2618,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(827,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_9) ).
thf(2833,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(551,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
thf(2281,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(354,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).
thf(1896,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(504,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).
thf(2190,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(1149,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff2_0) ).
thf(3421,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(304,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).
thf(1796,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(674,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
thf(2530,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(794,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).
thf(2772,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(989,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
thf(3157,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(409,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).
thf(2002,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(1037,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).
thf(3243,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(530,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_5) ).
thf(2242,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(808,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
thf(2799,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(727,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).
thf(2639,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(1090,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
thf(3327,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(118,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).
thf(1433,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(460,axiom,
! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
thf(2103,plain,
! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(103,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_4) ).
thf(1405,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(1028,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(3226,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(378,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_13) ).
thf(1943,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(766,axiom,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
thf(2718,plain,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(512,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).
thf(2205,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(254,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).
thf(1696,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(1003,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
thf(3184,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(701,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).
thf(2586,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(902,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_8) ).
thf(2982,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(853,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(2884,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(1157,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).
thf(3435,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(889,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).
thf(2954,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(1166,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
thf(3450,plain,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(1074,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).
thf(3303,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(251,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
thf(1691,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(121,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
thf(1438,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).
thf(1306,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(1004,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) ).
thf(3186,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(468,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).
thf(2118,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(67,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).
thf(1338,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(260,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).
thf(1708,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(776,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
thf(2737,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(728,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_14) ).
thf(2641,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(718,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
thf(2621,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(986,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
thf(3151,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(958,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_9) ).
thf(3097,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(917,axiom,
! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_1) ).
thf(3011,plain,
! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(15,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).
thf(1206,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(995,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).
thf(3169,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(1053,axiom,
tc_IntDef_Oint @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
thf(3265,plain,
tc_IntDef_Oint @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(593,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).
thf(2364,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(491,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_6) ).
thf(2164,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(432,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).
thf(2047,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(1084,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
thf(3318,plain,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).
thf(1311,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(525,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_8) ).
thf(2232,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(290,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
thf(1768,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(864,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).
thf(2905,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(340,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).
thf(1868,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(602,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_15) ).
thf(2382,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(439,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_11) ).
thf(2061,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(408,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
thf(2000,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(744,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
thf(2673,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(1051,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
thf(3261,plain,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(626,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).
thf(2428,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(689,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_32) ).
thf(2560,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(706,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_11) ).
thf(2596,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(242,axiom,
tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).
thf(1676,plain,
tc_nat @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(18,axiom,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).
thf(1217,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(923,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
thf(3022,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(237,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).
thf(1666,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(145,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).
thf(1487,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(897,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_25) ).
thf(2969,plain,
tc_nat @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1034,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__meet,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
thf(3239,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__meet,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(880,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
thf(2937,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(711,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).
thf(2606,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(977,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).
thf(3134,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(213,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
thf(1619,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(673,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
thf(2528,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(1098,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__abs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
thf(3339,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__abs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(759,axiom,
! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
thf(2705,plain,
! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(542,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).
thf(2264,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(616,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).
thf(2409,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(94,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).
thf(1387,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(356,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).
thf(1900,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(267,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).
thf(1723,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(194,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).
thf(1580,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(549,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).
thf(2277,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(424,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
thf(2032,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(904,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).
thf(2986,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(475,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_6) ).
thf(2132,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(856,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
thf(2890,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(1016,axiom,
tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff2_0) ).
thf(3207,plain,
tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(609,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_28) ).
thf(2396,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(1064,axiom,
tc_IntDef_Oint @ class_Nat_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).
thf(3286,plain,
tc_IntDef_Oint @ class_Nat_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(183,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).
thf(1560,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(366,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).
thf(1920,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).
thf(1178,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(316,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).
thf(1819,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(982,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_11) ).
thf(3144,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(499,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_4) ).
thf(2181,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(232,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
thf(1656,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(937,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff1_0) ).
thf(3050,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(583,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) ).
thf(2344,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(465,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_0) ).
thf(2112,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(190,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_2) ).
thf(1573,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1163,axiom,
tc_IntDef_Oint @ class_Parity_Oeven__odd,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_64) ).
thf(3445,plain,
tc_IntDef_Oint @ class_Parity_Oeven__odd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(734,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_10) ).
thf(2653,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(891,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) ).
thf(2958,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(1076,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
thf(3307,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(644,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).
thf(2464,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(375,axiom,
tc_nat @ class_OrderedGroup_Osemigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_14) ).
thf(1938,plain,
tc_nat @ class_OrderedGroup_Osemigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(325,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) ).
thf(1837,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(1057,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).
thf(3269,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(1136,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
thf(3403,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).
thf(1968,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(692,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).
thf(2565,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(1010,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
thf(3198,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(739,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_14) ).
thf(2663,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(577,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_8) ).
thf(2332,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(823,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).
thf(2826,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(1082,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).
thf(3314,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring__1__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(1071,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).
thf(3297,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(1106,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_1) ).
thf(3349,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(847,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
thf(2872,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__abs__if )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(382,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
thf(1951,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(350,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).
thf(1888,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
thf(1296,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(249,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) ).
thf(1687,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(130,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).
thf(1457,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(12,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).
thf(1195,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(104,axiom,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_28) ).
thf(1407,plain,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).
thf(1281,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(778,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).
thf(2741,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(929,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
thf(3033,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(1139,axiom,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(3408,plain,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(276,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_13) ).
thf(1740,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(361,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_1) ).
thf(1910,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).
thf(1234,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(488,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) ).
thf(2157,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(308,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).
thf(1804,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(831,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).
thf(2841,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
| ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).
thf(1375,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
| ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(1122,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
thf(3381,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(392,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).
thf(1970,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(1023,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
thf(3218,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(754,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) ).
thf(2694,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(240,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).
thf(1672,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(173,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).
thf(1540,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(265,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).
thf(1719,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(1033,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
thf(3237,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(79,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).
thf(1360,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(374,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).
thf(1936,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(962,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).
thf(3105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(200,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).
thf(1592,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(287,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).
thf(1762,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(1045,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_6) ).
thf(3254,plain,
tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(1143,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).
thf(3413,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(332,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).
thf(1851,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(292,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
thf(1772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(906,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_24) ).
thf(2990,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(599,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).
thf(2377,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(809,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
thf(2801,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(303,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_2) ).
thf(1794,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(383,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
thf(1953,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(345,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).
thf(1878,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(723,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_1) ).
thf(2631,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(1160,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).
thf(3440,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(1014,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).
thf(3205,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(999,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).
thf(3176,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(953,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
thf(3087,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(921,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_8) ).
thf(3018,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(99,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
thf(1397,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).
thf(1329,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1080,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(3311,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(1089,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
thf(3326,plain,
tc_IntDef_Oint @ class_OrderedGroup_Opordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(389,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).
thf(1964,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(912,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
thf(3000,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_0) ).
thf(1292,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(132,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).
thf(1461,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(845,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).
thf(2868,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(621,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_8) ).
thf(2419,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(448,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).
thf(2080,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(196,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).
thf(1584,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(256,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).
thf(1700,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(226,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).
thf(1644,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(110,axiom,
tc_nat @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_18) ).
thf(1419,plain,
tc_nat @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(642,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).
thf(2460,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(148,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_4) ).
thf(1493,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(246,axiom,
tc_nat @ class_Nat_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_12) ).
thf(1683,plain,
tc_nat @ class_Nat_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(1138,axiom,
tc_IntDef_Oint @ class_HOL_Oplus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_2) ).
thf(3407,plain,
tc_IntDef_Oint @ class_HOL_Oplus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(690,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).
thf(2561,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(1018,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
thf(3210,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(113,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_11) ).
thf(1424,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(567,axiom,
! [A: $i] :
( c_emptyset
= ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).
thf(2312,plain,
! [A: $i] :
( c_emptyset
= ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(435,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
thf(2053,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(507,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_3) ).
thf(2196,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(529,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) ).
thf(2240,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(311,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).
thf(1810,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(495,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).
thf(2172,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).
thf(1214,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1008,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_7) ).
thf(3194,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(463,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).
thf(2108,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(427,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_8) ).
thf(2038,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(125,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).
thf(1446,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(648,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_4) ).
thf(2472,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(732,axiom,
! [A: $i] :
( ( A @ class_Numeral_Onumber )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).
thf(2649,plain,
! [A: $i] :
( ( A @ class_Numeral_Onumber )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(1069,axiom,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff2_0) ).
thf(3294,plain,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(278,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
thf(1744,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(677,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).
thf(2536,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(127,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_8) ).
thf(1451,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(179,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).
thf(1552,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(698,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_20) ).
thf(2581,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(380,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
thf(1947,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(399,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).
thf(1984,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(816,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_4) ).
thf(2813,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(964,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).
thf(3109,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(479,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).
thf(2140,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(319,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).
thf(1825,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(553,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).
thf(2285,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(661,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
thf(2504,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(294,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).
thf(1776,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).
thf(1263,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(637,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__add_0) ).
thf(2450,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(198,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).
thf(1588,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(707,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).
thf(2598,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(940,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).
thf(3059,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( B @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).
thf(1266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( B @ ( D @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(322,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).
thf(1831,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).
thf(1231,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(486,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).
thf(2153,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(861,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).
thf(2900,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(238,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_1) ).
thf(1668,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(394,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).
thf(1974,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( A @ ( B @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff1_0) ).
thf(1192,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( A @ ( B @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(372,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_18) ).
thf(1932,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(411,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).
thf(2006,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(659,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq__iff1_0) ).
thf(2497,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(343,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).
thf(1874,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(967,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
thf(3115,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(1140,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
thf(3409,plain,
tc_IntDef_Oint @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(842,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_7) ).
thf(2862,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(791,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).
thf(2766,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(653,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
thf(2482,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).
thf(1246,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(263,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).
thf(1715,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(1094,axiom,
tc_IntDef_Oint @ class_HOL_Ozero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_4) ).
thf(3333,plain,
tc_IntDef_Oint @ class_HOL_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(951,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).
thf(3083,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0) ).
thf(1393,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(217,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
thf(1627,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(1021,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(3215,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(66,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).
thf(1333,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(511,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_1) ).
thf(2203,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(430,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).
thf(2043,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(997,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).
thf(3173,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(437,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).
thf(2057,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).
thf(1286,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(612,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
thf(2402,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(730,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
thf(2645,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(406,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).
thf(1996,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(623,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
thf(2423,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(866,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).
thf(2909,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(782,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_6) ).
thf(2749,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(119,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_6) ).
thf(1434,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(335,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).
thf(1857,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(403,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
thf(1991,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(802,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).
thf(2788,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) ).
thf(1318,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(313,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).
thf(1814,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(1027,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
thf(3225,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(682,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).
thf(2546,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(788,axiom,
tc_nat @ class_HOL_Oplus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_10) ).
thf(2761,plain,
tc_nat @ class_HOL_Oplus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(446,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_7) ).
thf(2076,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(2,negated_conjecture,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( c_0 @ ( A @ v_x @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(1170,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( c_0 @ ( A @ v_x @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(869,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_14) ).
thf(2915,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(632,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
= ( C @ ( A @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).
thf(2440,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
= ( C @ ( A @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(805,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
thf(2793,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(1006,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
thf(3190,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(481,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_3) ).
thf(2144,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(359,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) ).
thf(1906,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(497,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
thf(2176,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(283,axiom,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).
thf(1754,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(863,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_21) ).
thf(2904,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(933,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) ).
thf(3042,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).
thf(1219,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(143,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).
thf(1483,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(38,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).
thf(1273,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(177,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_1) ).
thf(1548,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(1052,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
thf(3262,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(1066,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
thf(3289,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(709,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_11) ).
thf(2602,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(858,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).
thf(2894,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(219,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).
thf(1631,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(772,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
thf(2729,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(228,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_5) ).
thf(1648,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(269,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_14) ).
thf(1727,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(157,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).
thf(1510,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).
thf(1251,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(288,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).
thf(1764,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(618,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
thf(2413,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(255,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_12) ).
thf(1698,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(687,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).
thf(2556,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(1110,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).
thf(3358,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(548,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).
thf(2275,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(484,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_29) ).
thf(2149,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(949,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
thf(3079,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(693,axiom,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff2_0) ).
thf(2570,plain,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(882,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) ).
thf(2941,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(422,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_3) ).
thf(2028,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(1118,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).
thf(3375,plain,
tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(774,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).
thf(2734,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(965,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).
thf(3111,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(1060,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
thf(3274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(671,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).
thf(2524,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(1131,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__join,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
thf(3396,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group__join,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(1102,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).
thf(3343,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(540,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_5) ).
thf(2260,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(1116,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).
thf(3372,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(1126,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).
thf(3387,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(323,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).
thf(1833,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(364,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).
thf(1916,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(840,axiom,
tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_13) ).
thf(2859,plain,
tc_nat @ class_Ring__and__Field_Oaxclass__0__neq__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(803,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).
thf(2789,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(736,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).
thf(2657,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(503,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).
thf(2188,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(1059,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
thf(3272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(102,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
thf(1403,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(610,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
thf(2398,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(765,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_12) ).
thf(2716,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).
thf(1256,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(476,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_5) ).
