TSTP Solution File: SWV284-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV284-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:14:46 EDT 2023
% Result : Unsatisfiable 11.03s 3.55s
% Output : Refutation 12.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 1031
% Syntax : Number of formulae : 1883 ( 409 unt; 180 typ; 0 def)
% Number of atoms : 3119 ( 388 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 11918 (1456 ~;1416 |; 0 &;9046 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 364 ( 364 >; 0 *; 0 +; 0 <<)
% Number of symbols : 182 ( 180 usr; 19 con; 0-6 aty)
% Number of variables : 2872 ( 0 ^;2872 !; 0 ?;2872 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_x_type,type,
v_x: $i > $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(c_Message_Omsg_ONonce_type,type,
c_Message_Omsg_ONonce: $i > $i ).
thf(c_Event_Oused_type,type,
c_Event_Oused: $i > $i ).
thf(v_list_type,type,
v_list: $i ).
thf(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
thf(v_N_type,type,
v_N: $i ).
thf(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
thf(c_insert_type,type,
c_insert: $i > $i > $i > $i ).
thf(v_msg_type,type,
v_msg: $i ).
thf(c_emptyset_type,type,
c_emptyset: $i ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
thf(c_List_Olistrel_type,type,
c_List_Olistrel: $i > $i > $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(c_Main_Olistrel__Cons2__1_type,type,
c_Main_Olistrel__Cons2__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Olistrel__Cons2__2_type,type,
c_Main_Olistrel__Cons2__2: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Olistrel__Cons1__1_type,type,
c_Main_Olistrel__Cons1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Olistrel__Cons1__2_type,type,
c_Main_Olistrel__Cons1__2: $i > $i > $i > $i > $i > $i ).
thf(c_append_type,type,
c_append: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i ).
thf(c_Datatype__Universe_Odprod_type,type,
c_Datatype__Universe_Odprod: $i > $i > $i > $i > $i ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(tc_Datatype__Universe_Onode_type,type,
tc_Datatype__Universe_Onode: $i > $i > $i ).
thf(c_Datatype__Universe_OScons_type,type,
c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__1_type,type,
c_Main_OdprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__2_type,type,
c_Main_OdprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__3_type,type,
c_Main_OdprodE__3: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__4_type,type,
c_Main_OdprodE__4: $i > $i > $i > $i > $i > $i ).
thf(c_Datatype__Universe_OIn0_type,type,
c_Datatype__Universe_OIn0: $i > $i > $i > $i ).
thf(c_Datatype__Universe_OIn1_type,type,
c_Datatype__Universe_OIn1: $i > $i > $i > $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_SetInterval_OgreaterThan_type,type,
c_SetInterval_OgreaterThan: $i > $i > $i ).
thf(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
thf(c_less_type,type,
c_less: $i > $i > $i > $o ).
thf(c_SetInterval_OlessThan_type,type,
c_SetInterval_OlessThan: $i > $i > $i ).
thf(c_Divides_Oop_Advd_type,type,
c_Divides_Oop_Advd: $i > $i > $i > $o ).
thf(c_times_type,type,
c_times: $i > $i > $i > $i ).
thf(tc_IntDef_Oint_type,type,
tc_IntDef_Oint: $i ).
thf(class_Ring__and__Field_Osemiring__0_type,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(class_HOL_Otimes_type,type,
class_HOL_Otimes: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_type,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__comm__semiring_type,type,
class_Ring__and__Field_Opordered__cancel__comm__semiring: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring__strict_type,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Osemiring_type,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__add_type,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Opordered__comm__semiring_type,type,
class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).
thf(class_HOL_Oplus_type,type,
class_HOL_Oplus: $i > $o ).
thf(class_OrderedGroup_Osemigroup__add_type,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1__cancel_type,type,
class_Ring__and__Field_Ocomm__semiring__1__cancel: $i > $o ).
thf(c_uminus_type,type,
c_uminus: $i > $i > $i ).
thf(class_Power_Orecpower_type,type,
class_Power_Orecpower: $i > $o ).
thf(class_Ring__and__Field_Osemiring__1__cancel_type,type,
class_Ring__and__Field_Osemiring__1__cancel: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__0_type,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
thf(c_0_type,type,
c_0: $i ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(class_LOrder_Ojoin__semilorder_type,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_List_Olists_type,type,
c_List_Olists: $i > $i > $i ).
thf(class_OrderedGroup_Oordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_Message_Omsg_OMPair_type,type,
c_Message_Omsg_OMPair: $i > $i > $i ).
thf(c_Message_OHPair_type,type,
c_Message_OHPair: $i > $i > $i ).
thf(c_Message_Omsg_OHash_type,type,
c_Message_Omsg_OHash: $i > $i ).
thf(class_OrderedGroup_Osemigroup__mult_type,type,
class_OrderedGroup_Osemigroup__mult: $i > $o ).
thf(c_GCD_Ogcd_type,type,
c_GCD_Ogcd: $i > $i ).
thf(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_Ring__and__Field_Osemiring__0__cancel_type,type,
class_Ring__and__Field_Osemiring__0__cancel: $i > $o ).
thf(c_Finite__Set_OFinites_type,type,
c_Finite__Set_OFinites: $i ).
thf(c_Relation_Oconverse_type,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Ocomm__semiring_type,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__0__cancel_type,type,
class_Ring__and__Field_Ocomm__semiring__0__cancel: $i > $o ).
thf(class_HOL_Ozero_type,type,
class_HOL_Ozero: $i > $o ).
thf(c_List_Oremdups_type,type,
c_List_Oremdups: $i > $i > $i ).
thf(c_Nat_Osize_type,type,
c_Nat_Osize: $i > $i > $i ).
thf(c_SetInterval_OgreaterThanAtMost_type,type,
c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(c_union_type,type,
c_union: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_type,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(class_LOrder_Olorder_type,type,
class_LOrder_Olorder: $i > $o ).
thf(c_Wellfounded__Recursion_Owf_type,type,
c_Wellfounded__Recursion_Owf: $i > $i > $o ).
thf(c_Wellfounded__Relations_Olex__prod_type,type,
c_Wellfounded__Relations_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_SetInterval_OatLeast_type,type,
c_SetInterval_OatLeast: $i > $i > $i ).
thf(class_Wellfounded__Recursion_Owellorder_type,type,
class_Wellfounded__Recursion_Owellorder: $i > $o ).
thf(class_LOrder_Omeet__semilorder_type,type,
class_LOrder_Omeet__semilorder: $i > $o ).
thf(c_Message_Omsg_OCrypt_type,type,
c_Message_Omsg_OCrypt: $i > $i > $i ).
thf(c_Message_Omsg_ONumber_type,type,
c_Message_Omsg_ONumber: $i > $i ).
thf(class_Ring__and__Field_Oaxclass__0__neq__1_type,type,
class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_type,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_type,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(class_Ring__and__Field_Osemiring__1_type,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_Nat_Opower_type,type,
class_Nat_Opower: $i > $o ).
thf(c_Relation_Orel__comp_type,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_OatLeastLessThan_type,type,
c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_Pow_type,type,
c_Pow: $i > $i > $i ).
thf(c_SetInterval_OatMost_type,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i > $i ).
thf(c_Message_Oagent_OServer_type,type,
c_Message_Oagent_OServer: $i ).
thf(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_OrderedGroup_Ocancel__semigroup__add_type,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(c_Datatype__Universe_Odsum_type,type,
c_Datatype__Universe_Odsum: $i > $i > $i > $i > $i ).
thf(class_HOL_Oone_type,type,
class_HOL_Oone: $i > $o ).
thf(c_List_Oset_type,type,
c_List_Oset: $i > $i > $i ).
thf(c_Relation_OId_type,type,
c_Relation_OId: $i ).
thf(c_1_type,type,
c_1: $i ).
thf(c_Wellfounded__Recursion_Oacyclic_type,type,
c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).
thf(c_Sum__Type_OInr_type,type,
c_Sum__Type_OInr: $i > $i > $i > $i ).
thf(c_Sum__Type_OInl_type,type,
c_Sum__Type_OInl: $i > $i > $i > $i ).
thf(c_Shared_OshrK_type,type,
c_Shared_OshrK: $i > $i ).
thf(c_inter_type,type,
c_inter: $i > $i > $i > $i ).
thf(c_List_Odistinct_type,type,
c_List_Odistinct: $i > $i > $o ).
thf(c_Transitive__Closure_Otrancl_type,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(class_HOL_Ominus_type,type,
class_HOL_Ominus: $i > $o ).
thf(c_plus_type,type,
c_plus: $i > $i > $i > $i ).
thf(c_IntDef_Oint_type,type,
c_IntDef_Oint: $i > $i ).
thf(c_Message_Omsg_OAgent_type,type,
c_Message_Omsg_OAgent: $i > $i ).
thf(c_SetInterval_OgreaterThanLessThan_type,type,
c_SetInterval_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Main_OImageE__1_type,type,
c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).
thf(c_List_Olex_type,type,
c_List_Olex: $i > $i > $i ).
thf(c_Sum__Type_OPlus_type,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(tc_sum_type,type,
tc_sum: $i > $i > $i ).
thf(c_Main_OPlusE__1_type,type,
c_Main_OPlusE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OPlusE__2_type,type,
c_Main_OPlusE__2: $i > $i > $i > $i > $i ).
thf(c_Relation_Odiag_type,type,
c_Relation_Odiag: $i > $i > $i ).
thf(c_Datatype__Universe_Ouprod_type,type,
c_Datatype__Universe_Ouprod: $i > $i > $i > $i > $i ).
thf(c_Divides_Oop_Amod_type,type,
c_Divides_Oop_Amod: $i > $i > $i > $i ).
thf(c_Main_Ozmod__eq__0D__dest__1_type,type,
c_Main_Ozmod__eq__0D__dest__1: $i > $i > $i ).
thf(c_Relation_Otrans_type,type,
c_Relation_Otrans: $i > $i > $o ).
thf(c_SetInterval_OatLeastAtMost_type,type,
c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).
thf(class_Numeral_Onumber_type,type,
class_Numeral_Onumber: $i > $o ).
thf(c_List_Olenlex_type,type,
c_List_Olenlex: $i > $i > $i ).
thf(c_Datatype_Ooption_OSome_type,type,
c_Datatype_Ooption_OSome: $i > $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(class_Divides_Odiv_type,type,
class_Divides_Odiv: $i > $o ).
thf(class_Parity_Oeven__odd_type,type,
class_Parity_Oeven__odd: $i > $o ).
thf(c_Relation_ORange_type,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Main_ORangeE__1_type,type,
c_Main_ORangeE__1: $i > $i > $i > $i > $i ).
thf(c_Union_type,type,
c_Union: $i > $i > $i ).
thf(c_Main_OUnionE__1_type,type,
c_Main_OUnionE__1: $i > $i > $i > $i ).
thf(c_Message_Osynth_type,type,
c_Message_Osynth: $i > $i ).
thf(c_Main_OsubsetI__1_type,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Main_OconverseE__1_type,type,
c_Main_OconverseE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OconverseE__2_type,type,
c_Main_OconverseE__2: $i > $i > $i > $i > $i ).
thf(c_Event_Obad_type,type,
c_Event_Obad: $i ).
thf(tc_Message_Oagent_type,type,
tc_Message_Oagent: $i ).
thf(c_minus_type,type,
c_minus: $i > $i > $i > $i ).
thf(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
thf(c_Equiv__Relations_Oquotient_type,type,
c_Equiv__Relations_Oquotient: $i > $i > $i > $i ).
thf(c_Main_Oin__listsI__1_type,type,
c_Main_Oin__listsI__1: $i > $i > $i > $i ).
thf(c_UNIV_type,type,
c_UNIV: $i ).
thf(c_Wellfounded__Relations_Oless__than_type,type,
c_Wellfounded__Relations_Oless__than: $i ).
thf(c_Inter_type,type,
c_Inter: $i > $i > $i ).
thf(c_Main_OInterI__1_type,type,
c_Main_OInterI__1: $i > $i > $i > $i ).
thf(c_Datatype_Oo2s_type,type,
c_Datatype_Oo2s: $i > $i > $i ).
thf(c_Main_OuprodE__1_type,type,
c_Main_OuprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OuprodE__2_type,type,
c_Main_OuprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Infinite__Set_Oatmost__one_type,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_Main_Orel__compE__1_type,type,
c_Main_Orel__compE__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_Orel__compE__3_type,type,
c_Main_Orel__compE__3: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_Ofinite__Union__1_type,type,
c_Main_Ofinite__Union__1: $i > $i > $i ).
thf(c_Main_OdiagE__1_type,type,
c_Main_OdiagE__1: $i > $i > $i > $i ).
thf(c_Event_OinitState_type,type,
c_Event_OinitState: $i > $i ).
thf(c_Main_Orel__compE__2_type,type,
c_Main_Orel__compE__2: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Event_Oknows_type,type,
c_Event_Oknows: $i > $i > $i ).
thf(c_Main_OIdE__1_type,type,
c_Main_OIdE__1: $i > $i > $i ).
thf(c_Main_Omod__eq__0D__dest__1_type,type,
c_Main_Omod__eq__0D__dest__1: $i > $i > $i ).
thf(c_Relation_ODomain_type,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Main_ODomainE__1_type,type,
c_Main_ODomainE__1: $i > $i > $i > $i > $i ).
thf(v_sko__upX_type,type,
v_sko__upX: $i > $i ).
thf(640,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OMPair_0) ).
thf(2163,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(392,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
thf(1665,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(495,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).
thf(1879,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(265,axiom,
! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).
thf(1411,plain,
! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ B @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(154,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).
thf(1190,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(594,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
thf(2072,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(698,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ A @ B ) @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).
thf(2263,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ A @ B ) @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(421,axiom,
! [A: $i] :
( c_0
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).
thf(1729,plain,
! [A: $i] :
( c_0
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(736,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
thf(2331,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(465,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
thf(1818,plain,
class_Ring__and__Field_Oordered__semidom @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(333,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) )
| ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).
thf(1549,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) )
| ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(691,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz__iff2_0) ).
thf(2250,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(351,axiom,
class_HOL_Ozero @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_4) ).
thf(1586,plain,
class_HOL_Ozero @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(308,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).
thf(1501,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(798,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).
thf(2452,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= A )
| ( ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff2_0) ).
thf(1024,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= A )
| ( ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(294,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).
thf(1469,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(713,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
thf(2295,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(720,axiom,
class_HOL_Otimes @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_11) ).
thf(2306,plain,
class_HOL_Otimes @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(741,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
thf(2341,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(286,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn0 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ E @ F @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).
thf(1454,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn0 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ E @ F @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(574,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).
thf(2031,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(338,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__iff1_1) ).
thf(1559,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(112,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_6) ).
thf(1105,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(778,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_ONonce @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_ANonce_AN_A_61_61_62_AR_0) ).
thf(2412,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_ONonce @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ~ ( c_in @ D @ ( c_List_Oset @ A @ C ) @ C )
| ( c_in @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
thf(1237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ~ ( c_in @ D @ ( c_List_Oset @ A @ C ) @ C )
| ( c_in @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(806,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).
thf(2463,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(505,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_0) ).
thf(1899,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(218,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).
thf(1315,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(481,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
thf(1850,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(827,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Sum__Type_OInl @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ B @ E @ C @ D ) @ ( tc_sum @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
thf(2499,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Sum__Type_OInl @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ B @ E @ C @ D ) @ ( tc_sum @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(816,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).
thf(2480,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(42,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).
thf(962,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(679,axiom,
c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
thf(2231,plain,
c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(318,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ C @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).
thf(1522,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ C @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(59,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).
thf(994,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(260,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).
thf(1401,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(162,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).
thf(1205,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(354,axiom,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
thf(1591,plain,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(763,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_union @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).
thf(2380,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_union @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(405,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) ).
thf(1692,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(213,axiom,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).
thf(1305,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(81,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) ).
thf(1041,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(145,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
thf(1173,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(753,axiom,
c_Relation_Otrans @ c_Wellfounded__Relations_Oless__than @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).
thf(2363,plain,
c_Relation_Otrans @ c_Wellfounded__Relations_Oless__than @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(159,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) ).
thf(1200,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(357,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).
thf(1596,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(609,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
thf(2104,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(270,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_0) ).
thf(1422,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(342,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).
thf(1569,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(690,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ ( c_Main_OInterI__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
thf(2248,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ ( c_Main_OInterI__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(614,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).
thf(2114,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__iff1_0) ).
thf(1142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(196,axiom,
class_Nat_Opower @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).
thf(1269,plain,
class_Nat_Opower @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(545,axiom,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
thf(1971,plain,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(324,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).
thf(1533,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(307,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_1) ).
thf(1497,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(395,axiom,
class_LOrder_Omeet__semilorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
thf(1671,plain,
class_LOrder_Omeet__semilorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(363,axiom,
! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(1608,plain,
! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(387,axiom,
class_LOrder_Olorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
thf(1655,plain,
class_LOrder_Olorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(128,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__3__iff1_0) ).
thf(1137,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(576,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ F @ ( tc_prod @ C @ E ) )
| ( c_in @ D @ ( c_Relation_OImage @ F @ B @ C @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
thf(2035,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ F @ ( tc_prod @ C @ E ) )
| ( c_in @ D @ ( c_Relation_OImage @ F @ B @ C @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(643,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
thf(2168,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(437,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).
thf(1761,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(288,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
thf(1458,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(98,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).
thf(1078,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(450,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff2_0) ).
thf(1788,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(140,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).
thf(1164,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(726,axiom,
c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OSpy_A_58_Abad_0) ).
thf(2316,plain,
c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(516,axiom,
! [A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
thf(1919,plain,
! [A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(553,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).
thf(1988,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(802,axiom,
class_HOL_Oplus @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_10) ).
thf(2459,plain,
class_HOL_Oplus @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(91,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONumber @ A )
!= ( c_Message_Omsg_ONumber @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2__iff1_0) ).
thf(1063,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONumber @ A )
!= ( c_Message_Omsg_ONumber @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(535,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).
thf(1954,plain,
class_Ring__and__Field_Ocomm__semiring @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(237,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_13) ).
thf(1354,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(631,axiom,
! [A: $i] :
( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff2_0) ).
thf(2146,plain,
! [A: $i] :
( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(311,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
thf(1507,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
thf(1222,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(157,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_0) ).
thf(1196,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(474,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( class_HOL_Oone @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).
thf(1835,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( class_HOL_Oone @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(512,axiom,
! [A: $i] : ( c_Divides_Oop_Advd @ A @ c_0 @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
thf(1914,plain,
! [A: $i] : ( c_Divides_Oop_Advd @ A @ c_0 @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(48,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) ).
thf(973,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(366,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff1_0) ).
thf(1613,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(599,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).
thf(2082,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(297,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).
thf(1475,plain,
class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(243,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
thf(1366,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(457,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_1) ).
thf(1803,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(844,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_17) ).
thf(2531,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(301,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Sum__Type_OInr @ A @ B @ C )
!= ( c_Sum__Type_OInl @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).
thf(1482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Sum__Type_OInr @ A @ B @ C )
!= ( c_Sum__Type_OInl @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(499,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_8) ).
thf(1887,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(744,axiom,
class_Parity_Oeven__odd @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_47) ).
thf(2348,plain,
class_Parity_Oeven__odd @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(61,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_5) ).
thf(1001,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(822,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_in @ C @ ( c_SetInterval_OatLeast @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff2_0) ).
thf(2491,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_in @ C @ ( c_SetInterval_OatLeast @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(447,axiom,
class_Ring__and__Field_Osemiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).
thf(1782,plain,
class_Ring__and__Field_Osemiring @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(677,axiom,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).
thf(2227,plain,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(255,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_3) ).
thf(1391,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(382,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).
thf(1645,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(517,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).
thf(1921,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(774,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Relation_OId @ ( tc_prod @ B @ B ) )
| ( A
= ( c_Pair @ ( c_Main_OIdE__1 @ A @ B ) @ ( c_Main_OIdE__1 @ A @ B ) @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
thf(2400,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Relation_OId @ ( tc_prod @ B @ B ) )
| ( A
= ( c_Pair @ ( c_Main_OIdE__1 @ A @ B ) @ ( c_Main_OIdE__1 @ A @ B ) @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(591,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
thf(2067,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(543,axiom,
! [A: $i] :
~ ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff1_0) ).