thf(2134,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(1020,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff1_0) ).
thf(3213,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(944,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_17) ).
thf(3070,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(771,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
thf(2727,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(898,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_14) ).
thf(2970,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(1085,axiom,
tc_IntDef_Oint @ class_Power_Orecpower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
thf(3319,plain,
tc_IntDef_Oint @ class_Power_Orecpower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(211,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).
thf(1615,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(298,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).
thf(1784,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
thf(1389,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(1046,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__ring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
thf(3255,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(804,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
thf(2791,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(1035,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
thf(3240,plain,
tc_IntDef_Oint @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(607,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_5) ).
thf(2393,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(282,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
thf(1752,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(230,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
thf(1652,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(950,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).
thf(3081,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(1063,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero__iff1_0) ).
thf(3283,plain,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(1054,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
thf(3266,plain,
tc_IntDef_Oint @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(745,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).
thf(2674,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(416,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_0) ).
thf(2016,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(666,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_4) ).
thf(2514,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(170,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).
thf(1535,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(812,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
thf(2806,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(907,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_10) ).
thf(2991,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(162,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
thf(1520,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(818,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).
thf(2817,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(153,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
thf(1503,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(299,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_16) ).
thf(1786,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(519,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).
thf(2220,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(574,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).
thf(2326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(557,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
thf(2293,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(1092,axiom,
tc_IntDef_Oint @ class_HOL_Otimes,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_3) ).
thf(3330,plain,
tc_IntDef_Oint @ class_HOL_Otimes,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(1017,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(3208,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(971,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
thf(3123,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(436,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
thf(2055,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(760,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).
thf(2706,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(492,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
thf(2166,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff2_0) ).
thf(1258,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1073,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).
thf(3302,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(1109,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
thf(3355,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(115,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).
thf(1428,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(1026,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
thf(3223,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
thf(1271,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(565,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_3) ).
thf(2308,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
thf(1371,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(948,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
thf(3077,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(221,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).
thf(1635,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(879,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff2_0) ).
thf(2935,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(913,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
thf(3002,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(272,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) ).
thf(1733,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(1099,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).
thf(3340,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).
thf(1239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(787,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_22) ).
thf(2759,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(784,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_18) ).
thf(2753,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(1158,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
| ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).
thf(3436,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
| ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(624,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).
thf(2425,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(1145,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_7) ).
thf(3416,plain,
tc_IntDef_Oint @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(955,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_1) ).
thf(3091,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(649,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(2474,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(590,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) ).
thf(2358,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
thf(1356,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(695,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_2) ).
thf(2573,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(483,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).
thf(2148,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(664,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_7) ).
thf(2510,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(584,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).
thf(2346,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(960,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
thf(3101,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(309,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
thf(1806,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(1147,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
thf(3419,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(538,axiom,
tc_nat @ class_OrderedGroup_Osemigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_16) ).
thf(2257,plain,
tc_nat @ class_OrderedGroup_Osemigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff1_0) ).
thf(1542,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(742,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
thf(2669,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(1124,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
thf(3384,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__0__neq__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(189,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_13) ).
thf(1571,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(441,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).
thf(2065,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(768,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).
thf(2721,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(1107,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
thf(3352,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(678,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_29) ).
thf(2538,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(333,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).
thf(1853,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(105,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) ).
thf(1408,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(651,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_2) ).
thf(2478,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(1043,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).
thf(3251,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(485,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).
thf(2151,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(988,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_21) ).
thf(3155,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(524,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).
thf(2229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(450,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).
thf(2084,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(516,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_0) ).
thf(2214,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(619,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).
thf(2415,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(353,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
thf(1894,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(657,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_12) ).
thf(2493,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(931,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_7) ).
thf(3038,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(726,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).
thf(2637,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(795,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) ).
thf(2774,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(1065,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
thf(3287,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(164,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).
thf(1524,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
thf(1349,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(457,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_6) ).
thf(2097,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(1058,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).
thf(3270,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(532,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).
thf(2246,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(205,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_13) ).
thf(1603,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(560,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).
thf(2299,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(467,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_17) ).
thf(2116,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(830,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_20) ).
thf(2839,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(883,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).
thf(2943,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(884,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).
thf(2945,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(810,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).
thf(2802,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(979,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_2) ).
thf(3138,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(1002,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).
thf(3182,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(859,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
thf(2896,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(137,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_19) ).
thf(1471,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(946,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
thf(3073,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(404,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) ).
thf(1993,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(993,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_0) ).
thf(3165,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(1007,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).
thf(3192,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(848,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
thf(2874,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__meet )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).
thf(1344,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(535,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
thf(2252,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) ).
thf(1381,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1024,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
thf(3219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(822,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).
thf(2824,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(713,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).
thf(2610,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(926,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).
thf(3027,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(568,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).
thf(2314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(582,axiom,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(2343,plain,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(720,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_12) ).
thf(2625,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(798,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_1) ).
thf(2780,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(544,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_5) ).
thf(2267,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(317,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_3) ).
thf(1821,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(271,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_2) ).
thf(1731,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(635,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
thf(2446,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(786,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_11) ).
thf(2757,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(873,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) ).
thf(2923,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).
thf(1325,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(915,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).
thf(3006,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(1167,axiom,
tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff2_0) ).
thf(3451,plain,
tc_nat @ ( c_1 @ ( c_0 @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(181,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).
thf(1556,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(680,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
thf(2542,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(555,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).
thf(2289,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(731,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_24) ).
thf(2647,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(762,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(2710,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(867,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
thf(2911,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(793,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).
thf(2770,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(515,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
thf(2212,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(828,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) ).
thf(2835,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(166,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__1__cancel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_30) ).
thf(1528,plain,
tc_nat @ class_Ring__and__Field_Osemiring__1__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(451,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_11) ).
thf(2086,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(877,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).
thf(2931,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(981,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_16) ).
thf(3142,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(459,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).
thf(2101,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(562,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
thf(2303,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(1000,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
thf(3178,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(513,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).
thf(2207,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(903,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).
thf(2984,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(443,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Oset ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).
thf(2069,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Oset ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( D @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).
thf(1198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( D @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(327,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_13) ).
thf(1841,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(369,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
thf(1926,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(893,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).
thf(2962,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(139,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).
thf(1474,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(586,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_24) ).
thf(2350,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(770,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_2) ).
thf(2725,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(201,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_7) ).
thf(1594,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(434,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_3) ).
thf(2051,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(1150,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
thf(3423,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(684,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).
thf(2550,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(990,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_20) ).
thf(3159,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(595,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
thf(2369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(1036,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).
thf(3241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(807,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).
thf(2797,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(920,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).
thf(3016,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(704,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_8) ).
thf(2592,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(531,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
thf(2244,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(724,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
thf(2633,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(419,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).
thf(2022,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1113,axiom,
! [A: $i] :
( c_0
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).
thf(3363,plain,
! [A: $i] :
( c_0
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(1079,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).
thf(3310,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(82,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
thf(1364,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(896,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) ).
thf(2967,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(606,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).
thf(2390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(253,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
thf(1694,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semidom )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(753,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_15) ).
thf(2693,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(662,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
thf(2506,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(1121,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
thf(3380,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(184,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).
thf(1562,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(916,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).
thf(3009,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(928,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).
thf(3031,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(888,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).
thf(2952,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(285,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
thf(1758,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).
thf(1203,plain,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(740,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).
thf(2665,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(1068,axiom,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ ( c_1 @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
thf(3293,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( A @ ( c_1 @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(983,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).
thf(3146,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).
thf(1340,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(138,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_4) ).
thf(1472,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(834,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_28) ).
thf(2846,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(386,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) ).
thf(1958,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(699,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).
thf(2582,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(235,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).
thf(1662,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(715,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).
thf(2614,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_13) ).
thf(1304,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(1152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
thf(3427,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(135,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
thf(1467,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(909,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).
thf(2994,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(570,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_8) ).
thf(2318,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(1130,axiom,
! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
thf(3395,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(800,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).
thf(2784,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(546,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) ).
thf(2271,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(1015,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).
thf(3206,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(991,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_9) ).
thf(3161,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(111,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
thf(1420,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(850,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).
thf(2878,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(247,axiom,
tc_nat @ class_HOL_Ozero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_1) ).
thf(1684,plain,
tc_nat @ class_HOL_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(471,axiom,
! [A: $i] :
( ( A @ class_Nat_Opower )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_0) ).
thf(2124,plain,
! [A: $i] :
( ( A @ class_Nat_Opower )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(526,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).
thf(2234,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(875,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).
thf(2927,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(722,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_1) ).
thf(2629,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(936,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
thf(3048,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(750,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).
thf(2684,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(329,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).
thf(1845,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(280,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).
thf(1748,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(738,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
thf(2661,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).
thf(1225,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(505,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_7) ).
thf(2192,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(974,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_3) ).
thf(3129,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(168,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
thf(1531,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(836,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).
thf(2850,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(855,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
thf(2888,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__ring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(852,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
thf(2882,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(826,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).
thf(2831,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(305,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_12) ).
thf(1798,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(1128,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_IntDef_Oint @ ( A @ ( B @ c_Main_Ozmod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
thf(3391,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_IntDef_Oint @ ( A @ ( B @ c_Main_Ozmod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(291,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).
thf(1770,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(1119,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
thf(3376,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(160,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
thf(1516,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(1083,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
thf(3315,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(203,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_3) ).
thf(1598,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(900,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(2977,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(209,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
thf(1611,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(598,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).
thf(2375,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(186,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).
thf(1566,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(414,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).
thf(2012,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).
thf(1605,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(1050,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
thf(3260,plain,
tc_IntDef_Oint @ class_OrderedGroup_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(702,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff2_0) ).
thf(2588,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(773,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
thf(2732,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(377,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_8) ).
thf(1941,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(747,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_11) ).
thf(2678,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(668,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
thf(2518,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(84,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_GCD_Ogcd @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).
thf(1368,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_GCD_Ogcd @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(1029,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_0) ).
thf(3228,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(296,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).
thf(1780,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(820,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_7) ).
thf(2821,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(615,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
thf(2407,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(604,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_23) ).
thf(2386,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(1040,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff1_0) ).
thf(3246,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(1165,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
thf(3448,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(454,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).
thf(2092,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(1075,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).
thf(3305,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(942,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).
thf(3063,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(1012,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
thf(3202,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ ( A @ c_times ) ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(579,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).
thf(2337,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__semiring__strict )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(973,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).
thf(3127,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(244,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).
thf(1679,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(646,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).
thf(2468,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(588,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).
thf(2354,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(261,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).
thf(1711,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(781,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_2) ).
thf(2747,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oaxclass__abs__if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(151,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
thf(1499,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(301,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
thf(1790,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(521,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).
thf(2224,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(639,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).
thf(2454,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_10) ).
thf(1300,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(222,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
thf(1637,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(752,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).
thf(2688,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(1095,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
thf(3334,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(757,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).
thf(2700,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).
thf(1186,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(397,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) ).
thf(1980,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(473,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).
thf(2128,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(233,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).
thf(1658,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(572,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).
thf(2322,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff2_0) ).
thf(1538,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(655,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq__iff1_0) ).
thf(2486,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(1111,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).
thf(3359,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(1091,axiom,
tc_IntDef_Oint @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
thf(3329,plain,
tc_IntDef_Oint @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(275,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
thf(1738,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(957,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).
thf(3095,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).
thf(1358,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(373,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).
thf(1934,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(617,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).
thf(2411,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(688,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).
thf(2558,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(625,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
thf(2426,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(307,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).
thf(1802,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_5) ).
thf(1284,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(881,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
thf(2939,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(945,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).
thf(3071,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(543,axiom,
tc_nat @ class_Numeral_Onumber,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_46) ).
thf(2266,plain,
tc_nat @ class_Numeral_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(212,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).
thf(1617,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(289,axiom,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
thf(1766,plain,
! [A: $i] :
( ( A @ class_HOL_Oone )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(963,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_26) ).
thf(3107,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(355,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
thf(1898,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(331,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).
thf(1849,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(257,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).
thf(1702,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(600,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_26) ).
thf(2379,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(550,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).
thf(2279,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(384,axiom,
tc_nat @ class_Power_Orecpower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_45) ).
thf(1955,plain,
tc_nat @ class_Power_Orecpower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(832,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_GCD_Ogcd @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).
thf(2843,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_GCD_Ogcd @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(144,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).
thf(1485,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(393,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).
thf(1972,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(571,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).
thf(2320,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(239,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).
thf(1670,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(924,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(3024,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(968,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff1_0) ).
thf(3117,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(841,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) ).
thf(2860,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(886,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) ).
thf(2949,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(264,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
thf(1717,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(423,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
thf(2030,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(1047,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
thf(3256,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(857,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_9) ).
thf(2892,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(835,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oidom )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).
thf(2848,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oidom )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(1114,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ ( A @ ( B @ c_Main_Omod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
thf(3366,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_nat @ ( A @ ( B @ c_Main_Omod__eq__0D__dest__1 ) @ ( B @ c_times ) ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(700,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) ).
thf(2584,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(1133,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff1_0) ).
thf(3398,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(1134,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).