thf(1967,plain,
! [A: $i] :
~ ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(316,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).
thf(1518,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(194,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).
thf(1265,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(410,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
thf(1703,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(373,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_2) ).
thf(1628,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(413,axiom,
! [B: $i,A: $i] :
( ( ( c_IntDef_Oint @ A )
!= ( c_IntDef_Oint @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq__iff1_0) ).
thf(1709,plain,
! [B: $i,A: $i] :
( ( ( c_IntDef_Oint @ A )
!= ( c_IntDef_Oint @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(734,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ C ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OCrypt_0) ).
thf(2328,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ C ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(452,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_12) ).
thf(1792,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(578,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_2) ).
thf(2039,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(740,axiom,
! [B: $i,A: $i] :
( ( c_Equiv__Relations_Oquotient @ c_emptyset @ A @ B )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty__iff2_0) ).
thf(2339,plain,
! [B: $i,A: $i] :
( ( c_Equiv__Relations_Oquotient @ c_emptyset @ A @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(701,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
thf(2269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(491,axiom,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
thf(1871,plain,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(222,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ~ ( c_in @ ( c_Pair @ F @ G @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ H @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ F @ A @ C @ D ) @ ( c_Datatype__Universe_OScons @ G @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odprod @ H @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).
thf(1323,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ~ ( c_in @ ( c_Pair @ F @ G @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ H @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ F @ A @ C @ D ) @ ( c_Datatype__Universe_OScons @ G @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odprod @ H @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(820,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_21) ).
thf(2488,plain,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(555,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
thf(1992,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_0) ).
thf(1059,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(88,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_11) ).
thf(1055,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(264,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_8) ).
thf(1409,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(390,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OAgent @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1__iff1_0) ).
thf(1660,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OAgent @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ c_Relation_OId @ ( tc_prod @ C @ C ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
thf(1298,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ c_Relation_OId @ ( tc_prod @ C @ C ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(509,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_15) ).
thf(1907,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(828,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_24) ).
thf(2501,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(225,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).
thf(1330,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(486,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_6) ).
thf(1860,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(670,axiom,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_38) ).
thf(2217,plain,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(313,axiom,
! [A: $i] :
( ~ ( c_Divides_Oop_Advd @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff1_0) ).
thf(1511,plain,
! [A: $i] :
( ~ ( c_Divides_Oop_Advd @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(703,axiom,
class_Wellfounded__Recursion_Owellorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_8) ).
thf(2274,plain,
class_Wellfounded__Recursion_Owellorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(217,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).
thf(1313,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
thf(1279,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(653,axiom,
~ ( c_in @ c_Message_Oagent_OServer @ c_Event_Obad @ tc_Message_Oagent ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OServer_A_58_Abad_A_61_61_62_AR_0) ).
thf(2185,plain,
~ ( c_in @ c_Message_Oagent_OServer @ c_Event_Obad @ tc_Message_Oagent ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(346,axiom,
class_Orderings_Oord @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
thf(1577,plain,
class_Orderings_Oord @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(808,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).
thf(2466,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(620,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_11) ).
thf(2126,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).
thf(902,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ v_N @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(853,plain,
! [A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ v_N @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(249,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_0) ).
thf(1379,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(583,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_7) ).
thf(2049,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(364,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).
thf(1609,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(117,axiom,
class_Ring__and__Field_Ocomm__semiring__0 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).
thf(1115,plain,
class_Ring__and__Field_Ocomm__semiring__0 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(523,axiom,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__4__iff1_0) ).
thf(1931,plain,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(838,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff2_0) ).
thf(2520,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(638,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_ONonce @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3__iff1_0) ).
thf(2158,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_ONonce @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(241,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
thf(1362,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(767,axiom,
! [A: $i] : ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
thf(2388,plain,
! [A: $i] : ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(176,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_HOL_Oone @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
thf(1232,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_HOL_Oone @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(330,axiom,
class_Power_Orecpower @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
thf(1545,plain,
class_Power_Orecpower @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(782,axiom,
! [A: $i] :
( ( c_List_Oset @ c_List_Olist_ONil @ A )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).
thf(2420,plain,
! [A: $i] :
( ( c_List_Oset @ c_List_Olist_ONil @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(644,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
thf(2169,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(775,axiom,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_1) ).
thf(2403,plain,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(102,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_9) ).
thf(1087,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(314,axiom,
! [A: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).
thf(1514,plain,
! [A: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(220,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).
thf(1319,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(411,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeast @ C @ A ) @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).
thf(1704,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeast @ C @ A ) @ ( c_SetInterval_OatLeast @ B @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(46,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_10) ).
thf(969,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(233,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).
thf(1347,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(570,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).
thf(2024,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(379,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_5) ).
thf(1641,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(493,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_1) ).
thf(1875,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(445,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
thf(1778,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(674,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_less @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff1_0) ).
thf(2222,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_less @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(304,axiom,
! [B: $i,A: $i] :
( ( ( c_Shared_OshrK @ A )
!= ( c_Shared_OshrK @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Shared_O_91_124_AshrK_Ax_A_61_AshrK_Ay_59_Ax_A_61_Ay_A_61_61_62_AP_A_124_93_A_61_61_62_AP_0) ).
thf(1489,plain,
! [B: $i,A: $i] :
( ( ( c_Shared_OshrK @ A )
!= ( c_Shared_OshrK @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(391,axiom,
class_Ring__and__Field_Osemiring__0__cancel @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
thf(1664,plain,
class_Ring__and__Field_Osemiring__0__cancel @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(603,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_3) ).
thf(2090,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(696,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).
thf(2259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(682,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).
thf(2236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(227,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
thf(1334,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(32,axiom,
! [A: $i] :
( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff2_0) ).
thf(937,plain,
! [A: $i] :
( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(398,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).
thf(1677,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(539,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(1960,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(566,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).
thf(2017,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(530,axiom,
class_Orderings_Oorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
thf(1946,plain,
class_Orderings_Oorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(292,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_5) ).
thf(1465,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(732,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(2324,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(572,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).
thf(2027,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B )
= ( c_Message_OHPair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair__iff2_0) ).
thf(1109,plain,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B )
= ( c_Message_OHPair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(375,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_23) ).
thf(1632,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(810,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
| ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).
thf(2469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
| ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(485,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).
thf(1858,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(488,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
thf(1864,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(618,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
thf(2122,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(251,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
thf(1383,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(71,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_1) ).
thf(1020,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(693,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).
thf(2254,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(349,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).
thf(1581,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(44,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).
thf(966,plain,
class_Ring__and__Field_Osemiring__0 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(143,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_22) ).
thf(1169,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(706,axiom,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).
thf(2281,plain,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(168,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_2) ).
thf(1215,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(275,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OHash @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_AHash_AZ_A_61_61_62_AR_0) ).
thf(1433,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OHash @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(262,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).
thf(1405,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(359,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
thf(1600,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(182,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).
thf(1242,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(1696,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(547,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).
thf(1975,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(756,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_ONumber_0) ).
thf(2367,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(790,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff2_0) ).
thf(2437,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(521,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
thf(1928,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ B @ A @ C ) )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff1_0) ).
thf(877,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ B @ A @ C ) )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(656,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OHash_0) ).
thf(2190,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(282,axiom,
! [B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
= ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair__iff2_0) ).
thf(1447,plain,
! [B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
= ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(817,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_13) ).
thf(2483,plain,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(840,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype_Oo2s @ B @ C ) @ C )
| ( B
= ( c_Datatype_Ooption_OSome @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).
thf(2523,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype_Oo2s @ B @ C ) @ C )
| ( B
= ( c_Datatype_Ooption_OSome @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(95,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) ).
thf(1072,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(371,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).
thf(1622,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(758,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
thf(2371,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(320,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_8) ).
thf(1526,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(626,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).
thf(2137,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(560,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ C @ ( c_SetInterval_OgreaterThan @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff2_0) ).
thf(2002,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ C @ ( c_SetInterval_OgreaterThan @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( A
= ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair__iff1_0) ).
thf(998,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( A
= ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(685,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ ( c_insert @ B @ C @ D ) @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).
thf(2242,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ ( c_insert @ B @ C @ D ) @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(232,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).
thf(1345,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(770,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ C @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
thf(2392,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ C @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(636,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ A @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
thf(2154,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ A @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(385,axiom,
! [A: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
thf(1651,plain,
! [A: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(563,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Orderings_Olinorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).
thf(2011,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Orderings_Olinorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn1 @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).
thf(942,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn1 @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(664,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).
thf(2204,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(812,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).
thf(2473,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(277,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_6) ).
thf(1438,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(27,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ E @ A @ B @ C @ D ) @ B @ D @ D ) @ E @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).
thf(925,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ E @ A @ B @ C @ D ) @ B @ D @ D ) @ E @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(754,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
thf(2364,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(134,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).
thf(1153,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(616,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).
thf(2118,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(229,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( C
= ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair__iff1_0) ).
thf(1338,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( C
= ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(582,axiom,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).
thf(2047,plain,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(448,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).
thf(1783,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(764,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
| ( c_less @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff1_0) ).
thf(2382,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
| ( c_less @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(96,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_4) ).
thf(1074,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(361,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_9) ).
thf(1604,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(513,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_7) ).
thf(1915,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(605,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).
thf(2093,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(216,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).
thf(1311,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(680,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) )
| ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(2232,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) )
| ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(721,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oset @ A @ B )
!= c_emptyset )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).
thf(2307,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oset @ A @ B )
!= c_emptyset )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(92,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_6) ).
thf(1067,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(424,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_5) ).
thf(1736,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(825,axiom,
class_LOrder_Ojoin__semilorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).
thf(2496,plain,
class_LOrder_Ojoin__semilorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(588,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).
thf(2061,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(559,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).
thf(2000,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(377,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
thf(1636,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ~ ( c_Wellfounded__Recursion_Owf @ C @ D )
| ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ C @ A @ D @ B ) @ ( tc_prod @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
thf(1047,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ~ ( c_Wellfounded__Recursion_Owf @ C @ D )
| ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ C @ A @ D @ B ) @ ( tc_prod @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(89,axiom,
! [A: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).