thf(3400,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(1156,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
thf(3433,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(326,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).
thf(1839,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(452,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).
thf(2088,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
thf(1180,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(390,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
thf(1966,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(248,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
thf(1685,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(755,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) ).
thf(2696,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(447,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
thf(2078,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(566,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_9) ).
thf(2310,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(514,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_emptyset
!= ( B @ ( A @ c_List_Oset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).
thf(2209,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_emptyset
!= ( B @ ( A @ c_List_Oset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(339,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(1866,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(865,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).
thf(2907,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(407,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_9) ).
thf(1998,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(1168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
thf(3452,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(641,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).
thf(2458,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(365,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).
thf(1918,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
thf(1316,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(587,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).
thf(2352,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(131,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).
thf(1459,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__mult )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(431,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).
thf(2045,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(381,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
thf(1949,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(846,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
thf(2870,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(824,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
thf(2828,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(996,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).
thf(3171,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(892,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
thf(2960,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(1005,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).
thf(3188,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(506,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
thf(2194,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(231,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).
thf(1654,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff2_0) ).
thf(1412,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(779,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_3) ).
thf(2743,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).
thf(1448,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(1104,axiom,
tc_IntDef_Oint @ class_LOrder_Olorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
thf(3346,plain,
tc_IntDef_Oint @ class_LOrder_Olorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(502,axiom,
tc_nat @ class_LOrder_Omeet__semilorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).
thf(2187,plain,
tc_nat @ class_LOrder_Omeet__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(10,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).
thf(1189,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(464,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
thf(2110,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(1086,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
thf(3320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(563,axiom,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_42) ).
thf(2305,plain,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(871,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).
thf(2919,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(191,axiom,
tc_nat @ class_HOL_Oone,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_0) ).
thf(1575,plain,
tc_nat @ class_HOL_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(522,axiom,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
thf(2226,plain,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(128,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).
thf(1453,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(729,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).
thf(2643,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).
thf(1253,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(547,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
thf(2273,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(837,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
thf(2853,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(614,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_33) ).
thf(2406,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(686,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Olorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
thf(2554,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Olorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(142,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).
thf(1481,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(421,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).
thf(2026,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(474,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
thf(2130,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(672,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).
thf(2526,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(952,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_14) ).
thf(3085,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).
thf(1276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(199,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).
thf(1590,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(227,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_6) ).
thf(1646,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(633,axiom,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
thf(2443,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(905,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).
thf(2988,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(93,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_1) ).
thf(1385,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(705,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_11) ).
thf(2594,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(266,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_10) ).
thf(1721,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(496,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
thf(2174,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(552,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) ).
thf(2283,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).
thf(1476,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(241,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).
thf(1674,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(838,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
thf(2855,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(223,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).
thf(1639,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(675,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_5) ).
thf(2532,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(156,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
thf(1508,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1115,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(3369,plain,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(821,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
thf(2823,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(815,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_0) ).
thf(2811,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Pair ) ) ) @ c_GCD_Ogcd @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(218,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).
thf(1629,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(410,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).
thf(2004,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(712,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).
thf(2608,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(1032,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).
thf(3235,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff2_0) ).
thf(1244,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(790,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_0) ).
thf(2764,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(1093,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
thf(3331,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(978,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).
thf(3136,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(182,axiom,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_0) ).
thf(1558,plain,
! [A: $i] :
( ( A @ class_HOL_Ominus )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(541,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
thf(2262,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(337,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
thf(1861,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(250,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).
thf(1689,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1088,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
thf(3324,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(429,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
thf(2041,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(1153,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
thf(3430,plain,
tc_IntDef_Oint @ class_OrderedGroup_Olordered__ab__group,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(697,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).
thf(2576,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(259,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Olordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
thf(1706,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Olordered__ring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(207,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_22) ).
thf(1607,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(456,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).
thf(2095,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(426,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_4) ).
thf(2036,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(890,axiom,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).
thf(2956,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(147,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).
thf(1491,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(603,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_6) ).
thf(2384,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(801,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
thf(2786,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(1055,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_8) ).
thf(3267,plain,
tc_IntDef_Oint @ class_OrderedGroup_Osemigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).
thf(1294,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(643,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).
thf(2462,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(122,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_9) ).
thf(1440,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(985,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).
thf(3149,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(576,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
thf(2330,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
thf(1308,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(508,axiom,
tc_nat @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).
thf(2198,plain,
tc_nat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(592,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff1_0) ).
thf(2362,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(490,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).
thf(2162,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(748,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).
thf(2680,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(500,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
thf(2183,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__join )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(862,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_16) ).
thf(2902,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(469,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).
thf(2120,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(777,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_8) ).
thf(2739,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(124,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
thf(1444,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(123,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_9) ).
thf(1442,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(870,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).
thf(2917,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring )
| ~ ( A @ class_Ring__and__Field_Opordered__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(719,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
thf(2623,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(1148,axiom,
tc_IntDef_Oint @ class_Numeral_Onumber,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).
thf(3420,plain,
tc_IntDef_Oint @ class_Numeral_Onumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(622,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
thf(2421,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(72,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
thf(1348,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(554,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).
thf(2287,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(225,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).
thf(1642,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(268,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).
thf(1725,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(193,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_5) ).
thf(1578,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1067,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
thf(3291,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(767,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
thf(2719,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(176,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).
thf(1546,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Osemiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(670,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) ).
thf(2522,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(710,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).
thf(2604,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(887,axiom,
tc_nat @ class_LOrder_Ojoin__semilorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).
thf(2951,plain,
tc_nat @ class_LOrder_Ojoin__semilorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(344,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
thf(1876,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(1096,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
thf(3337,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(792,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).
thf(2768,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(1013,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
thf(3203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(360,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).
thf(1908,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(480,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_1) ).
thf(2142,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(1120,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(3379,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(518,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).
thf(2218,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(539,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).
thf(2258,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__0__neq__1 )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(158,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).
thf(1512,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(293,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
thf(1774,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(487,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) ).
thf(2155,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(1031,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).
thf(3232,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(676,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_14) ).
thf(2534,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(537,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) ).
thf(2255,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(98,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).
thf(1395,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(216,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).
thf(1625,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(817,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).
thf(2815,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(775,axiom,
tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).
thf(2736,plain,
tc_nat @ class_Ring__and__Field_Opordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(412,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_4) ).
thf(2008,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(400,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
thf(1986,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(976,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_13) ).
thf(3132,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
thf(1248,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1078,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(3309,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(783,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
thf(2751,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(81,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
thf(1363,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(578,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
thf(2334,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).
thf(1288,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(806,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Power_Orecpower ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_8) ).
thf(2795,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Power_Orecpower ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(428,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_31) ).
thf(2040,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__0__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(733,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_26) ).
thf(2651,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(277,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).
thf(1742,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(120,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).
thf(1436,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oaxclass__no__zero__divisors )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(336,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) ).
thf(1859,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(510,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_5) ).
thf(2201,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(402,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).
thf(1989,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring__1 )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(314,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_13) ).
thf(1816,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(149,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_22) ).
thf(1495,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(1105,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
thf(3347,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(1061,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(3277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(3,axiom,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
thf(1172,plain,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(106,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_7) ).
thf(1410,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(620,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
thf(2417,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(868,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff1_0) ).
thf(2913,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(613,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_3) ).
thf(2404,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(764,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
thf(2714,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(1009,axiom,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_5) ).
thf(3196,plain,
! [A: $i] :
( ( A @ class_HOL_Otimes )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(71,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
thf(1346,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(440,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).
thf(2063,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(371,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_8) ).
thf(1930,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(1038,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
thf(3244,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(660,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).
thf(2502,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(321,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).
thf(1829,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(939,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
thf(3057,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(1112,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_1 @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff1_0) ).
thf(3360,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_1 @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(195,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_9) ).
thf(1582,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(1049,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).
thf(3259,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(262,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
thf(1713,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(489,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).
thf(2159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(814,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(2810,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff2_0) ).
thf(1352,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(925,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
| ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
thf(3025,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
| ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(320,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).
thf(1827,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(895,axiom,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).
thf(2966,plain,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(627,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).
thf(2430,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(708,axiom,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
thf(2600,plain,
! [A: $i] :
( ( A @ class_LOrder_Olorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(860,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
thf(2898,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__comm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(1142,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
thf(3411,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(171,axiom,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_38) ).
thf(1537,plain,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(395,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
thf(1976,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(178,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).
thf(1550,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(1039,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1__cancel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).
thf(3245,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__1__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(922,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).
thf(3020,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1__cancel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(843,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).
thf(2864,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(346,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).
thf(1880,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(117,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_5) ).
thf(1431,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(966,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
thf(3113,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(357,axiom,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_8) ).
thf(1902,plain,
! [A: $i] :
( ( A @ class_HOL_Ozero )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(1129,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Olordered__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
thf(3394,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Olordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(654,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
thf(2484,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(348,axiom,
tc_nat @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_41) ).
thf(1885,plain,
tc_nat @ class_Ring__and__Field_Opordered__cancel__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(154,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).
thf(1505,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(100,axiom,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
thf(1399,plain,
! [A: $i] :
( ( A @ class_LOrder_Omeet__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(214,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).
thf(1621,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(478,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).
thf(2138,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(1100,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
thf(3341,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Osemiring__0__cancel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).
thf(1331,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0__cancel )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff__iff1_0) ).
thf(1320,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(388,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).
thf(1962,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(691,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_1) ).
thf(2563,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(379,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).
thf(1945,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Ocancel__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(274,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff2_0) ).
thf(1737,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(630,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
thf(2436,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(438,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
thf(2059,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(1155,axiom,
tc_IntDef_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).
thf(3432,plain,
tc_IntDef_Oint @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(938,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).
thf(3052,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(494,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).
thf(2170,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oring )
| ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(462,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).
thf(2106,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(647,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) ).
thf(2470,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(1070,axiom,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__no__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).
thf(3296,plain,
tc_IntDef_Oint @ class_Ring__and__Field_Oaxclass__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(735,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).
thf(2655,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(245,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_4) ).
thf(1681,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).
thf(1184,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
thf(3405,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(445,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).
thf(2074,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__1__cancel )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(133,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_2) ).
thf(1463,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Numeral_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(911,axiom,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_10) ).
thf(2998,plain,
! [A: $i] :
( ( A @ class_HOL_Oplus )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(417,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_2) ).
thf(2018,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(844,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
thf(2866,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(559,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
thf(2297,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(1162,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
thf(3443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(631,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
thf(2438,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_LOrder_Omeet__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(528,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).
thf(2238,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(908,axiom,
tc_nat @ class_Divides_Odiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_44) ).
thf(2993,plain,
tc_nat @ class_Divides_Odiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(1011,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
thf(3200,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(312,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_6) ).
thf(1812,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(362,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_1) ).
thf(1912,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(901,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).
thf(2980,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Osemiring__0 )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(930,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatMost ) )
!= ( A @ ( C @ c_SetInterval_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff__iff1_0) ).
thf(3035,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatMost ) )
!= ( A @ ( C @ c_SetInterval_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).