thf(1057,plain,
! [A: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(104,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).
thf(1091,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(785,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_20) ).
thf(2428,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(231,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).
thf(1343,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(850,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
thf(2541,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(348,axiom,
class_HOL_Otimes @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_3) ).
thf(1580,plain,
class_HOL_Otimes @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(189,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
thf(1255,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(169,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) ).
thf(1217,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(432,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( class_HOL_Oone @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
thf(1751,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( class_HOL_Oone @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(303,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
thf(1487,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(623,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).
thf(2132,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(842,axiom,
class_Ring__and__Field_Ocomm__semiring__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_22) ).
thf(2528,plain,
class_Ring__and__Field_Ocomm__semiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(772,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
thf(2396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(565,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) ).
thf(2015,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(497,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).
thf(1883,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(199,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_ONumber @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__3__iff1_0) ).
thf(1274,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_ONumber @ A )
!= ( c_Message_OHPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(792,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_15) ).
thf(2441,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(699,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( A
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
thf(2264,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( A
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(777,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Oop_Amod @ A @ B @ tc_nat )
!= c_0 )
| ( A
= ( c_times @ B @ ( c_Main_Omod__eq__0D__dest__1 @ B @ A ) @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
thf(2409,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Oop_Amod @ A @ B @ tc_nat )
!= c_0 )
| ( A
= ( c_times @ B @ ( c_Main_Omod__eq__0D__dest__1 @ B @ A ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(253,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).
thf(1387,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(418,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
thf(1723,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(39,axiom,
! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
thf(957,plain,
! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ A @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(16,axiom,
! [A: $i] :
( c_List_Olist_ONil
= ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).
thf(894,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(369,axiom,
class_HOL_Ominus @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(1619,plain,
class_HOL_Ominus @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).
thf(1370,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_uminus @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(526,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( D = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair__iff1_1) ).
thf(1938,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( D = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(148,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).
thf(1178,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(533,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
thf(1951,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(209,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) ).
thf(1296,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(662,axiom,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_0) ).
thf(2200,plain,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(650,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(2179,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(137,axiom,
class_Ring__and__Field_Osemiring__1__cancel @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).
thf(1159,plain,
class_Ring__and__Field_Osemiring__1__cancel @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(651,axiom,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).
thf(2181,plain,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(743,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( c_lessequals @ D @ ( c_insert @ A @ c_emptyset @ B ) @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).
thf(2345,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( c_lessequals @ D @ ( c_insert @ A @ c_emptyset @ B ) @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(376,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).
thf(1634,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(426,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
thf(1740,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(344,axiom,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
thf(1573,plain,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(67,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
thf(1012,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(24,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( A
= ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).
thf(916,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( A
= ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(794,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_ONonce__synth_0) ).
thf(2445,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(77,axiom,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff2_0) ).
thf(1032,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(475,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_2) ).
thf(1837,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(360,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Oordered__semiring__strict @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).
thf(1602,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Oordered__semiring__strict @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(788,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).
thf(2433,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(814,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
thf(2477,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(1,negated_conjecture,
! [A: $i] : ( c_lessequals @ A @ ( v_x @ A ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(852,plain,
! [A: $i] : ( c_lessequals @ A @ ( v_x @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(336,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).
thf(1555,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(466,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_4) ).
thf(1819,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(372,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_0) ).
thf(1624,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(165,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).
thf(1210,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(388,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_8) ).
thf(1656,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
thf(1027,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(668,axiom,
class_Ring__and__Field_Osemiring__1__cancel @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_30) ).
thf(2213,plain,
class_Ring__and__Field_Osemiring__1__cancel @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(667,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).
thf(2211,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(263,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_3) ).
thf(1407,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(724,axiom,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(2313,plain,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(123,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
thf(1128,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(613,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_Wellfounded__Recursion_Oacyclic @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).
thf(2112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_Wellfounded__Recursion_Oacyclic @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(206,axiom,
! [A: $i] : ( c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
thf(1291,plain,
! [A: $i] : ( c_Divides_Oop_Advd @ ( c_Suc @ c_0 ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(10,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).
thf(874,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(836,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_Equiv__Relations_Oquotient @ A @ B @ C ) )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2__iff1_0) ).
thf(2515,plain,
! [C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_Equiv__Relations_Oquotient @ A @ B @ C ) )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(453,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__1__iff1_0) ).
thf(1794,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_OHPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(224,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_5) ).
thf(1328,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(751,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0) ).
thf(2359,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(115,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).
thf(1111,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(484,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
thf(1856,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(64,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).
thf(1006,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( A
= ( c_append @ A @ c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).
thf(869,plain,
! [B: $i,A: $i] :
( A
= ( c_append @ A @ c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(434,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
thf(1755,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(119,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_1) ).
thf(1118,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_List_Olist_OCons @ A @ D @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
thf(989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_List_Olist_OCons @ A @ D @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(240,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
thf(1360,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(687,axiom,
class_Nat_Opower @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_12) ).
thf(2245,plain,
class_Nat_Opower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(235,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_18) ).
thf(1350,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(525,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_7) ).
thf(1936,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(355,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_Wellfounded__Recursion_Owf @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).
thf(1592,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_Wellfounded__Recursion_Owf @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(716,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz__iff1_0) ).
thf(2300,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(103,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
thf(1089,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(177,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_16) ).
thf(1234,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(328,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_5) ).
thf(1541,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ ( c_GCD_Ogcd @ ( c_Pair @ B @ C @ tc_nat @ tc_nat ) ) @ tc_nat )
| ( c_Divides_Oop_Advd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_1) ).
thf(1270,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ ( c_GCD_Ogcd @ ( c_Pair @ B @ C @ tc_nat @ tc_nat ) ) @ tc_nat )
| ( c_Divides_Oop_Advd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(442,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).
thf(1772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(191,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_2) ).
thf(1259,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(51,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).
thf(980,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(352,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).
thf(1587,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(107,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
thf(1096,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(396,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).
thf(1672,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(4,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( A
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ E @ A @ B @ C @ D ) @ ( c_Main_Olistrel__Cons2__2 @ E @ A @ B @ C @ D ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).
thf(857,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( A
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ E @ A @ B @ C @ D ) @ ( c_Main_Olistrel__Cons2__2 @ E @ A @ B @ C @ D ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(258,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Oordered__semiring__strict @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
thf(1397,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Oordered__semiring__strict @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(341,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).
thf(1567,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(138,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
thf(1160,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(731,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).
thf(2323,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(207,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_3) ).
thf(1292,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(150,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).
thf(1182,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(290,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_6) ).
thf(1461,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(781,axiom,
class_LOrder_Olorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).
thf(2419,plain,
class_LOrder_Olorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(598,axiom,
! [A: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).
thf(2080,plain,
! [A: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(409,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__5__iff1_0) ).
thf(1700,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_OHPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(745,axiom,
class_OrderedGroup_Osemigroup__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_16) ).
thf(2349,plain,
class_OrderedGroup_Osemigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(611,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_1) ).
thf(2108,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(80,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
thf(1039,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(803,axiom,
! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(2460,plain,
! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(305,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).
thf(1493,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(401,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
thf(1683,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(100,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_4) ).
thf(1082,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(569,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).
thf(2023,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(541,axiom,
class_Numeral_Onumber @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).
thf(1964,plain,
class_Numeral_Onumber @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(528,axiom,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
thf(1942,plain,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OlessThan @ B @ A )
!= ( c_SetInterval_OlessThan @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).
thf(1424,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OlessThan @ B @ A )
!= ( c_SetInterval_OlessThan @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(723,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_31) ).
thf(2312,plain,
class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(800,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).
thf(2455,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(267,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
thf(1414,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(585,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A )
| ( c_less @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff1_0) ).
thf(2053,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A )
| ( c_less @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(659,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
thf(2196,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(461,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).
thf(1810,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(646,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeast @ C @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff1_0) ).
thf(2172,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatLeast @ C @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(69,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_4) ).
thf(1016,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(163,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
thf(1207,plain,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(500,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_HOL_Oone @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).
thf(1889,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_HOL_Oone @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(381,axiom,
class_HOL_Oone @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
thf(1644,plain,
class_HOL_Oone @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(727,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).
thf(2317,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(135,axiom,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
thf(1155,plain,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(428,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).
thf(1744,plain,
class_Ring__and__Field_Osemiring__1 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(847,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_insert @ B @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ ( v_sko__upX @ B ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg__Nonce__supply_0) ).
thf(2536,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_insert @ B @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ ( v_sko__upX @ B ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(471,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) ).
thf(1831,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_nat )
| ~ ( c_Divides_Oop_Advd @ A @ C @ tc_nat )
| ( c_Divides_Oop_Advd @ A @ ( c_GCD_Ogcd @ ( c_Pair @ C @ B @ tc_nat @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff2_0) ).
thf(1131,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_nat )
| ~ ( c_Divides_Oop_Advd @ A @ C @ tc_nat )
| ( c_Divides_Oop_Advd @ A @ ( c_GCD_Ogcd @ ( c_Pair @ C @ B @ tc_nat @ tc_nat ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(807,axiom,
! [A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Shared_OshrK @ A ) ) @ ( c_Event_OinitState @ A ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Shared_OshrK__in__initState_0) ).
thf(2465,plain,
! [A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Shared_OshrK @ A ) ) @ ( c_Event_OinitState @ A ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(826,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).
thf(2497,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(455,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_1) ).
thf(1799,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(531,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).
thf(1947,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(551,axiom,
! [A: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
thf(1984,plain,
! [A: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(482,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ~ ( c_in @ E @ F @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ E @ A @ C @ D ) @ ( c_Datatype__Universe_Ouprod @ F @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
thf(1852,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ~ ( c_in @ E @ F @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ E @ A @ C @ D ) @ ( c_Datatype__Universe_Ouprod @ F @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(273,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
thf(1429,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(184,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
thf(1246,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(415,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).
thf(1715,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(549,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) ).
thf(1979,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(628,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_2) ).
thf(2140,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(468,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).
thf(1825,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(708,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
thf(2285,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(444,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).
thf(1776,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(193,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
thf(1263,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(797,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_minus @ D @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).
thf(2450,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_minus @ D @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(109,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_Ring__and__Field_Osemiring__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).
thf(1099,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_Ring__and__Field_Osemiring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(54,axiom,
! [A: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
thf(985,plain,
! [A: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_ACrypt_AK_AX_H_A_61_61_62_AR_0) ).
thf(1150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(299,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) ).
thf(1478,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(284,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).
thf(1451,plain,
class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(718,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_35) ).
thf(2304,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(322,axiom,
! [B: $i,A: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).
thf(1530,plain,
! [B: $i,A: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(327,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
thf(1539,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(287,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Nat_Opower @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_0) ).
thf(1456,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Nat_Opower @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(749,axiom,
! [A: $i] :
( c_emptyset
= ( c_List_Oset @ c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).
thf(2355,plain,
! [A: $i] :
( c_emptyset
= ( c_List_Oset @ c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(155,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).
thf(1192,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= A )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).
thf(911,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= A )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(831,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(2505,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).
thf(1759,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OgreaterThan @ C @ A ) @ ( c_SetInterval_OgreaterThan @ B @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(256,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).
thf(1393,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(463,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).
thf(1814,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(580,axiom,
class_Divides_Odiv @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_61) ).
thf(2043,plain,
class_Divides_Odiv @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(339,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) ).
thf(1563,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(596,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( c_Relation_Oconverse @ E @ C @ D ) @ ( tc_prod @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).
thf(2076,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( c_Relation_Oconverse @ E @ C @ D ) @ ( tc_prod @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(94,axiom,
class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
thf(1071,plain,
class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(673,axiom,
class_HOL_Oone @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_0) ).
thf(2221,plain,
class_HOL_Oone @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(655,axiom,
class_Ring__and__Field_Osemiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_18) ).
thf(2189,plain,
class_Ring__and__Field_Osemiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( c_append @ c_List_Olist_ONil @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).
thf(953,plain,
! [B: $i,A: $i] :
( ( c_append @ c_List_Olist_ONil @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(557,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
thf(1996,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(843,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).
thf(2529,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(422,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).
thf(1732,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(160,axiom,
! [A: $i] : ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
thf(1202,plain,
! [A: $i] : ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(663,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_19) ).
thf(2203,plain,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(479,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).
thf(1846,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(87,axiom,
class_Ring__and__Field_Oordered__semiring__strict @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
thf(1054,plain,
class_Ring__and__Field_Oordered__semiring__strict @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(204,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_6) ).
thf(1286,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(78,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).
thf(1035,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(757,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
| ( A
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
thf(2368,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
| ( A
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(503,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).
thf(1895,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).
thf(1167,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(127,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_2) ).
thf(1135,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(420,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) ).
thf(1727,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(769,axiom,
c_lessequals @ c_0 @ c_0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).
thf(2391,plain,
c_lessequals @ c_0 @ c_0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(170,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).
thf(1219,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(430,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
thf(1747,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(211,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).
thf(1301,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(247,axiom,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).
thf(1374,plain,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(761,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).
thf(2376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(630,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) ).
thf(2144,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(20,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ B @ ( c_Main_Olistrel__Cons1__2 @ E @ D @ A @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).
thf(906,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ B @ ( c_Main_Olistrel__Cons1__2 @ E @ D @ A @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(131,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_7) ).
thf(1146,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(712,axiom,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).
thf(2292,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(408,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_12) ).
thf(1698,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(538,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_7) ).
thf(1959,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(111,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
thf(1103,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(704,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Infinite__Set_Oatmost__one @ A @ B )
| ~ ( c_in @ C @ A @ B )
| ~ ( c_in @ D @ A @ B )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(2275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Infinite__Set_Oatmost__one @ A @ B )
| ~ ( c_in @ C @ A @ B )
| ~ ( c_in @ D @ A @ B )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(575,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
thf(2033,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(633,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_7) ).
thf(2149,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(332,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ c_Relation_OId @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
thf(1548,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ c_Relation_OId @ ( tc_prod @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(520,axiom,
! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) ) @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).
thf(1927,plain,
! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_uminus @ C @ ( tc_set @ B ) ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff__iff1_0) ).
thf(975,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_uminus @ C @ ( tc_set @ B ) ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(472,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
thf(1833,plain,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(676,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ A @ B @ C ) @ A @ C )
| ( c_in @ B @ ( c_List_Olists @ A @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
thf(2225,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ A @ B @ C ) @ A @ C )
| ( c_in @ B @ ( c_List_Olists @ A @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(325,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) ).
thf(1535,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(773,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OKey__synth_0) ).
thf(2398,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(542,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
thf(1965,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(317,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).
thf(1520,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OKey @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4__iff1_0) ).
thf(1124,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OKey @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(624,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
thf(2134,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(367,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
thf(1615,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(449,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).
thf(1784,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(254,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) ).
thf(1389,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(370,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) ).
thf(1620,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(821,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
thf(2489,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(40,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_5) ).
thf(958,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(261,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).
thf(1403,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(309,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
thf(1503,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(394,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).
thf(1669,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(672,axiom,
! [A: $i] : ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
thf(2220,plain,
! [A: $i] : ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(573,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_8) ).
thf(2029,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff1_0) ).
thf(1107,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatMost @ B @ A ) @ ( c_SetInterval_OatMost @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(180,axiom,
class_Orderings_Olinorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
thf(1239,plain,
class_Orderings_Olinorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(226,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) ).
thf(1332,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(793,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( c_lessequals @ B @ ( c_insert @ D @ c_emptyset @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).
thf(2442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( c_lessequals @ B @ ( c_insert @ D @ c_emptyset @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(586,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Sum__Type_OInl @ A @ B @ C )
!= ( c_Sum__Type_OInl @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).
thf(2055,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Sum__Type_OInl @ A @ B @ C )
!= ( c_Sum__Type_OInl @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(784,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ c_emptyset @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(2425,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ c_emptyset @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(378,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Sum__Type_OInl @ A @ B @ C )
!= ( c_Sum__Type_OInr @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).
thf(1638,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Sum__Type_OInl @ A @ B @ C )
!= ( c_Sum__Type_OInr @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(642,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_insert @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
thf(2166,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_insert @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(439,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).
thf(1765,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(801,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ~ ( c_in @ D @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ D @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).
thf(2457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ~ ( c_in @ D @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ D @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(504,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) ).
thf(1897,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn1 @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).
thf(919,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn1 @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(632,axiom,
class_Parity_Oeven__odd @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_64) ).
thf(2148,plain,
class_Parity_Oeven__odd @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(728,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).
thf(2319,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(238,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
thf(1356,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(834,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
thf(2510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(156,axiom,
! [A: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ A )
| ( class_Orderings_Olinorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).
thf(1194,plain,
! [A: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ A )
| ( class_Orderings_Olinorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(752,axiom,
! [B: $i,A: $i] :
( c_emptyset
= ( c_Equiv__Relations_Oquotient @ c_emptyset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2__iff2_0) ).
thf(2361,plain,
! [B: $i,A: $i] :
( c_emptyset
= ( c_Equiv__Relations_Oquotient @ c_emptyset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(848,axiom,
class_Ring__and__Field_Osemiring__0__cancel @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_29) ).
thf(2538,plain,
class_Ring__and__Field_Osemiring__0__cancel @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(202,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).
thf(1282,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(783,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E )
| ( A
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
thf(2422,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E )
| ( A
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(319,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
thf(1524,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(607,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( B = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).
thf(2097,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(688,axiom,
class_HOL_Ozero @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_1) ).
thf(2246,plain,
class_HOL_Ozero @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(615,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_11) ).
thf(2116,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(441,axiom,
c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff2_0) ).
thf(1771,plain,
c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(121,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).
thf(1122,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(404,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).
thf(1690,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(634,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(2151,plain,
class_HOL_Ominus @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(678,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff1_0) ).
thf(2229,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(600,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).
thf(2084,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(669,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Equiv__Relations_Oquotient @ A @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty__iff1_0) ).
thf(2214,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Equiv__Relations_Oquotient @ A @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(779,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(2415,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(823,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_25) ).
thf(2493,plain,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(695,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth_0) ).
thf(2257,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(353,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(1589,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(12,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).
thf(880,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(82,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).
thf(1043,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(456,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).
thf(1801,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(343,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).
thf(1571,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OKey @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__4__iff1_0) ).
thf(1376,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OKey @ A )
!= ( c_Message_OHPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(660,axiom,
! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).
thf(2197,plain,
! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(544,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_9) ).
thf(1969,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(6,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).
thf(863,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(590,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_HOL_Oone @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).
thf(2065,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_HOL_Oone @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(146,axiom,
class_OrderedGroup_Osemigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_6) ).
thf(1175,plain,
class_OrderedGroup_Osemigroup__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(99,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).
thf(1080,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(337,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
thf(1557,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(374,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_6) ).
thf(1630,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(700,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( c_uminus @ C @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
| ( c_lessequals @ C @ A @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).
thf(2267,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( c_uminus @ C @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
| ( c_lessequals @ C @ A @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(467,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Sum__Type_OInr @ A @ B @ C )
!= ( c_Sum__Type_OInr @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).
thf(1821,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Sum__Type_OInr @ A @ B @ C )
!= ( c_Sum__Type_OInr @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(487,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).
thf(1862,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OKey @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_AKey_AK_A_61_61_62_AR_0) ).
thf(1325,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OKey @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(75,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
thf(1029,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_IntDef_Oint ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(43,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
thf(964,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(705,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( A
= ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ F @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
thf(2278,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( A
= ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ F @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(250,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
thf(1381,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(804,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).
thf(2461,plain,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(403,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).
thf(1688,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(15,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).
thf(890,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(393,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
thf(1667,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(494,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_HOL_Oone @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).
thf(1877,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_HOL_Oone @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(295,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Osemiring__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).
thf(1471,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Osemiring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(725,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_insert @ C @ c_emptyset @ D ) @ D @ E ) @ E )
| ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).
thf(2314,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_insert @ C @ c_emptyset @ D ) @ D @ E ) @ E )
| ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(742,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
thf(2343,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(510,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OAgent @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_AAgent_AA_A_61_61_62_AR_0) ).
thf(1909,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OAgent @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(139,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).
thf(1162,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(289,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
thf(1460,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(710,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_41) ).
thf(2289,plain,
class_Ring__and__Field_Opordered__cancel__comm__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(72,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) ).