thf(1417,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(341,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
thf(1870,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(3460,plain,
$false,
inference(e,[status(thm)],[2199,2094,2072,1995,1729,3167,2921,3397,1315,2544,1818,1956,1554,2250,1586,1501,2452,2612,1469,1369,1823,2295,2306,3345,2341,1633,2778,2876,1237,2480,1982,1855,1750,1211,2512,1924,2495,2395,3012,2099,2380,1692,3382,1173,1596,2104,1290,1882,2808,1522,2776,1808,2659,3417,3040,3153,2590,1401,1422,2947,1569,1939,2248,2671,1544,2676,2014,2114,2837,3402,1533,1497,3439,3120,2686,3004,3175,1327,2844,2575,1788,1426,3217,1756,1310,3044,1735,2316,3446,2448,3338,2933,2434,1872,2712,2476,2627,2168,1260,3253,1988,3414,1342,3121,1354,2146,1507,1222,2360,1835,2216,2972,3249,2020,1613,1650,2886,2082,3140,1366,2516,2819,1746,3103,2348,2723,2432,1914,2491,2548,1782,2227,1391,1576,3308,2010,2400,2067,1529,2136,1904,1518,1228,1623,3221,2328,3029,2667,2755,3061,2708,2444,1313,3089,3353,2703,3248,3442,3425,1792,1430,2698,1660,1298,1760,3131,2339,3046,3342,2269,1323,3148,2682,3125,3410,2185,1455,3280,2466,2126,2745,2571,2356,1922,2857,1514,2373,2301,1362,3180,1778,3231,2388,1847,2829,3099,1800,1892,1379,3374,3385,2049,2552,1704,1890,1479,1609,2635,2929,3312,1568,3014,2520,2024,1641,3268,3258,2456,3322,3431,2324,3075,2090,2782,3163,2236,2880,1183,2178,2222,1489,1415,2616,1465,1302,1664,1373,2996,1864,2122,2925,1978,2291,1383,2254,1677,2540,2034,1960,3300,3093,1843,1169,1886,2371,1526,1351,2804,1600,3211,1564,2762,3389,2508,2964,2367,1928,3068,1377,2618,2833,2281,1896,2190,3421,1796,2530,2772,3157,2002,3243,2242,2799,2639,3327,1433,2103,1405,3226,1943,2718,2205,1696,3184,2586,2982,2884,3435,2954,3450,3303,1691,1438,1306,3186,2118,1338,1708,2737,2641,2621,3151,3097,3011,1206,3169,3265,2364,2164,2047,3318,1311,2232,1768,2905,1868,2382,2061,2000,2673,3261,2428,2560,2596,1676,1217,3022,1666,1487,2969,3239,2937,2606,3134,1619,2528,3339,2705,2264,2409,1387,1900,1723,1580,2277,2032,2986,2132,2890,3207,2396,3286,1560,1920,1178,1819,3144,2181,1656,3050,2344,2112,1573,3445,2653,2958,3307,2464,1938,1837,3269,3403,1968,2565,3198,2663,2332,2826,3314,3297,3349,2872,1951,1888,1296,1687,1457,1195,1407,1281,2741,3033,3408,1740,1910,1234,2157,1804,2841,1375,3381,1970,3218,2694,1672,1540,1719,3237,1360,1936,3105,1592,1762,3254,3413,1851,1772,2990,2377,2801,1794,1953,1878,2631,3440,3205,3176,3087,3018,1397,1329,3311,3326,1964,3000,1292,1461,2868,2419,2080,1584,1700,1644,1419,2460,1493,1683,3407,2561,3210,1424,2312,2053,2196,2240,1810,2172,1214,3194,2108,2038,1446,2472,2649,3294,1744,2536,1451,1552,2581,1947,1984,2813,3109,2140,1825,2285,2504,1776,1263,2450,1588,2598,3059,1266,1831,1231,2153,2900,1668,1974,1192,1932,2006,2497,1874,3115,3409,2862,2766,2482,1246,1715,3333,3083,1393,1627,3215,1333,2203,2043,3173,2057,1286,2402,2645,1996,2423,2909,2749,1434,1857,1991,2788,1318,1814,3225,2546,2761,2076,1170,2915,2440,2793,3190,2144,1906,2176,1754,2904,3042,1219,1483,1273,1548,3262,3289,2602,2894,1631,2729,1648,1727,1510,1251,1764,2413,1698,2556,3358,2275,2149,3079,2570,2941,2028,3375,2734,3111,3274,2524,3396,3343,2260,3372,3387,1833,1916,2859,2789,2657,2188,3272,1403,2398,2716,1256,2134,3213,3070,2727,2970,3319,1615,1784,1389,3255,2791,3240,2393,1752,1652,3081,3283,3266,2674,2016,2514,1535,2806,2991,1520,2817,1503,1786,2220,2326,2293,3330,3208,3123,2055,2706,2166,1258,3302,3355,1428,3223,1271,2308,1371,3077,1635,2935,3002,1733,3340,1239,2759,2753,3436,2425,3416,3091,2474,2358,1356,2573,2148,2510,2346,3101,1806,3419,2257,1542,2669,3384,1571,2065,2721,3352,2538,1853,1408,2478,3251,2151,3155,2229,2084,2214,2415,1894,2493,3038,2637,2774,3287,1524,1349,2097,3270,2246,1603,2299,2116,2839,2943,2945,2802,3138,3182,2896,1471,3073,1993,3165,3192,2874,1344,2252,1381,3219,2824,2610,3027,2314,2343,2625,2780,2267,1821,1731,2446,2757,2923,1325,3006,3451,1556,2542,2289,2647,2710,2911,2770,2212,2835,1528,2086,2931,3142,2101,2303,3178,2207,2984,2069,1198,1841,1926,2962,1474,2350,2725,1594,2051,3423,2550,3159,2369,3241,2797,3016,2592,2244,2633,2022,3363,3310,1364,2967,2390,1694,2693,2506,3380,1562,3009,3031,2952,1758,1203,2665,3293,3146,1340,1472,2846,1958,2582,1662,2614,1304,3427,1467,2994,2318,3395,2784,2271,3206,3161,1420,2878,1684,2124,2234,2927,2629,3048,2684,1845,1748,2661,1225,2192,3129,1531,2850,2888,2882,2831,1798,3391,1770,3376,1516,3315,1598,2977,1611,2375,1566,2012,1605,3260,2588,2732,1941,2678,2518,1368,3228,1780,2821,2407,2386,3246,3448,2092,3305,3063,3202,2337,3127,1679,2468,2354,1711,2747,1499,1790,2224,2454,1300,1637,2688,3334,2700,1186,1980,2128,1658,2322,1538,2486,3359,3329,1738,3095,1358,1934,2411,2558,2426,1802,1284,2939,3071,2266,1617,1766,3107,1898,1849,1702,2379,2279,1955,2843,1485,1972,2320,1670,3024,3117,2860,2949,1717,2030,3256,2892,2848,3366,2584,3398,3400,3433,1839,2088,1180,1966,1685,2696,2078,2310,2209,1866,2907,1998,3452,2458,1918,1316,2352,1459,2045,1949,2870,2828,3171,2960,3188,2194,1654,1412,2743,1448,3346,2187,1189,2110,3320,2305,2919,1575,2226,1453,2643,1253,2273,2853,2406,2554,1481,2026,2130,2526,3085,1276,1590,1646,2443,2988,1385,2594,1721,2174,2283,1476,1674,2855,1639,2532,1508,3369,2823,2811,1629,2004,2608,3235,1244,2764,3331,3136,1558,2262,1861,1689,3324,2041,3430,2576,1706,1607,2095,2036,2956,1491,2384,2786,3267,1294,2462,1440,3149,2330,1308,2198,2362,2162,2680,2183,2902,2120,2739,1444,1442,2917,2623,3420,2421,1348,2287,1642,1725,1578,3291,2719,1546,2522,2604,2951,1876,3337,2768,3203,1908,2142,3379,2218,2258,1512,1774,2155,3232,2534,2255,1395,1625,2815,2736,2008,1986,3132,1248,3309,2751,1363,2334,1288,2795,2040,2651,1742,1436,1859,2201,1989,1816,1495,3347,3277,1172,1410,2417,2913,2404,2714,3196,1346,2063,1930,3244,2502,1829,3057,3360,1582,3259,1713,2159,2810,1352,3025,1827,2966,2430,2600,2898,3411,1537,1976,1550,3245,3020,2864,1880,1431,3113,1902,3394,2484,1885,1505,1399,1621,2138,3341,1331,1320,1962,2563,1945,1737,2436,2059,3432,3052,2170,2106,2470,3296,2655,1681,1184,3405,2074,1463,2998,2018,2866,2297,3443,2438,2238,2993,3200,1812,1912,2980,3035,1417,1870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET818-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.24/0.51 % Computer : n017.cluster.edu
% 0.24/0.51 % Model : x86_64 x86_64
% 0.24/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.51 % Memory : 8046.5625MB
% 0.24/0.51 % OS : Linux 6.8.0-71-generic
% 0.24/0.51 % CPULimit : 300
% 0.24/0.51 % WCLimit : 300
% 0.24/0.51 % DateTime : Sat Sep 26 08:13:33 UTC 2026
% 0.24/0.51 % CPUTime :
% 0.24/0.51 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.40/1.37 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.22/1.97 % [INFO] Parsing done (590ms).
% 3.22/1.99 % [INFO] Running in sequential loop mode.
% 4.53/2.56 % [INFO] eprover registered as external prover.
% 4.53/2.58 % [INFO] Scanning for conjecture ...
% 5.34/2.85 % [INFO] Found a conjecture (or negated_conjecture) and 1357 axioms. Running axiom selection ...
% 8.58/3.62 % [INFO] Axiom selection finished. Selected 1166 axioms (removed 191 axioms).
% 9.59/3.98 % [INFO] Problem is propositional (TPTP CNF).
% 9.59/4.02 % [INFO] Type checking passed.
% 9.59/4.03 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 22.23/7.67 % External prover 'e' found a proof!
% 22.23/7.67 % [INFO] Killing All external provers ...
% 22.23/7.67 % Time passed: 6955ms (effective reasoning time: 5670ms)
% 22.23/7.69 % Axioms used in derivation (1166): clsrel_Ring__and__Field_Osemiring__1__cancel_9, clsrel_Ring__and__Field_Oidom_20, clsrel_Ring__and__Field_Oordered__idom_3, clsrel_OrderedGroup_Ocancel__semigroup__add_1, cls_Finite__Set_Ofinite__Union_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4, clsrel_Ring__and__Field_Oidom_17, clsarity_IntDef__Oint_57, clsrel_OrderedGroup_Olordered__ab__group__abs_3, clsrel_Ring__and__Field_Osemiring__1__cancel_12, cls_Nat_Ole__0__eq__iff1_0, clsrel_Ring__and__Field_Opordered__semiring_10, clsarity_IntDef__Oint_34, clsrel_Ring__and__Field_Opordered__comm__semiring_14, clsrel_Ring__and__Field_Opordered__ring_2, cls_Finite__Set_Ofinite__converse__iff1_0, clsrel_Ring__and__Field_Oordered__semiring__strict_5, clsrel_Ring__and__Field_Oring__1_7, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19, cls_IntDiv_Ozdvd__0__right_0, clsrel_Ring__and__Field_Opordered__semiring_3, clsrel_Ring__and__Field_Opordered__cancel__semiring_11, cls_SetInterval_OgreaterThan__subset__iff__iff1_0, clsarity_IntDef__Oint_4, cls_List_Ofinite__set_0, clsrel_Ring__and__Field_Oordered__idom_32, cls_Finite__Set_Ofinite__Un__iff1_1, cls_Datatype__Universe_OdprodE_0, cls_SetInterval_OlessThan__iff__iff2_0, cls_List_Oset__empty2__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13, clsrel_Ring__and__Field_Ocomm__ring_3, clsrel_Ring__and__Field_Opordered__semiring_6, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7, cls_Datatype__Universe_OuprodI_0, clsrel_Ring__and__Field_Oordered__semidom_16, clsrel_OrderedGroup_Opordered__ab__group__add_6, clsarity_nat_32, clsarity_nat_26, clsrel_Numeral_Onumber__ring_1, clsrel_Ring__and__Field_Olordered__ring_8, clsrel_Ring__and__Field_Ocomm__ring_12, cls_Set_OsubsetI_1, clsrel_Ring__and__Field_Oordered__ring__strict_7, clsrel_Ring__and__Field_Osemiring__1__cancel_7, clsrel_Ring__and__Field_Ocomm__semiring__1_12, clsrel_Ring__and__Field_Oordered__semiring__strict_22, clsrel_Ring__and__Field_Ocomm__semiring__1_15, clsrel_Ring__and__Field_Oordered__semidom_2, clsrel_Ring__and__Field_Olordered__ring_14, cls_List_Oappend__in__lists__conv__iff2_0, cls_Datatype__Universe_Odsum__In0I_0, clsrel_Ring__and__Field_Ocomm__semiring__0_2, cls_List_Oset__empty2__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14, clsrel_Ring__and__Field_Opordered__cancel__semiring_6, clsrel_Ring__and__Field_Osemiring__0__cancel_9, clsrel_Ring__and__Field_Ocomm__ring_17, cls_List_Olists_ONil_0, cls_Set_OInterD_0, clsarity_IntDef__Oint_45, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20, clsrel_Power_Orecpower_17, cls_List_ONil__notin__lex__iff1_0, cls_Relation_OImageI_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7, clsrel_OrderedGroup_Olordered__ab__group_13, cls_Divides_Omod__eq__0D__dest_0, clsrel_OrderedGroup_Olordered__ab__group__meet_1, cls_SetInterval_OatLeast__subset__iff__iff2_0, clsrel_Ring__and__Field_Ocomm__ring_6, clsrel_Ring__and__Field_Ocomm__semiring__1_3, clsrel_Ring__and__Field_Oordered__idom_43, clsrel_OrderedGroup_Olordered__ab__group_3, clsrel_Orderings_Olinorder_0, clsrel_Ring__and__Field_Ocomm__semiring_4, cls_Sum__Type_OInr__not__Inl__iff1_0, clsrel_OrderedGroup_Olordered__ab__group_7, clsarity_IntDef__Oint_46, clsrel_Ring__and__Field_Oring_13, clsarity_nat_21, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22, clsrel_OrderedGroup_Omonoid__mult_2, clsrel_Power_Orecpower_21, clsrel_Ring__and__Field_Oordered__semiring__strict_12, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1, clsrel_OrderedGroup_Olordered__ab__group__join_3, cls_SetInterval_OgreaterThan__iff__iff2_0, clsrel_OrderedGroup_Ocomm__monoid__add_2, clsrel_Ring__and__Field_Oordered__semidom_39, clsarity_IntDef__Oint_13, clsrel_Ring__and__Field_Oordered__idom_12, cls_Set_OUNIV__not__empty__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0, clsarity_nat_15, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4, cls_List_ONil__is__append__conv__iff2_0, clsrel_OrderedGroup_Opordered__ab__group__add_1, clsrel_Ring__and__Field_Oordered__ring__strict_10, clsrel_Ring__and__Field_Olordered__ring_3, clsrel_Power_Orecpower_14, clsrel_Ring__and__Field_Oordered__idom_23, clsarity_IntDef__Oint_52, clsrel_OrderedGroup_Ocomm__monoid__mult_0, clsrel_Ring__and__Field_Oidom_29, clsarity_IntDef__Oint_24, clsrel_Ring__and__Field_Oidom_26, clsrel_OrderedGroup_Osemigroup__add_0, clsrel_Ring__and__Field_Oring_10, clsrel_Numeral_Onumber__ring_16, clsrel_OrderedGroup_Olordered__ab__group_9, clsrel_Power_Orecpower_6, clsarity_nat_10, clsrel_Ring__and__Field_Oordered__ring__strict_26, clsarity_nat_7, clsrel_Ring__and__Field_Oordered__semidom_9, clsrel_Ring__and__Field_Oidom_13, clsrel_Ring__and__Field_Opordered__ring_14, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1, cls_Sum__Type_OInr__eq__iff1_0, clsrel_Ring__and__Field_Ocomm__ring__1_1, clsrel_Ring__and__Field_Oring__1_18, clsrel_OrderedGroup_Oab__group__add_6, cls_Set_OemptyE_0, clsrel_Ring__and__Field_Oordered__semidom_28, clsrel_Ring__and__Field_Oordered__semidom_34, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21, clsrel_OrderedGroup_Olordered__ab__group__abs_8, cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0, cls_List_Oappend__self__conv2__iff1_0, cls_Relation_OImageE_0, clsrel_Ring__and__Field_Ocomm__ring__1_16, cls_Nat_Oless__Suc0__iff1_0, clsrel_Ring__and__Field_Osemiring__0__cancel_4, clsrel_Numeral_Onumber__ring_27, clsrel_OrderedGroup_Olordered__ab__group__join_6, cls_Wellfounded__Recursion_Owf__insert__iff1_0, cls_Datatype_Ooption_Oinject__iff1_0, cls_Transitive__Closure_Otrancl_Or__into__trancl_0, clsrel_Ring__and__Field_Opordered__ring_19, cls_Finite__Set_OFinites_OemptyI_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10, clsrel_Numeral_Onumber__ring_24, clsrel_Ring__and__Field_Oordered__semidom_23, cls_Set_Osingleton__inject__dest_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_1, clsrel_OrderedGroup_Olordered__ab__group__abs_18, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13, clsarity_nat_40, clsrel_Power_Orecpower_5, clsarity_IntDef__Oint_6, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4, clsrel_OrderedGroup_Olordered__ab__group__abs_13, clsrel_Ring__and__Field_Ocomm__ring__1_20, cls_IntDiv_Ozdvd__0__left__iff2_0, clsrel_Orderings_Olinorder_4, clsrel_Power_Orecpower_0, cls_Set_Osingleton__insert__inj__eq__iff1_1, clsrel_Ring__and__Field_Oordered__idom_48, clsrel_Ring__and__Field_Osemiring__1__cancel_3, clsrel_Ring__and__Field_Oordered__semiring__strict_9, clsrel_OrderedGroup_Opordered__ab__semigroup__add_1, clsrel_Ring__and__Field_Olordered__ring_4, clsrel_Ring__and__Field_Osemiring_1, clsrel_Ring__and__Field_Oordered__idom_37, clsrel_Ring__and__Field_Oordered__ring__strict_22, cls_Nat_Oadd__is__0__iff1_1, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6, clsrel_Ring__and__Field_Oordered__ring__strict_14, clsrel_Ring__and__Field_Oordered__idom_56, clsarity_IntDef__Oint_56, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7, cls_Finite__Set_OFinites_OinsertI_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21, clsrel_Ring__and__Field_Oidom_10, clsarity_set_2, clsarity_nat_25, clsrel_Ring__and__Field_Oordered__idom_17, clsrel_Ring__and__Field_Oordered__ring__strict_33, cls_Set_OUnionE_1, clsrel_Ring__and__Field_Oring_6, clsrel_OrderedGroup_Olordered__ab__group__join_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8, clsrel_Ring__and__Field_Opordered__comm__semiring_3, clsrel_Ring__and__Field_Oring__1_19, clsrel_OrderedGroup_Oab__group__add_5, clsrel_Ring__and__Field_Olordered__ring_1, clsarity_nat_14, cls_Nat_Oless__irrefl_0, cls_IntDiv_Ozminus__dvd__iff__iff1_0, clsrel_Ring__and__Field_Oring__1_14, cls_List_Olistrel__Nil1_0, clsrel_Numeral_Onumber__ring_12, clsrel_Ring__and__Field_Ocomm__semiring__1_4, clsarity_nat_3, clsrel_Power_Orecpower_24, clsrel_Ring__and__Field_Ocomm__ring__1_5, clsarity_IntDef__Oint_3, cls_Nat_Onot__less0__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10, clsrel_Ring__and__Field_Ocomm__ring__1_13, clsrel_OrderedGroup_Olordered__ab__group__meet_9, clsarity_IntDef__Oint_60, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8, clsrel_Numeral_Onumber__ring_23, clsrel_Numeral_Onumber__ring_20, clsrel_Ring__and__Field_Oaxclass__abs__if_0, cls_Nat_Oless__one__iff1_0, clsrel_Ring__and__Field_Ocomm__ring_9, clsrel_Power_Orecpower_1, cls_Datatype__Universe_OIn1__eq__iff1_0, clsrel_Ring__and__Field_Oidom_1, cls_Nat_Oadd__gr__0__iff2_0, cls_SetInterval_Ofinite__atLeastLessThan__int_0, cls_Set_OComplI_0, clsrel_OrderedGroup_Opordered__ab__group__add_8, clsarity_nat_29, clsarity_IntDef__Oint_27, clsrel_Ring__and__Field_Opordered__cancel__semiring_3, clsrel_Ring__and__Field_Ocomm__ring__1_24, clsrel_Ring__and__Field_Ocomm__semiring__0_7, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0, clsrel_Ring__and__Field_Opordered__comm__semiring_8, clsrel_Ring__and__Field_Ocomm__ring__1_27, cls_Relation_OconverseE_1, clsrel_Ring__and__Field_Olordered__ring_21, clsrel_OrderedGroup_Oab__group__add_0, clsarity_nat_47, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10, cls_Nat_Oneq0__conv__iff2_0, cls_Sum__Type_OPlusE_0, cls_Nat_Oadd__is__0__iff2_0, clsrel_OrderedGroup_Olordered__ab__group__join_14, cls_Finite__Set_Ofinite__Int_0, clsrel_Ring__and__Field_Ocomm__ring__1_7, cls_List_ONil__is__append__conv__iff1_0, cls_Relation_Orel__compE_0, clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1, clsrel_OrderedGroup_Opordered__ab__group__add_10, clsrel_Ring__and__Field_Oordered__idom_28, cls_Finite__Set_Ofinite__Pow__iff__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1, cls_Sum__Type_OInlI_0, clsrel_Ring__and__Field_Oordered__semiring__strict_19, clsarity_IntDef__Oint_0, cls_Infinite__Set_Onat__not__finite_0, clsrel_Ring__and__Field_Osemiring__1_4, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19, cls_Set_OpsubsetI_0, cls_Relation_Oconverse__iff__iff2_0, cls_Set_Osubset__refl_0, cls_List_Olist_Oinject__iff1_0, clsrel_Ring__and__Field_Oidom_21, clsarity_IntDef__Oint_49, clsrel_Ring__and__Field_Ocomm__ring_10, clsrel_Ring__and__Field_Ocomm__semiring__1_8, clsrel_Ring__and__Field_Opordered__comm__semiring_10, clsrel_Ring__and__Field_Opordered__ring_6, clsarity_IntDef__Oint_38, clsrel_Ring__and__Field_Oring_1, clsrel_Ring__and__Field_Oidom_7, clsrel_Ring__and__Field_Opordered__ring_11, clsrel_OrderedGroup_Oab__semigroup__mult_0, clsrel_Ring__and__Field_Opordered__semiring_2, clsrel_Ring__and__Field_Opordered__ring_22, clsrel_Ring__and__Field_Osemiring__0_2, clsrel_Ring__and__Field_Ocomm__ring_13, cls_SetInterval_OlessThan__iff__iff1_0, clsrel_Ring__and__Field_Oordered__idom_49, clsrel_Ring__and__Field_Osemiring__0_7, cls_Set_OUnCI_1, clsrel_OrderedGroup_Olordered__ab__group__meet_12, clsrel_Ring__and__Field_Oring__1_2, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14, clsarity_IntDef__Oint_16, clsrel_Ring__and__Field_Oordered__semiring__strict_3, clsrel_Ring__and__Field_Osemiring__1_10, cls_Relation_ORangeE_0, clsrel_Ring__and__Field_Oordered__semiring__strict_8, cls_Set_OInterI_1, clsrel_Numeral_Onumber__ring_19, cls_Nat_OSuc__Suc__eq__iff1_0, clsrel_OrderedGroup_Olordered__ab__group__abs_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4, clsrel_OrderedGroup_Olordered__ab__group__abs_10, cls_List_Oset__empty__iff2_0, clsrel_Numeral_Onumber__ring_5, clsrel_Ring__and__Field_Ocomm__semiring__1_16, cls_SetInterval_Ofinite__greaterThanAtMost_0, clsarity_IntDef__Oint_35, clsarity_nat_36, clsrel_Ring__and__Field_Olordered__ring_25, clsrel_Ring__and__Field_Ocomm__ring_0, clsarity_nat_18, clsrel_Ring__and__Field_Oordered__semidom_13, cls_Product__Type_OPair__eq__iff1_0, clsrel_Ring__and__Field_Oordered__idom_55, clsrel_Ring__and__Field_Oordered__ring__strict_19, cls_Set_OinsertCI_0, clsrel_Ring__and__Field_Olordered__ring_10, clsrel_Ring__and__Field_Osemiring__1__cancel_10, clsarity_nat_33, cls_Set_OPow__iff__iff2_0, clsrel_Ring__and__Field_Oring__1_11, cls_Finite__Set_Ofinite__converse__iff2_0, clsrel_Ring__and__Field_Osemiring__1_8, cls_SetInterval_OatMost__iff__iff2_0, clsarity_IntDef__Oint_48, clsrel_OrderedGroup_Opordered__ab__group__add_11, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11, clsrel_Power_Orecpower_13, clsrel_Ring__and__Field_Oordered__semidom_24, clsarity_IntDef__Oint_19, clsrel_Ring__and__Field_Oordered__semiring__strict_16, cls_Set_Osingleton__insert__inj__eq_H__iff2_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5, clsrel_OrderedGroup_Olordered__ab__group_4, cls_List_Oappend__in__lists__conv__iff1_0, clsrel_Ring__and__Field_Osemiring__0_0, clsrel_Ring__and__Field_Oordered__semiring__strict_21, cls_SetInterval_Ofinite__greaterThanAtMost__int_0, clsrel_Ring__and__Field_Oring__1_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add_4, clsrel_Ring__and__Field_Oordered__semidom_35, clsarity_IntDef__Oint_47, clsrel_Ring__and__Field_Oidom_25, clsrel_Ring__and__Field_Osemiring_2, clsrel_Ring__and__Field_Oordered__ring__strict_1, clsrel_Ring__and__Field_Opordered__cancel__semiring_9, clsarity_IntDef__Oint_59, clsarity_nat_22, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8, cls_Nat_Ole__0__eq__iff2_0, cls_Relation_OdiagI_0, clsrel_OrderedGroup_Ocomm__monoid__mult_3, cls_Set_OCompl__subset__Compl__iff__iff2_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29, cls_Datatype__Universe_OIn0__not__In1__iff1_0, clsrel_Power_Orecpower_18, clsrel_Ring__and__Field_Oidom_6, clsrel_Ring__and__Field_Opordered__ring_18, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2, clsarity_nat_44, clsrel_OrderedGroup_Olordered__ab__group__abs_4, cls_Set_OsubsetI_0, cls_Sum__Type_OPlusE_3, clsrel_Ring__and__Field_Osemiring__1__cancel_4, clsarity_nat_11, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18, clsrel_Ring__and__Field_Oring__1_6, clsrel_Ring__and__Field_Oordered__idom_51, clsrel_Ring__and__Field_Osemiring__1_3, cls_Finite__Set_Ofinite__Un__iff1_0, clsrel_Numeral_Onumber__ring_6, clsrel_OrderedGroup_Olordered__ab__group__abs_14, cls_Datatype__Universe_OdprodE_1, clsrel_OrderedGroup_Olordered__ab__group_6, clsrel_Orderings_Olinorder_1, clsarity_IntDef__Oint_36, cls_Set_OUNIV__I_