thf(1022,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(692,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__leE_1) ).
thf(2252,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OgreaterThan @ B @ A )
!= ( c_SetInterval_OgreaterThan @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).
thf(932,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OgreaterThan @ B @ A )
!= ( c_SetInterval_OgreaterThan @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(534,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).
thf(1952,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(144,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).
thf(1171,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(746,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ F @ D ) @ C @ ( tc_prod @ F @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
thf(2350,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ F @ D ) @ C @ ( tc_prod @ F @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(356,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_8) ).
thf(1594,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(167,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).
thf(1213,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(584,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) ).
thf(2051,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(601,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_9) ).
thf(2086,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(380,axiom,
! [B: $i,A: $i] : ( c_less @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
thf(1643,plain,
! [B: $i,A: $i] : ( c_less @ ( c_uminus @ ( c_IntDef_Oint @ ( c_Suc @ A ) ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(147,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).
thf(1176,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(116,axiom,
! [B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).
thf(1113,plain,
! [B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(686,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
thf(2244,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(608,axiom,
! [A: $i] :
( ~ ( c_less @ A @ ( c_Suc @ c_0 ) @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff1_0) ).
thf(2101,plain,
! [A: $i] :
( ~ ( c_less @ A @ ( c_Suc @ c_0 ) @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(637,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).
thf(2156,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(665,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__analzD__dest_0) ).
thf(2207,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(592,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ A @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).
thf(2069,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ A @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(832,axiom,
class_Divides_Odiv @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_44) ).
thf(2506,plain,
class_Divides_Odiv @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(53,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
thf(983,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(780,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_32) ).
thf(2418,plain,
class_Ring__and__Field_Ocomm__semiring__1__cancel @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(158,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
thf(1198,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(477,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( A
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) )
| ( A
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
thf(1841,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( A
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) )
| ( A
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(791,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff2_0) ).
thf(2439,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(281,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).
thf(1445,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(321,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).
thf(1528,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(627,axiom,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(2139,plain,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ A @ D @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).
thf(883,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ A @ D @ C ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(242,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) ).
thf(1364,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(186,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
thf(1250,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(406,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_4) ).
thf(1694,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).
thf(922,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(546,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).
thf(1973,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(458,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).
thf(1805,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(97,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).
thf(1076,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(350,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_OHPair @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__6__iff1_0) ).
thf(1583,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_OHPair @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(460,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_List_Oset @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
thf(1809,plain,
! [B: $i,A: $i] : ( c_in @ ( c_List_Oset @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(492,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) ).
thf(1873,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(141,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
thf(1166,plain,
class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(293,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).
thf(1467,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(702,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
| ( A
= ( c_Pair @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
thf(2271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
| ( A
= ( c_Pair @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(811,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff1_0) ).
thf(2471,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(830,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
thf(2503,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(554,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).
thf(1990,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= B )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).
thf(939,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= B )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(334,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
thf(1551,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OatLeast @ B @ A )
!= ( c_SetInterval_OatLeast @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).
thf(1049,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OatLeast @ B @ A )
!= ( c_SetInterval_OatLeast @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThan @ C @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff1_0) ).
thf(1203,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_in @ B @ ( c_SetInterval_OgreaterThan @ C @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(164,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
thf(1208,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(508,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
thf(1905,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(269,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).
thf(1420,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(28,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ ( c_Main_Olistrel__Cons1__1 @ E @ D @ A @ B @ C ) @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).
thf(927,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ ( c_Main_Olistrel__Cons1__1 @ E @ D @ A @ B @ C ) @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(577,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_10) ).
thf(2037,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(200,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).
thf(1277,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(619,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_9) ).
thf(2124,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(681,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).
thf(2234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(796,axiom,
class_Ring__and__Field_Opordered__comm__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).
thf(2449,plain,
class_Ring__and__Field_Opordered__comm__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(312,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).
thf(1509,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(737,axiom,
class_LOrder_Omeet__semilorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).
thf(2333,plain,
class_LOrder_Omeet__semilorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(70,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) ).
thf(1018,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(694,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).
thf(2256,plain,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(835,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Message_Omsg_OKey @ ( c_Shared_OshrK @ A ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Shared_OSpy__knows__Spy__bad_0) ).
thf(2513,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Message_Omsg_OKey @ ( c_Shared_OshrK @ A ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(715,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Shared_Oanalz__Decrypt_H__dest_0) ).
thf(2298,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(62,axiom,
! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) ) @ B @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).
thf(1003,plain,
! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ ( c_GCD_Ogcd @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OHash @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5__iff1_0) ).
thf(1225,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OHash @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(47,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_2) ).
thf(971,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(383,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
thf(1647,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(837,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Main_OInterI__1 @ A @ B @ C ) @ C )
| ( c_in @ A @ ( c_Inter @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
thf(2518,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Main_OInterI__1 @ A @ B @ C ) @ C )
| ( c_in @ A @ ( c_Inter @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(446,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_11) ).
thf(1780,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(323,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_Orderings_Olinorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
thf(1531,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_Orderings_Olinorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(175,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn1 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ F @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).
thf(1230,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn1 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ F @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(315,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).
thf(1516,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(358,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
thf(1598,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(365,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) ).
thf(1611,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(760,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_26) ).
thf(2375,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(657,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
thf(2192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).
thf(887,plain,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(527,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).
thf(1941,plain,
class_OrderedGroup_Ocancel__semigroup__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(187,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
thf(1252,plain,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(244,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).
thf(1368,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(648,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_0) ).
thf(2175,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(433,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_HOL_Oone @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
thf(1753,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_HOL_Oone @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(195,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).
thf(1267,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(604,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).
thf(2092,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(641,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_23) ).
thf(2165,plain,
class_OrderedGroup_Omonoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(285,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).
thf(1452,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(490,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).
thf(1869,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(786,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(2429,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(739,axiom,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ B ) ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Shared_ONonce__notin__initState__iff1_0) ).
thf(2337,plain,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ B ) ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(621,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_0) ).
thf(2128,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(506,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).
thf(1901,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(389,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__add_0) ).
thf(1658,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(819,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Union @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
thf(2486,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Union @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(399,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_append @ D @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).
thf(1679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_append @ D @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(581,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OatMost @ B @ A )
!= ( c_SetInterval_OatMost @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff__iff1_0) ).
thf(2044,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_OatMost @ B @ A )
!= ( c_SetInterval_OatMost @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(425,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) ).
thf(1738,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(228,axiom,
! [B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ ( c_uminus @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).
thf(1336,plain,
! [B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ ( c_uminus @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(809,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
thf(2468,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(451,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_8) ).
thf(1790,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(675,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
thf(2224,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_uminus @ ( c_IntDef_Oint @ A ) @ tc_IntDef_Oint ) @ ( c_IntDef_Oint @ B ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(799,axiom,
! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
thf(2454,plain,
! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(153,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).
thf(1188,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(152,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_1) ).
thf(1186,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(219,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) ).
thf(1317,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(438,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_1) ).
thf(1763,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(524,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) ).
thf(1934,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(329,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).
thf(1543,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(190,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_0) ).
thf(1257,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(550,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair__iff1_1) ).
thf(1981,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(762,axiom,
! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).
thf(2379,plain,
! [B: $i,A: $i] : ( c_Divides_Oop_Advd @ A @ ( c_times @ A @ B @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(851,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
thf(2543,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(454,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) ).
thf(1797,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(65,axiom,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).
thf(1008,plain,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(416,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq__iff1_0) ).
thf(1717,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(246,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_4) ).
thf(1372,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(239,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) ).
thf(1358,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(689,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OAgent_0) ).
thf(2247,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(171,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
thf(1221,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ B @ A ) @ ( c_SetInterval_OatLeast @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).
thf(1284,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeast @ B @ A ) @ ( c_SetInterval_OatLeast @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(750,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz__iff1_1) ).
thf(2357,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(536,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
thf(1955,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(302,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_6) ).
thf(1485,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(729,axiom,
c_less @ c_0 @ c_1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff2_0) ).
thf(2320,plain,
c_less @ c_0 @ c_1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(86,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_8) ).
thf(1052,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(431,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).
thf(1749,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(272,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).
thf(1427,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(106,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ F @ A @ G @ C ) @ H @ ( tc_prod @ G @ C ) )
| ( c_in @ ( c_Pair @ F @ B @ G @ D ) @ ( c_Relation_Orel__comp @ E @ H @ C @ D @ G ) @ ( tc_prod @ G @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
thf(1094,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ F @ A @ G @ C ) @ H @ ( tc_prod @ G @ C ) )
| ( c_in @ ( c_Pair @ F @ B @ G @ D ) @ ( c_Relation_Orel__comp @ E @ H @ C @ D @ G ) @ ( tc_prod @ G @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(50,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).
thf(978,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_Ring__and__Field_Osemiring__1__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(129,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
thf(1140,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(496,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
thf(1881,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(198,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) ).
thf(1272,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(181,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
thf(1240,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(57,axiom,
! [A: $i] : ( class_Orderings_Oord @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).
thf(991,plain,
! [A: $i] : ( class_Orderings_Oord @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(368,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).
thf(1617,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(789,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
| ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).
thf(2435,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
| ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(564,axiom,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).
thf(2013,plain,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(476,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
thf(1839,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(815,axiom,
! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(2479,plain,
! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(602,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Osemigroup__mult @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__mult_0) ).
thf(2088,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Osemigroup__mult @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(149,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
thf(1180,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(402,axiom,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) )
| ( ( c_List_Oremdups @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff1_0) ).
thf(1685,plain,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) )
| ( ( c_List_Oremdups @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(335,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) ).
thf(1553,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(532,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
thf(1949,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(658,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
thf(2194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(266,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_7) ).
thf(1412,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(733,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
| ( A
= ( c_Pair @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
thf(2325,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
| ( A
= ( c_Pair @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(666,axiom,
! [A: $i] :
~ ( c_in @ A @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__emptyE_0) ).
thf(2209,plain,
! [A: $i] :
~ ( c_in @ A @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(654,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).
thf(2187,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(558,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) ).
thf(1998,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(515,axiom,
class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
thf(1918,plain,
class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(384,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_3) ).
thf(1649,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(747,axiom,
class_Numeral_Onumber @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_46) ).
thf(2352,plain,
class_Numeral_Onumber @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(101,axiom,
! [A: $i] :
( ~ ( c_Divides_Oop_Advd @ c_0 @ A @ tc_IntDef_Oint )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).
thf(1084,plain,
! [A: $i] :
( ~ ( c_Divides_Oop_Advd @ c_0 @ A @ tc_IntDef_Oint )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(136,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) ).
thf(1157,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(597,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_HOL_Oone @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).
thf(2078,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_HOL_Oone @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(221,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_1) ).
thf(1321,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(473,axiom,
! [A: $i] : ( c_Divides_Oop_Advd @ A @ c_0 @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
thf(1834,plain,
! [A: $i] : ( c_Divides_Oop_Advd @ A @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(722,axiom,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).
thf(2310,plain,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(478,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
thf(1844,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(612,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).
thf(2110,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) )
| ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).
thf(1010,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) )
| ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(719,axiom,
class_Power_Orecpower @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_45) ).
thf(2305,plain,
class_Power_Orecpower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(345,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
thf(1575,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(489,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint )
!= c_0 )
| ( A
= ( c_times @ B @ ( c_Main_Ozmod__eq__0D__dest__1 @ B @ A ) @ tc_IntDef_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
thf(1866,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Oop_Amod @ A @ B @ tc_IntDef_Oint )
!= c_0 )
| ( A
= ( c_times @ B @ ( c_Main_Ozmod__eq__0D__dest__1 @ B @ A ) @ tc_IntDef_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(593,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).
thf(2071,plain,
class_Ring__and__Field_Ocomm__semiring__0__cancel @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(423,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
thf(1734,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(459,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
thf(1807,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(188,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_5) ).
thf(1253,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(397,axiom,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= c_0 )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff1_0) ).
thf(1674,plain,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= c_0 )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(711,axiom,
( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff2_0) ).
thf(2290,plain,
( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(845,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__leE_0) ).
thf(2532,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(561,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Datatype_Ooption_OSome @ A @ B )
!= ( c_Datatype_Ooption_OSome @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).
thf(2004,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Datatype_Ooption_OSome @ A @ B )
!= ( c_Datatype_Ooption_OSome @ C @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(429,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).
thf(1745,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0__cancel @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(571,axiom,
! [B: $i,A: $i] : ( class_Nat_Opower @ ( tc_fun @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_1) ).
thf(2026,plain,
! [B: $i,A: $i] : ( class_Nat_Opower @ ( tc_fun @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(483,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_8) ).
thf(1854,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(183,axiom,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).
thf(1244,plain,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(622,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_3) ).
thf(2130,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(841,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
| ( c_in @ ( c_Pair @ A @ ( c_Main_ODomainE__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
thf(2526,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
| ( c_in @ ( c_Pair @ A @ ( c_Main_ODomainE__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(771,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ B @ ( c_Relation_OImage @ E @ ( c_insert @ A @ c_emptyset @ C ) @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).
thf(2394,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ B @ ( c_Relation_OImage @ E @ ( c_insert @ A @ c_emptyset @ C ) @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(252,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
thf(1385,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(417,axiom,
! [A: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).
thf(1721,plain,
! [A: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(647,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_28) ).
thf(2174,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(707,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Sum__Type_OInr @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ E @ B @ D @ C ) @ ( tc_sum @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
thf(2283,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Sum__Type_OInr @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ E @ B @ D @ C ) @ ( tc_sum @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(768,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth__synthD__dest_0) ).
thf(2389,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(298,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).
thf(1476,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(230,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) ).
thf(1341,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).
thf(896,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(507,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) ).
thf(1903,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(625,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_union @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).
thf(2135,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_union @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(776,axiom,
! [A: $i] :
( ~ ( c_less @ A @ c_1 @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff1_0) ).
thf(2406,plain,
! [A: $i] :
( ~ ( c_less @ A @ c_1 @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn0 @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).
thf(946,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn0 @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).
thf(1101,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(635,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
| ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ A @ B @ D @ C ) @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
thf(2152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
| ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ A @ B @ D @ C ) @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(697,axiom,
! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(2262,plain,
! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(795,axiom,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(2447,plain,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(76,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_7) ).
thf(1030,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(23,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ E @ A @ B @ C @ D ) @ C @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).
thf(914,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ E @ A @ B @ C @ D ) @ C @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(579,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).
thf(2041,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(412,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_ONumber @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_ANumber_AN_A_61_61_62_AR_0) ).
thf(1706,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_ONumber @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(639,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_27) ).
thf(2162,plain,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).
thf(899,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(617,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).
thf(2120,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(606,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
thf(2095,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(556,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) ).
thf(1994,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(567,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_10) ).
thf(2019,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(83,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_5) ).
thf(1045,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(765,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_33) ).
thf(2384,plain,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(813,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
| ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
thf(2475,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
| ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(208,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).
thf(1294,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(805,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
thf(2462,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(278,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
thf(1440,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn0 @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).
thf(929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn0 @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(735,axiom,
class_Orderings_Oord @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).
thf(2330,plain,
class_Orderings_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(214,axiom,
! [A: $i] : ( c_Divides_Oop_Advd @ c_1 @ A @ tc_IntDef_Oint ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
thf(1308,plain,
! [A: $i] : ( c_Divides_Oop_Advd @ c_1 @ A @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(661,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(2198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(652,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
| ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
thf(2183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
| ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(166,axiom,
class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
thf(1212,plain,
class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(502,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Relation_Otrans @ A @ B )
| ~ ( c_Relation_Otrans @ C @ D )
| ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ C @ A @ D @ B ) @ ( tc_prod @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
thf(1893,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Relation_Otrans @ A @ B )
| ~ ( c_Relation_Otrans @ C @ D )
| ( c_Relation_Otrans @ ( c_Wellfounded__Relations_Olex__prod @ C @ A @ D @ B ) @ ( tc_prod @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(215,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
thf(1309,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(824,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__partsD__dest_0) ).
thf(2494,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(280,axiom,
! [B: $i,A: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ A @ B ) @ ( tc_List_Olist @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
thf(1444,plain,
! [B: $i,A: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ A @ B ) @ ( tc_List_Olist @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(279,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_HOL_Oone @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).
thf(1442,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_HOL_Oone @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(709,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_Main_Oin__listsI__1 @ B @ A @ C ) @ ( c_List_Oset @ A @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
thf(2287,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_Main_Oin__listsI__1 @ B @ A @ C ) @ ( c_List_Oset @ A @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(443,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) ).
thf(1774,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(717,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).
thf(2302,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(419,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
thf(1725,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(766,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ c_emptyset @ C )
= ( c_insert @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).
thf(2385,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ c_emptyset @ C )
= ( c_insert @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(846,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).
thf(2534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(45,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_0) ).
thf(967,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(174,axiom,
c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff2_0) ).
thf(1229,plain,
c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(331,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
thf(1546,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(257,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
thf(1395,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(839,axiom,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(2522,plain,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(132,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Orderings_Olinorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
thf(1148,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Orderings_Olinorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(185,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).
thf(1248,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(300,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) ).
thf(1480,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(118,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).
thf(1116,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(629,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
thf(2142,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(671,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_minus @ B @ C @ ( tc_set @ D ) ) @ D )
| ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).
thf(2218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_minus @ B @ C @ ( tc_set @ D ) ) @ D )
| ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(126,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
thf(1133,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(759,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Shared_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Shared_OshrK__in__used_0) ).
thf(2374,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Shared_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(234,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
thf(1348,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(347,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).
thf(1578,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_Ring__and__Field_Ocomm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(537,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).
thf(1957,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).
thf(950,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(108,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
thf(1097,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(854,plain,
! [A: $i] :
( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(552,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) ).
thf(1986,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(562,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_less @ A @ B @ ( tc_set @ C ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(2008,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_less @ A @ B @ ( tc_set @ C ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(212,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ B @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).
thf(1303,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ B @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( c_append @ A @ c_List_Olist_ONil @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).
thf(867,plain,
! [B: $i,A: $i] :
( ( c_append @ A @ c_List_Olist_ONil @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(435,axiom,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
thf(1757,plain,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(276,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).
thf(1436,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( class_Ring__and__Field_Osemiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(738,axiom,
! [B: $i,A: $i] :
( ( c_emptyset
!= ( c_List_Oset @ A @ B ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).
thf(2334,plain,
! [B: $i,A: $i] :
( ( c_emptyset
!= ( c_List_Oset @ A @ B ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(755,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_42) ).
thf(2366,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(205,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero__iff1_0) ).
thf(1288,plain,
! [A: $i] :
( ( c_Suc @ A )
!= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(501,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
thf(1891,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff2_0) ).
thf(955,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_in @ B @ ( c_SetInterval_OlessThan @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(427,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_1) ).
thf(1742,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(464,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
thf(1816,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(306,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ A @ C @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
thf(1495,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ A @ C @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(41,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).
thf(960,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(296,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_3) ).
thf(1473,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(568,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).
thf(2021,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(589,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).
thf(2063,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).
thf(1352,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OlessThan @ B @ A ) @ ( c_SetInterval_OlessThan @ C @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(787,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__2__iff1_0) ).
thf(2430,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_OHPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(5,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( D
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ E @ D @ A @ B @ C ) @ ( c_Main_Olistrel__Cons1__2 @ E @ D @ A @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).
thf(860,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( D
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ E @ D @ A @ B @ C ) @ ( c_Main_Olistrel__Cons1__2 @ E @ D @ A @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(326,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_5) ).
thf(1537,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(518,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_9) ).
thf(1923,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(833,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ A @ C )
= ( c_insert @ B @ c_emptyset @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).
thf(2507,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ A @ C )
= ( c_insert @ B @ c_emptyset @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(519,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) ).
thf(1925,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_OrderedGroup_Osemigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).
thf(871,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(120,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).
thf(1120,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(105,axiom,
! [A: $i] : ( class_Nat_Opower @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_4) ).
thf(1093,plain,
! [A: $i] : ( class_Nat_Opower @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(522,axiom,
class_HOL_Oplus @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_2) ).
thf(1930,plain,
class_HOL_Oplus @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(748,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ( c_in @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
thf(2353,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ( c_in @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(178,axiom,
class_OrderedGroup_Osemigroup__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_8) ).