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9, clsrel_Ring__and__Field_Ocomm__semiring_2, clsrel_Numeral_Onumber__ring_28, clsarity_IntDef__Oint_58, cls_Set_OCompl__eq__Compl__iff__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12, clsrel_Ring__and__Field_Oordered__idom_38, clsrel_Ring__and__Field_Oordered__idom_2, clsrel_OrderedGroup_Olordered__ab__group__abs_5, cls_Finite__Set_Ofinite__Diff__insert__iff1_0, clsrel_Ring__and__Field_Oordered__idom_21, clsrel_Ring__and__Field_Oordered__semidom_3, clsrel_Ring__and__Field_Opordered__ring_3, cls_List_OlistsE_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5, cls_List_Olength__0__conv__iff2_0, clsrel_Power_Orecpower_4, cls_Divides_Odvd__0__left__iff__iff2_0, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0, cls_List_Oself__append__conv__iff2_0, clsrel_Ring__and__Field_Oordered__idom_42, clsrel_Power_Orecpower_7, clsrel_Ring__and__Field_Olordered__ring_15, clsrel_Ring__and__Field_Oordered__semiring__strict_11, clsarity_IntDef__Oint_53, cls_List_Owf__lex_0, cls_SetInterval_OatMost__eq__iff__iff1_0, clsrel_Ring__and__Field_Oordered__idom_36, clsarity_nat_27, cls_Relation_ODomainI_0, clsrel_Ring__and__Field_Osemiring__0__cancel_3, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2, clsrel_Ring__and__Field_Ocomm__semiring_5, clsrel_Ring__and__Field_Oordered__idom_26, cls_Set_OinsertE_0, clsrel_Ring__and__Field_Osemiring__1__cancel_6, clsrel_Ring__and__Field_Oring__1_15, clsrel_Ring__and__Field_Oordered__ring__strict_8, clsrel_Ring__and__Field_Oordered__idom_52, clsrel_Ring__and__Field_Oordered__ring__strict_25, clsrel_Ring__and__Field_Opordered__semiring_7, clsrel_Ring__and__Field_Ocomm__ring__1_0, clsarity_IntDef__Oint_64, clsrel_Ring__and__Field_Opordered__ring_13, clsrel_OrderedGroup_Opordered__ab__semigroup__add_0, clsrel_OrderedGroup_Olordered__ab__group__join_17, clsrel_OrderedGroup_Ocomm__monoid__add_1, clsrel_Ring__and__Field_Oordered__ring__strict_27, cls_Set_Onot__psubset__empty__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1_14, clsarity_IntDef__Oint_14, clsrel_Ring__and__Field_Opordered__comm__semiring_13, clsarity_IntDef__Oint_7, cls_Set_OUnE_0, clsrel_Ring__and__Field_Oring_9, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15, clsrel_OrderedGroup_Oab__semigroup__add_1, clsrel_Ring__and__Field_Ocomm__ring__1_10, clsrel_OrderedGroup_Olordered__ab__group_0, clsarity_nat_16, clsrel_Ring__and__Field_Opordered__cancel__semiring_12, cls_SetInterval_OlessThan__subset__iff__iff2_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12, cls_SetInterval_OgreaterThan__subset__iff__iff2_0, clsrel_OrderedGroup_Olordered__ab__group_14, clsrel_Ring__and__Field_Oidom_14, clsrel_Ring__and__Field_Ocomm__semiring__1_11, clsrel_Ring__and__Field_Oordered__idom_10, clsrel_OrderedGroup_Olordered__ab__group__meet_5, clsrel_Ring__and__Field_Oordered__ring__strict_36, clsrel_Ring__and__Field_Osemiring__1__cancel_13, clsrel_Ring__and__Field_Oordered__ring__strict_11, clsrel_Ring__and__Field_Ocomm__ring_16, clsrel_Ring__and__Field_Olordered__ring_19, clsarity_IntDef__Oint_25, clsrel_Ring__and__Field_Oaxclass__0__neq__1_0, clsrel_Ring__and__Field_Ocomm__ring__1_21, clsrel_Ring__and__Field_Oordered__idom_47, clsrel_Ring__and__Field_Ocomm__ring_2, clsarity_nat_38, clsrel_Ring__and__Field_Oordered__ring__strict_5, clsrel_Numeral_Onumber__ring_2, clsrel_Numeral_Onumber__ring_17, cls_Set_OComplD__dest_0, clsrel_Ring__and__Field_Ocomm__semiring__0_3, clsrel_Ring__and__Field_Oordered__semidom_8, cls_Set_OUn__empty__iff1_1, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12, cls_Relation_Orel__compE_2, clsrel_Ring__and__Field_Oordered__idom_15, clsrel_Ring__and__Field_Ocomm__ring__1_19, clsrel_OrderedGroup_Olordered__ab__group_17, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3, cls_Relation_OImageE_1, cls_Set_OsingletonD__dest_0, clsrel_Ring__and__Field_Olordered__ring_7, clsarity_IntDef__Oint_20, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11, clsrel_Ring__and__Field_Oordered__idom_18, clsrel_Ring__and__Field_Ocomm__ring__1_4, cls_SetInterval_OatLeast__subset__iff__iff1_0, clsrel_Ring__and__Field_Oordered__ring__strict_16, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26, clsrel_Ring__and__Field_Ocomm__ring__1_14, clsrel_Ring__and__Field_Oordered__idom_31, cls_IntDiv_Ozdvd__triv__right_0, clsrel_Ring__and__Field_Opordered__semiring_1, cls_Nat_OZero__not__Suc__iff1_0, cls_Relation_OdiagE_0, clsrel_Ring__and__Field_Ocomm__ring__1_26, cls_SetInterval_Ofinite__atLeastAtMost_0, clsrel_Ring__and__Field_Oordered__ring__strict_21, cls_SetInterval_OatMost__subset__iff__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0, cls_GCD_Ogcd__dvd1_0, clsrel_Ring__and__Field_Oring_5, cls_SetInterval_Ofinite__atLeastLessThan_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19, clsrel_OrderedGroup_Olordered__ab__group__join_7, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5, clsrel_Ring__and__Field_Olordered__ring_26, cls_Set_OUn__empty__iff1_0, clsrel_Ring__and__Field_Oordered__idom_22, clsrel_Power_Orecpower_10, cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, clsrel_Ring__and__Field_Opordered__comm__semiring_2, clsrel_Ring__and__Field_Oordered__idom_57, clsrel_Ring__and__Field_Opordered__cancel__semiring_2, cls_Wellfounded__Recursion_Owf__insert__iff2_0, clsrel_OrderedGroup_Olordered__ab__group__meet_4, clsrel_Ring__and__Field_Opordered__ring_12, clsrel_Ring__and__Field_Osemiring__0_6, clsrel_Ring__and__Field_Oordered__ring__strict_4, cls_Set_Oempty__subsetI_0, clsrel_Numeral_Onumber__ring_13, clsrel_Ring__and__Field_Ocomm__ring__1_25, clsrel_OrderedGroup_Olordered__ab__group__join_13, clsrel_Ring__and__Field_Oordered__ring__strict_32, cls_Relation_OIdI_0, clsarity_IntDef__Oint_26, clsrel_Ring__and__Field_Ocomm__ring__1_15, clsarity_IntDef__Oint_2, cls_Finite__Set_Ofinite__Int_1, clsarity_IntDef__Oint_31, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15, cls_List_Oappend__is__Nil__conv__iff2_0, clsrel_OrderedGroup_Oab__group__add_1, clsrel_Ring__and__Field_Oordered__idom_11, clsrel_Ring__and__Field_Oordered__semidom_17, cls_SetInterval_Ofinite__atLeastAtMost__int_0, cls_Nat_OSuc__less__eq__iff2_0, clsrel_Ring__and__Field_Oordered__idom_29, cls_Divides_Odvd__0__left__iff__iff1_0, cls_SetInterval_Ofinite__lessThan_0, cls_List_Olength__greater__0__conv__iff1_0, cls_List_Oappend1__eq__conv__iff1_1, clsrel_Ring__and__Field_Oordered__ring__strict_15, clsrel_OrderedGroup_Olordered__ab__group__meet_6, clsrel_Ring__and__Field_Osemiring__1_0, clsrel_Ring__and__Field_Osemiring__1__cancel_14, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16, cls_SetInterval_OlessThan__eq__iff__iff1_0, clsrel_Ring__and__Field_Osemiring__1_11, clsrel_OrderedGroup_Olordered__ab__group__meet_17, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2, cls_Nat_Oadd__gr__0__iff2_1, clsrel_Ring__and__Field_Opordered__ring_9, clsrel_Ring__and__Field_Opordered__cancel__semiring_15, clsrel_Ring__and__Field_Oordered__semiring__strict_2, cls_Set_OsingletonI_0, cls_Nat_Oless__Suc0__iff2_0, clsrel_Ring__and__Field_Ocomm__ring__1_8, clsrel_LOrder_Olorder_0, cls_Set_Osubset__antisym_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0, cls_List_Oself__append__conv__iff1_0, clsrel_Ring__and__Field_Oring_2, cls_Set_OsubsetD_0, clsrel_Ring__and__Field_Oordered__idom_7, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9, clsrel_Ring__and__Field_Olordered__ring_22, clsarity_nat_37, cls_Product__Type_OPair__eq__iff1_1, cls_IntDiv_Ozdvd__triv__left_0, cls_Nat_Ozero__less__Suc_0, cls_List_Oin__listsI_1, clsrel_Ring__and__Field_Oaxclass__abs__if_1, clsrel_Ring__and__Field_Oidom_11, clsrel_Ring__and__Field_Ocomm__semiring__1_7, clsrel_Ring__and__Field_Oordered__semidom_31, clsrel_Ring__and__Field_Opordered__cancel__semiring_8, cls_List_Osame__append__eq__iff1_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0, clsrel_Ring__and__Field_Oordered__semiring__strict_17, clsarity_IntDef__Oint_15, clsrel_Ring__and__Field_Oidom_2, cls_Wellfounded__Relations_Oless__than__iff__iff1_0, clsrel_Ring__and__Field_Osemiring__1__cancel_5, clsrel_Ring__and__Field_Oordered__semidom_20, clsrel_OrderedGroup_Ocancel__semigroup__add_0, clsrel_Ring__and__Field_Oring__1_1, cls_SetInterval_OatLeast__iff__iff2_0, cls_GCD_Ogcd__greatest__iff__iff1_0, clsrel_Ring__and__Field_Osemiring__1__cancel_0, clsrel_OrderedGroup_Opordered__ab__group__add_2, cls_Datatype_Oelem__o2s__iff1_0, clsrel_OrderedGroup_Olordered__ab__group__meet_11, clsrel_Ring__and__Field_Olordered__ring_11, clsarity_nat_6, clsrel_Ring__and__Field_Ocomm__semiring__0_10, clsrel_Ring__and__Field_Opordered__ring_7, cls_Relation_OconverseE_0, clsarity_IntDef__Oint_42, clsrel_OrderedGroup_Oab__group__add_4, cls_IntDiv_Ozdvd__1__left_0, cls_List_Olength__greater__0__conv__iff2_0, clsrel_Numeral_Onumber__ring_30, clsarity_IntDef__Oint_37, clsrel_Ring__and__Field_Oordered__idom_39, cls_SetInterval_OatMost__subset__iff__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0_6, clsrel_Ring__and__Field_Opordered__comm__semiring_9, clsrel_Ring__and__Field_Oordered__semidom_12, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0, cls_GCD_Ogcd__greatest__iff__iff2_0, clsrel_Ring__and__Field_Ocomm__ring_11, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6, clsarity_nat_0, cls_Datatype__Universe_OuprodE_2, clsarity_nat_43, clsrel_Orderings_Oorder_0, cls_SetInterval_Ofinite__greaterThanLessThan__int_0, cls_Relation_Oconverse__iff__iff1_0, clsrel_OrderedGroup_Ocomm__monoid__add_0, clsrel_Ring__and__Field_Osemiring__1_7, cls_Datatype__Universe_OIn1__not__In0__iff1_0, clsarity_IntDef__Oint_18, cls_List_Olist_Oinject__iff1_1, clsrel_OrderedGroup_Olordered__ab__group__meet_13, clsrel_Ring__and__Field_Opordered__cancel__semiring_1, clsrel_OrderedGroup_Olordered__ab__group__abs_15, clsrel_Ring__and__Field_Oaxclass__0__neq__1_1, clsrel_Numeral_Onumber__ring_7, clsarity_nat_34, clsrel_Ring__and__Field_Ocomm__semiring__1_10, clsrel_OrderedGroup_Olordered__ab__group_5, clsrel_Ring__and__Field_Opordered__ring_17, clsrel_OrderedGroup_Olordered__ab__group__abs_6, clsrel_OrderedGroup_Opordered__ab__semigroup__add_3, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3, clsrel_OrderedGroup_Olordered__ab__group__abs_16, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12, cls_Datatype__Universe_OScons__Scons__eq__iff1_0, cls_SetInterval_OatMost__iff__iff1_0, cls_Datatype_Oelem__o2s__iff2_0, clsrel_OrderedGroup_Olordered__ab__group__join_8, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8, clsrel_Ring__and__Field_Oordered__semidom_25, clsrel_OrderedGroup_Opordered__ab__group__add_4, clsrel_LOrder_Omeet__semilorder_0, clsrel_Ring__and__Field_Olordered__ring_18, clsrel_Power_Orecpower_3, clsarity_IntDef__Oint_29, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1, clsrel_Ring__and__Field_Osemiring__0_1, cls_GCD_Ogcd__greatest__iff__iff1_1, clsrel_Orderings_Olinorder_2, cls_Datatype__Universe_OuprodE_0, clsrel_OrderedGroup_Olordered__ab__group_1, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8, clsrel_Ring__and__Field_Olordered__ring_23, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6, clsrel_Ring__and__Field_Ocomm__semiring_1, clsrel_Ring__and__Field_Oordered__idom_46, clsrel_Ring__and__Field_Oordered__semidom_38, clsrel_OrderedGroup_Olordered__ab__group__meet_10, clsrel_Ring__and__Field_Oordered__idom_19, clsarity_nat_45, cls_Set_ODiffE_0, clsrel_OrderedGroup_Olordered__ab__group__meet_15, clsrel_Ring__and__Field_Olordered__ring_12, clsrel_Ring__and__Field_Osemiring__1_2, clsrel_Ring__and__Field_Oordered__semidom_7, cls_Sum__Type_OInl__not__Inr__iff1_0, cls_Infinite__Set_Oatmost__one__unique_0, clsrel_OrderedGroup_Ocomm__monoid__mult_2, clsarity_nat_17, clsrel_Ring__and__Field_Opordered__comm__semiring_5, clsarity_set_1, cls_Datatype__Universe_OdprodE_2, clsrel_Ring__and__Field_Ocomm__ring__1_2, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4, clsrel_Ring__and__Field_Oidom_9, cls_Relation_ORangeI_0, cls_Divides_Odvd__triv__right_0, cls_Nat_OSuc__le__mono__iff1_0, clsrel_Ring__and__Field_Oordered__idom_14, cls_SetInterval_OgreaterThan__eq__iff__iff1_0, clsrel_Ring__and__Field_Oordered__ring__strict_35, clsrel_Ring__and__Field_Oordered__idom_20, clsrel_Ring__and__Field_Opordered__comm__semiring_12, clsrel_Ring__and__Field_Ocomm__ring_1, clsrel_OrderedGroup_Olordered__ab__group__join_11, clsrel_Ring__and__Field_Opordered__cancel__semiring_5, clsrel_Ring__and__Field_Oordered__semidom_27, cls_List_Oself__append__conv2__iff2_0, cls_Set_OIntE_1, clsrel_Ring__and__Field_Oidom_15, cls_List_Oset__empty__iff1_0, clsrel_Ring__and__Field_Oordered__semidom_36, clsrel_Ring__and__Field_Oidom_24, clsrel_Ring__and__Field_Oordered__semidom_4, clsrel_Numeral_Onumber__ring_22, cls_Nat_Onot__add__less1__iff1_0, clsrel_Numeral_Onumber__ring_11, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11, clsrel_Ring__and__Field_Oordered__idom_53, clsarity_IntDef__Oint_40, clsrel_OrderedGroup_Olordered__ab__group__join_16, clsrel_Ring__and__Field_Oordered__idom_35, clsarity_IntDef__Oint_8, clsrel_Ring__and__Field_Opordered__cancel__semiring_14, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16, cls_Relation_Opair__in__Id__conv__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__0_4, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4, clsrel_Ring__and__Field_Opordered__ring_0, clsarity_IntDef__Oint_54, clsarity_nat_28, clsrel_Ring__and__Field_Ocomm__semiring_6, cls_Set_OIntI_0, clsrel_Ring__and__Field_Ocomm__ring_8, clsrel_Ring__and__Field_Osemiring__0__cancel_6, clsarity_nat_39, cls_Finite__Set_Ofinite__Union_1, clsrel_LOrder_Ojoin__semilorder_1, cls_Sum__Type_OPlusE_2, cls_Set_Osingleton__insert__inj__eq__iff2_0, clsrel_OrderedGroup_Osemigroup__mult_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20, clsrel_Ring__and__Field_Oordered__idom_1, clsarity_nat_23, clsrel_Ring__and__Field_Oidom_22, clsrel_Ring__and__Field_Oidom_5, clsrel_Ring__and__Field_Oordered__idom_50, clsrel_LOrder_Olorder_2, clsrel_Ring__and__Field_Oordered__semiring__strict_10, clsrel_Ring__and__Field_Opordered__semiring_8, clsrel_OrderedGroup_Oab__group__add_3, clsrel_Ring__and__Field_Oring__1_12, cls_IntDef_Oint__int__eq__iff1_0, cls_IntDiv_Ozdvd__0__left__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6, clsrel_Ring__and__Field_Olordered__ring_29, cls_Wellfounded__Relations_Oless__than__iff__iff2_0, clsrel_Power_Orecpower_12, cls_Nat_Oadd__gr__0__iff1_0, clsrel_Ring__and__Field_Opordered__comm__semiring_1, clsarity_IntDef__Oint_1, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9, cls_Divides_Odvd__triv__left_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3, clsrel_Ring__and__Field_Oidom_19, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8, cls_Divides_Odvd__0__right_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11, clsrel_OrderedGroup_Olordered__ab__group__abs_1, clsrel_Ring__and__Field_Oordered__ring__strict_24, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22, clsrel_OrderedGroup_Olordered__ab__group__join_12, cls_IntDiv_Odvd__zminus__iff__iff1_0, clsrel_Ring__and__Field_Oordered__semidom_18, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5, clsrel_Ring__and__Field_Ocomm__ring__1_11, clsrel_Ring__and__Field_Oordered__semidom_0, cls_Finite__Set_Ofinite__Diff__insert__iff2_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2, cls_SetInterval_Ofinite__greaterThanLessThan_0, clsrel_Ring__and__Field_Oordered__idom_41, clsrel_Ring__and__Field_Osemiring__1__cancel_1, clsrel_Ring__and__Field_Oaxclass__abs__if_2, clsrel_Ring__and__Field_Oordered__ring__strict_9, clsarity_IntDef__Oint_32, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27, clsrel_Ring__and__Field_Oidom_3, clsrel_Ring__and__Field_Osemiring__1__cancel_2, cls_Wellfounded__Recursion_Owf__empty_0, cls_Wellfounded__Relations_Owf__less__than_0, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1, clsrel_Ring__and__Field_Ocomm__ring_15, clsrel_Numeral_Onumber__ring_25, clsrel_Ring__and__Field_Osemiring__0__cancel_7, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15, clsrel_OrderedGroup_Olordered__ab__group__meet_7, cls_List_Olist_Odistinct__2__iff1_0, clsrel_Power_Orecpower_15, clsrel_OrderedGroup_Olordered__ab__group__meet_18, clsrel_OrderedGroup_Olordered__ab__group_16, cls_Transitive__Closure_Or__into__rtrancl_0, clsrel_Numeral_Onumber__ring_0, clsrel_Ring__and__Field_Osemiring__1__cancel_11, clsrel_Ring__and__Field_Ocomm__semiring__0_9, clsarity_IntDef__Oint_10, clsrel_Ring__and__Field_Osemiring__0__cancel_2, clsrel_OrderedGroup_Olordered__ab__group_15, cls_Datatype__Universe_OdprodI_0, clsrel_OrderedGroup_Oab__group__add_2, clsrel_Ring__and__Field_Oordered__ring__strict_28, cls_List_Oappend__self__conv2__iff2_0, clsrel_Ring__and__Field_Oring_8, cls_List_Oappend__self__conv__iff2_0, cls_List_Oappend__same__eq__iff1_0, clsrel_Ring__and__Field_Oring_3, clsrel_Numeral_Onumber__ring_14, clsrel_Ring__and__Field_Oordered__ring__strict_3, cls_Set_ODiffI_0, clsrel_OrderedGroup_Oab__semigroup__add_0, clsrel_Ring__and__Field_Opordered__ring_20, clsrel_Ring__and__Field_Opordered__semiring_4, cls_Sum__Type_OInrI_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3, clsarity_fun_1, clsrel_Ring__and__Field_Oring_11, cls_List_OlistsE_1, clsarity_nat_12, clsrel_Ring__and__Field_Oordered__ring__strict_17, clsrel_Ring__and__Field_Opordered__ring_4, clsrel_Ring__and__Field_Oordered__ring__strict_12, clsrel_OrderedGroup_Olordered__ab__group__join_2, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4, cls_Nat_OSuc__le__mono__iff2_0, clsrel_LOrder_Ojoin__semilorder_0, cls_IntDiv_Odvd__zminus__iff__iff2_0, cls_Set_OUn__empty__iff2_0, clsarity_IntDef__Oint_62, clsrel_Ring__and__Field_Oring__1_9, clsarity_IntDef__Oint_22, clsrel_OrderedGroup_Olordered__ab__group_10, clsrel_Ring__and__Field_Oordered__idom_30, cls_SetInterval_OgreaterThan__iff__iff1_0, clsarity_IntDef__Oint_5, clsrel_Ring__and__Field_Oring_12, cls_Set_OCompl__subset__Compl__iff__iff1_0, clsarity_nat_20, cls_Orderings_Oorder__less__irrefl__iff1_0, clsrel_Power_Orecpower_22, clsarity_IntDef__Oint_21, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1, clsrel_Ring__and__Field_Oordered__semiring__strict_14, clsarity_nat_5, cls_Datatype__Universe_Odsum__In1I_0, cls_Datatype__Universe_OuprodE_1, clsrel_Ring__and__Field_Oidom_30, cls_Set_OpsubsetE_0, clsrel_Ring__and__Field_Ocomm__ring__1_18, clsarity_IntDef__Oint_43, clsrel_Ring__and__Field_Oordered__semidom_11, clsrel_Ring__and__Field_Opordered__ring_8, clsrel_OrderedGroup_Opordered__ab__group__add_3, clsrel_Ring__and__Field_Osemiring__1_9, cls_List_Olistrel__Nil2_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7, clsrel_OrderedGroup_Olordered__ab__group__join_4, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9, clsrel_LOrder_Olorder_1, cls_Relation_Orel__compI_0, clsarity_nat_42, cls_Finite__Set_Ofinite__Pow__iff__iff2_0, clsrel_Ring__and__Field_Oordered__semidom_21, cls_List_Oappend__is__Nil__conv__iff1_0, cls_Set_OUnionI_0, clsrel_Ring__and__Field_Oordered__idom_8, clsrel_Ring__and__Field_Osemiring__0_5, clsrel_OrderedGroup_Olordered__ab__group_11, clsrel_OrderedGroup_Olordered__ab__group__meet_3, clsrel_Ring__and__Field_Opordered__semiring_0, clsrel_OrderedGroup_Olordered__ab__group__abs_9, clsrel_Ring__and__Field_Opordered__comm__semiring_6, clsrel_Ring__and__Field_Ocomm__semiring__0_5, clsrel_OrderedGroup_Opordered__ab__semigroup__add_2, clsrel_Ring__and__Field_Ocomm__ring__1_22, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3, cls_Datatype__Universe_OScons__Scons__eq__iff1_1, clsrel_OrderedGroup_Olordered__ab__group__meet_14, clsrel_Ring__and__Field_Olordered__ring_6, clsrel_Ring__and__Field_Oordered__semiring__strict_1, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5, clsrel_Ring__and__Field_Oordered__semiring__strict_20, clsrel_Ring__and__Field_Ocomm__ring__1_9, clsrel_Ring__and__Field_Osemiring_3, clsrel_Numeral_Onumber__ring_3, clsarity_nat_31, cls_Datatype__Universe_OIn0__eq__iff1_0, clsrel_Ring__and__Field_Oordered__idom_40, clsrel_OrderedGroup_Ocomm__monoid__add_3, clsrel_Ring__and__Field_Oordered__idom_25, clsrel_Ring__and__Field_Opordered__comm__semiring_15, clsrel_Ring__and__Field_Oordered__semidom_32, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1, cls_Nat_OSuc__less__eq__iff1_0, cls_GCD_Ogcd__dvd2_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23, clsrel_Power_Orecpower_8, cls_Relation_OdiagE_1, clsrel_Ring__and__Field_Oordered__ring__strict_0, clsarity_nat_9, clsrel_Ring__and__Field_Ocomm__ring__1_3, clsrel_Ring__and__Field_Opordered__semiring_11, clsrel_Ring__and__Field_Oordered__semidom_26, clsrel_Ring__and__Field_Ocomm__semiring__1_6, cls_IntDiv_Ozmod__eq__0D__dest_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18, clsrel_Ring__and__Field_Oordered__ring__strict_31, clsrel_Ring__and__Field_Oring__1_5, cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0, clsrel_Ring__and__Field_Oordered__idom_9, clsrel_Ring__and__Field_Osemiring__1_6, clsrel_Ring__and__Field_Ocomm__ring_5, clsrel_Ring__and__Field_Oidom_12, clsrel_Numeral_Onumber__ring_8, cls_Relation_OImage__singleton__iff__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7, clsrel_Ring__and__Field_Oordered__semidom_10, clsrel_Ring__and__Field_Opordered__cancel__semiring_7, cls_List_ONil2__notin__lex__iff1_0, clsrel_OrderedGroup_Olordered__ab__group_8, clsrel_Ring__and__Field_Ocomm__semiring__1_9, clsarity_IntDef__Oint_33, clsrel_Ring__and__Field_Oordered__ring__strict_34, clsrel_Ring__and__Field_Ocomm__ring_4, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9, clsrel_Power_Orecpower_2, clsrel_Ring__and__Field_Olordered__ring_17, clsrel_Ring__and__Field_Oordered__semidom_15, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14, clsarity_nat_46, clsrel_Ring__and__Field_Oidom_16, cls_List_Oself__append__conv2__iff1_0, clsrel_Ring__and__Field_Olordered__ring_28, clsrel_Ring__and__Field_Oordered__semidom_5, clsrel_Ring__and__Field_Ocomm__semiring__0_1, clsrel_Ring__and__Field_Oordered__semidom_6, clsrel_Ring__and__Field_Oordered__semiring__strict_6, clsrel_Ring__and__Field_Oordered__idom_4, clsrel_OrderedGroup_Opordered__ab__group__add_7, clsarity_IntDef__Oint_44, cls_Nat_Oneq0__conv__iff1_0, clsrel_Ring__and__Field_Oring_0, clsrel_OrderedGroup_Olordered__ab__group__meet_16, clsrel_Ring__and__Field_Opordered__ring_15, clsrel_Ring__and__Field_Olordered__ring_9, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2, clsrel_OrderedGroup_Olordered__ab__group__abs_17, clsrel_OrderedGroup_Opordered__ab__group__add_5, clsrel_Ring__and__Field_Ocomm__semiring__0_0, clsrel_Ring__and__Field_Oordered__semidom_22, clsrel_Ring__and__Field_Opordered__cancel__semiring_0, clsrel_Ring__and__Field_Oordered__idom_33, cls_Nat_Oadd__is__0__iff1_0, cls_Set_OInterI_0, clsrel_Ring__and__Field_Oordered__ring__strict_20, clsrel_Ring__and__Field_Oordered__idom_44, clsrel_Ring__and__Field_Ocomm__semiring__1_2, clsrel_Ring__and__Field_Oordered__semidom_37, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5, clsarity_nat_35, clsrel_Ring__and__Field_Oidom_8, clsrel_Ring__and__Field_Oidom_18, cls_List_Olist_Odistinct__1__iff1_0, clsrel_Ring__and__Field_Oordered__idom_54, clsrel_Power_Orecpower_9, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7, clsrel_Ring__and__Field_Oordered__ring__strict_18, clsrel_OrderedGroup_Olordered__ab__group_2, clsrel_Ring__and__Field_Oordered__ring__strict_23, clsrel_Ring__and__Field_Oordered__semiring__strict_23, clsrel_Ring__and__Field_Oordered__ring__strict_29, clsrel_Ring__and__Field_Oordered__ring__strict_6, clsrel_Ring__and__Field_Oring__1_17, clsrel_OrderedGroup_Opordered__ab__group__add_13, clsrel_Ring__and__Field_Oordered__semiring__strict_4, clsrel_Ring__and__Field_Opordered__comm__semiring_11, clsarity_IntDef__Oint_17, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3, cls_SetInterval_OatLeast__eq__iff__iff1_0, clsrel_Ring__and__Field_Opordered__comm__semiring_0, cls_Orderings_Oorder__class_Oaxioms__1_0, clsrel_OrderedGroup_Olordered__ab__group__abs_12, clsrel_OrderedGroup_Olordered__ab__group_12, cls_Sum__Type_OPlusE_1, clsrel_Ring__and__Field_Oordered__semidom_29, clsrel_Ring__and__Field_Oordered__idom_0, cls_Set_OUnionE_0, clsrel_Ring__and__Field_Oordered__semidom_19, clsrel_Ring__and__Field_Osemiring__1__cancel_15, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14, clsrel_Ring__and__Field_Osemiring__1_1, clsarity_IntDef__Oint_28, clsarity_IntDef__Oint_30, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3, clsrel_Ring__and__Field_Osemiring__0_4, cls_Relation_ODomainE_0, clsrel_Orderings_Olinorder_3, cls_Divides_Odvd__1__left_0, cls_List_Oin__listsI_0, clsrel_Ring__and__Field_Ocomm__ring_7, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10, clsarity_IntDef__Oint_39, clsrel_Ring__and__Field_Ocomm__ring_18, cls_IntDef_Onegative__zle_0, clsrel_OrderedGroup_Olordered__ab__group__abs_2, clsarity_nat_13, cls_SetInterval_OatLeast__iff__iff1_0, cls_Wellfounded__Recursion_Owf__insert__iff1_1, clsrel_Ring__and__Field_Oordered__idom_13, clsrel_OrderedGroup_Olordered__ab__group__abs_7, clsrel_Numeral_Onumber__ring_21, clsrel_Ring__and__Field_Oordered__idom_45, clsrel_OrderedGroup_Opordered__ab__group__add_0, clsrel_OrderedGroup_Omonoid__mult_1, clsrel_Power_Orecpower_20, clsrel_Ring__and__Field_Oordered__semidom_1, clsrel_Ring__and__Field_Oring__1_13, clsrel_Ring__and__Field_Osemiring__0__cancel_5, clsrel_OrderedGroup_Olordered__ab__group__join_10, clsarity_IntDef__Oint_41, clsrel_Ring__and__Field_Oordered__semiring__strict_0, clsarity_nat_24, cls_List_Oappend1__eq__conv__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1_0, clsrel_Ring__and__Field_Oidom_28, clsrel_Ring__and__Field_Oordered__idom_34, clsrel_Ring__and__Field_Osemiring_0, clsrel_Ring__and__Field_Opordered__ring_1, clsrel_Ring__and__Field_Oring_4, clsarity_IntDef__Oint_11, clsrel_Ring__and__Field_Oordered__semiring__strict_13, clsrel_Ring__and__Field_Opordered__semiring_9, clsrel_Ring__and__Field_Ocomm__semiring_3, clsrel_Ring__and__Field_Osemiring__1__cancel_8, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6, clsrel_Ring__and__Field_Olordered__ring_5, clsrel_OrderedGroup_Olordered__ab__group__join_15, clsrel_Ring__and__Field_Oidom_27, clsrel_Ring__and__Field_Oordered__semidom_33, clsrel_OrderedGroup_Olordered__ab__group__join_9, clsrel_Ring__and__Field_Oordered__idom_6, clsrel_Ring__and__Field_Oidom_23, clsrel_Ring__and__Field_Olordered__ring_30, clsarity_nat_1, clsrel_Power_Orecpower_11, clsrel_Ring__and__Field_Oordered__idom_24, clsrel_Ring__and__Field_Opordered__cancel__semiring_10, clsrel_LOrder_Omeet__semilorder_1, clsrel_Ring__and__Field_Oidom_4, clsarity_set_0, clsarity_IntDef__Oint_51, clsrel_Numeral_Onumber__ring_10, clsrel_OrderedGroup_Ocomm__monoid__mult_1, clsrel_OrderedGroup_Olordered__ab__group__meet_0, cls_List_Oin__listsD__dest_0, cls_Set_OPow__iff__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__semiring_4, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0, cls_Nat_OSuc__not__Zero__iff1_0, clsrel_Numeral_Onumber__ring_26, cls_Set_Osingleton__insert__inj__eq_H__iff1_0, clsarity_nat_4, clsrel_Ring__and__Field_Ocomm__ring__1_6, clsrel_Ring__and__Field_Opordered__ring_5, clsrel_Ring__and__Field_Oordered__idom_27, clsrel_Ring__and__Field_Oordered__ring__strict_13, clsrel_OrderedGroup_Opordered__ab__group__add_9, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3, clsrel_Ring__and__Field_Opordered__ring_10, clsrel_Ring__and__Field_Olordered__ring_0, cls_Nat_Ole0_0, clsrel_OrderedGroup_Oab__semigroup__mult_1, cls_Nat_Oless__one__iff2_0, clsrel_Ring__and__Field_Ocomm__ring__1_23, clsrel_Numeral_Onumber__ring_15, clsarity_IntDef__Oint_63, clsrel_Ring__and__Field_Oring__1_8, cls_Set_Osingleton__insert__inj__eq__iff1_0, clsarity_nat_19, cls_Sum__Type_OInl__eq__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring_0, clsrel_Ring__and__Field_Oordered__semiring__strict_15, cls_Relation_OImage__singleton__iff__iff2_0, clsrel_Ring__and__Field_Olordered__ring_2, clsrel_Ring__and__Field_Ocomm__ring_14, clsarity_IntDef__Oint_23, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2, clsrel_Ring__and__Field_Osemiring__0__cancel_10, clsrel_Ring__and__Field_Oordered__semidom_30, clsrel_OrderedGroup_Ocomm__monoid__mult_4, clsrel_Ring__and__Field_Osemiring__1_5, clsrel_OrderedGroup_Olordered__ab__group__meet_8, clsrel_Ring__and__Field_Ocomm__semiring__0_8, cls_List_Olength__0__conv__iff1_0, clsrel_Ring__and__Field_Opordered__semiring_5, clsrel_OrderedGroup_Omonoid__mult_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2, clsrel_Ring__and__Field_Osemiring_4, clsarity_IntDef__Oint_12, clsrel_Ring__and__Field_Opordered__cancel__semiring_13, cls_Relation_OIdE_0, clsrel_Ring__and__Field_Oidom_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28, clsrel_Numeral_Onumber__ring_29, clsrel_Ring__and__Field_Osemiring__0__cancel_8, clsrel_Power_Orecpower_16, cls_Set_OpsubsetE_1, clsarity_IntDef__Oint_55, clsrel_Ring__and__Field_Osemiring__0__cancel_1, clsrel_OrderedGroup_Opordered__ab__group__add_12, clsarity_IntDef__Oint_61, clsrel_LOrder_Olorder_3, clsrel_Ring__and__Field_Oordered__idom_5, clsrel_Numeral_Onumber__ring_9, clsrel_Ring__and__Field_Oordered__semiring__strict_7, clsrel_Ring__and__Field_Ocomm__semiring__1_1, clsrel_Ring__and__Field_Olordered__ring_20, clsarity_IntDef__Oint_50, clsrel_Ring__and__Field_Opordered__ring_21, clsrel_Ring__and__Field_Ocomm__semiring__1_5, clsrel_OrderedGroup_Oab__group__add_7, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20, clsrel_Ring__and__Field_Oordered__idom_16, clsrel_Ring__and__Field_Osemiring__0_3, clsrel_OrderedGroup_Olordered__ab__group__join_5, clsrel_Ring__and__Field_Oring__1_16, clsrel_Ring__and__Field_Ocomm__ring__1_12, clsarity_nat_2, clsrel_OrderedGroup_Olordered__ab__group__meet_2, clsrel_Numeral_Onumber__ring_4, clsrel_Ring__and__Field_Ocomm__semiring__1_13, clsrel_Ring__and__Field_Olordered__ring_16, clsrel_Ring__and__Field_Opordered__comm__semiring_7, cls_Nat_OlessI_0, cls_SetInterval_Ofinite__atMost_0, clsrel_Ring__and__Field_Oring__1_3, cls_Set_OIntE_0, clsarity_nat_30, cls_Relation_Orel__compE_1, clsarity_set_4, clsrel_Ring__and__Field_Oring__1_10, cls_List_Oappend__is__Nil__conv__iff1_1, clsrel_Ring__and__Field_Oring__1_4, clsrel_Numeral_Onumber__ring_18, clsrel_Ring__and__Field_Ocomm__ring__1_17, clsrel_Ring__and__Field_Osemiring__0__cancel_0, clsrel_Ring__and__Field_Oordered__semidom_14, clsrel_Ring__and__Field_Oordered__ring__strict_2, clsarity_nat_41, clsrel_Ring__and__Field_Oordered__ring__strict_30, cls_Finite__Set_Ofinite__Un__iff2_0, clsrel_OrderedGroup_Olordered__ab__group__abs_11, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7, clsrel_Ring__and__Field_Ocomm__ring__1_28, clsrel_Ring__and__Field_Olordered__ring_24, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24, clsrel_Power_Orecpower_23, cls_Set_ODiffE_1, cls_IntDef_Onegative__zless_0, cls_List_ONil__is__append__conv__iff1_1, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13, clsrel_Ring__and__Field_Oring_7, cls_IntDiv_Ozminus__dvd__iff__iff2_0, clsarity_IntDef__Oint_9, clsrel_Ring__and__Field_Oordered__semiring__strict_18, clsrel_Ring__and__Field_Opordered__comm__semiring_4, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0, cls_Nat_Onot__add__less2__iff1_0, cls_Set_OUnCI_0, cls_List_Olists_OCons_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0, cls_List_Oappend__in__lists__conv__iff1_1, cls_SetInterval_OlessThan__subset__iff__iff1_0, clsrel_Ring__and__Field_Olordered__ring_27, cls_Set_OinsertCI_1, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6, clsrel_Ring__and__Field_Olordered__ring_13, clsrel_OrderedGroup_Olordered__ab__group__join_18, cls_Transitive__Closure_Otrancl__into__rtrancl_0, clsrel_Ring__and__Field_Opordered__ring_16, clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0, clsrel_Power_Orecpower_19, clsrel_OrderedGroup_Olordered__ab__group__join_1, cls_List_Oappend__self__conv__iff1_0
% 22.23/7.69 % No. of inferences in proof: 2337
% 22.23/7.69 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 6955 ms resp. 5670 ms w/o parsing
% 23.27/8.00 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.27/8.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------