thf(1236,plain,
class_OrderedGroup_Osemigroup__mult @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(829,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).
thf(2502,plain,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(684,axiom,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_39) ).
thf(2241,plain,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(55,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_HOL_Otimes @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).
thf(987,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1__cancel @ A )
| ( class_HOL_Otimes @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(470,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) ).
thf(1829,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(548,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_5) ).
thf(1977,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(124,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).
thf(1129,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_Ring__and__Field_Osemiring__0__cancel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(469,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Olinorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
thf(1827,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Olinorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(192,axiom,
! [A: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
thf(1261,plain,
! [A: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).
thf(908,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(58,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
thf(992,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(849,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).
thf(2539,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(414,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).
thf(1713,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Ocancel__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(52,axiom,
c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_IntDef_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff2_0) ).
thf(982,plain,
c_Divides_Oop_Advd @ c_0 @ c_0 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(274,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).
thf(1431,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0__cancel @ A )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(63,axiom,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
thf(1004,plain,
! [A: $i] :
( ~ ( class_Power_Orecpower @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(818,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
thf(2484,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(498,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
thf(1885,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(310,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_1) ).
thf(1505,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(259,axiom,
! [A: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).
thf(1399,plain,
! [A: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(362,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
thf(1606,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(540,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).
thf(1962,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Osemiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( A
= ( c_append @ c_List_Olist_ONil @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).
thf(935,plain,
! [B: $i,A: $i] :
( A
= ( c_append @ c_List_Olist_ONil @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(268,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_1) ).
thf(1416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(645,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(2170,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(610,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_Orderings_Oord @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
thf(2106,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_Orderings_Oord @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(93,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
thf(1069,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(511,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ ( c_GCD_Ogcd @ ( c_Pair @ B @ C @ tc_nat @ tc_nat ) ) @ tc_nat )
| ( c_Divides_Oop_Advd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_0) ).
thf(1912,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ ( c_GCD_Ogcd @ ( c_Pair @ B @ C @ tc_nat @ tc_nat ) ) @ tc_nat )
| ( c_Divides_Oop_Advd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(649,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(2177,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(68,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_2) ).
thf(1014,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Osemigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(730,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff2_0) ).
thf(2321,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oord @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_in @ B @ ( c_SetInterval_OatMost @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(386,axiom,
! [B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ ( c_uminus @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).
thf(1653,plain,
! [B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ ( c_uminus @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(529,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_20) ).
thf(1944,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_OrderedGroup_Oab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(400,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Osemiring__1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).
thf(1681,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( class_Ring__and__Field_Osemiring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(151,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
thf(1184,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(595,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
thf(2074,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__comm__semiring @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(291,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).
thf(1463,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1__cancel @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(340,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).
thf(1565,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(480,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_3) ).
thf(1848,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(587,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
thf(2059,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(683,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(2238,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(714,axiom,
class_OrderedGroup_Osemigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_14) ).
thf(2297,plain,
class_OrderedGroup_Osemigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(440,axiom,
! [B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).
thf(1769,plain,
! [B: $i,A: $i] :
( ~ ( c_Divides_Oop_Advd @ A @ ( c_uminus @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_Divides_Oop_Advd @ A @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(514,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
thf(1917,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(283,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
thf(1449,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(462,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( class_HOL_Oplus @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_1) ).
thf(1812,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( class_HOL_Oplus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(2545,plain,
$false,
inference(e,[status(thm)],[2163,1665,1879,1411,1190,2072,2263,1729,2331,1818,1549,2250,1586,1501,2452,1024,1469,2295,2306,2341,1454,2031,1559,1105,2412,1237,2463,1899,1315,1850,2499,2480,962,2231,1522,994,1401,1205,1591,2380,1692,1305,1041,1173,2363,1200,1596,2104,1422,1569,2248,2114,1142,1269,1971,1533,1497,1671,1608,1655,1137,2035,2168,1761,1458,1078,1788,1164,2316,1919,1988,2459,1063,1954,1354,2146,1507,1222,1196,1835,1914,973,1613,2082,1475,1366,1803,2531,1482,1887,2348,1001,2491,1782,2227,1391,1645,1921,2400,2067,1967,1518,1265,1703,1628,1709,2328,1792,2039,2339,2269,1871,1323,2488,1992,1059,1055,1409,1660,1298,1907,2501,1330,1860,2217,1511,2274,1313,1279,2185,1577,2466,2126,902,853,1379,2049,1609,1115,1931,2520,2158,1362,2388,1232,1545,2420,2169,2403,1087,1514,1319,1704,969,1347,2024,1641,1875,1778,2222,1489,1664,2090,2259,2236,1334,937,1677,1960,2017,1946,1465,2324,2027,1109,1632,2469,1858,1864,2122,1383,1020,2254,1581,966,1169,2281,1215,1433,1405,1600,1242,1696,1975,2367,2437,1928,877,2190,1447,2483,2523,1072,1622,2371,1526,2137,2002,998,2242,1345,2392,2154,1651,2011,942,2204,2473,1438,925,2364,1153,2118,1338,2047,1783,2382,1074,1604,1915,2093,1311,2232,2307,1067,1736,2496,2061,2000,1636,1047,1057,1091,2428,1343,2541,1580,1255,1217,1751,1487,2132,2528,2396,2015,1883,1274,2441,2264,2409,1387,1723,957,894,1619,1370,1938,1178,1951,1296,2200,2179,1159,2181,2345,1634,1740,1573,1012,916,2445,1032,1837,1602,2433,2477,852,1555,1819,1624,1210,1656,1027,2213,2211,1407,2313,1128,2112,1291,874,2515,1794,1328,2359,1111,1856,1006,869,1755,1118,989,1360,2245,1350,1936,1592,2300,1089,1234,1541,1270,1772,1259,980,1587,1096,1672,857,1397,1567,1160,2323,1292,1182,1461,2419,2080,1700,2349,2108,1039,2460,1493,1683,1082,2023,1964,1942,1424,2312,2455,1414,2053,2196,1810,2172,1016,1207,1889,1644,2317,1155,1744,2536,1831,1131,2465,2497,1799,1947,1984,1852,1429,1246,1715,1979,2140,1825,2285,1776,1263,2450,1099,985,1150,1478,1451,2304,1530,1539,1456,2355,1192,911,2505,1759,1393,1814,2043,1563,2076,1071,2221,2189,953,1996,2529,1732,1202,2203,1846,1054,1286,1035,2368,1895,1167,1135,1727,2391,1219,1747,1301,1374,2376,2144,906,1146,2292,1698,1959,1103,2275,2033,2149,1548,1927,975,1833,2225,1535,2398,1965,1520,1124,2134,1615,1784,1389,1620,2489,958,1403,1503,1669,2220,2029,1107,1239,1332,2442,2055,2425,1638,2166,1765,2457,1897,919,2148,2319,1356,2510,1194,2361,2538,1282,2422,1524,2097,2246,2116,1771,1122,1690,2151,2229,2084,2214,2415,2493,2257,1589,880,1043,1801,1571,1376,2197,1969,863,2065,1175,1080,1557,1630,2267,1821,1862,1325,1029,964,2278,1381,2461,1688,890,1667,1877,1471,2314,2343,1909,1162,1460,2289,1022,2252,932,1952,1171,2350,1594,1213,2051,2086,1643,1176,1113,2244,2101,2156,2207,2069,2506,983,2418,1198,1841,2439,1445,1528,2139,883,1364,1250,1694,922,1973,1805,1076,1583,1809,1873,1166,1467,2271,2471,2503,1990,939,1551,1049,1203,1208,1905,1420,927,2037,1277,2124,2234,2449,1509,2333,1018,2256,2513,2298,1003,1225,971,1647,2518,1780,1531,1230,1516,1598,1611,2375,2192,887,1941,1252,1368,2175,1753,1267,2092,2165,1452,1869,2429,2337,2128,1901,1658,2486,1679,2044,1738,1336,2468,1790,2224,2454,1188,1186,1317,1763,1934,1543,1257,1981,2379,2543,1797,1008,1717,1372,1358,2247,1221,1284,2357,1955,1485,2320,1052,1749,1427,1094,978,1140,1881,1272,1240,991,1617,2435,2013,1839,2479,2088,1180,1685,1553,1949,2194,1412,2325,2209,2187,1998,1918,1649,2352,1084,1157,2078,1321,1834,2310,1844,2110,1010,2305,1575,1866,2071,1734,1807,1253,1674,2290,2532,2004,1745,2026,1854,1244,2130,2526,2394,1385,1721,2174,2283,2389,1476,1341,896,1903,2135,2406,946,1101,2152,2262,2447,1030,914,2041,1706,2162,899,2120,2095,1994,2019,1045,2384,2475,1294,2462,1440,929,2330,1308,2198,2183,1212,1893,1309,2494,1444,1442,2287,1774,2302,1725,2385,2534,967,1229,1546,1395,2522,1148,1248,1480,1116,2142,2218,1133,2374,1348,1578,1957,950,1097,854,1986,2008,1303,867,1757,1436,2334,2366,1288,1891,955,1742,1816,1495,960,1473,2021,2063,1352,2430,860,1537,1923,2507,1925,871,1120,1093,1930,2353,1236,2502,2241,987,1829,1977,1129,1827,1261,908,992,2539,1713,982,1431,1004,2484,1885,1505,1399,1606,1962,935,1416,2170,2106,1069,1912,2177,1014,2321,1653,1944,1681,1184,2074,1463,1565,1848,2059,2238,1037,2297,1769,1917,1449,1812]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV284-1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 19 02:38:06 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.98/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.82/1.16 % [INFO] Parsing done (262ms).
% 1.82/1.17 % [INFO] Running in sequential loop mode.
% 2.34/1.37 % [INFO] eprover registered as external prover.
% 2.34/1.37 % [INFO] cvc4 registered as external prover.
% 2.34/1.37 % [INFO] Scanning for conjecture ...
% 2.74/1.49 % [INFO] Found a conjecture and 1445 axioms. Running axiom selection ...
% 3.91/1.73 % [INFO] Axiom selection finished. Selected 848 axioms (removed 597 axioms).
% 4.25/1.88 % [INFO] Problem is propositional (TPTP CNF).
% 4.49/1.90 % [INFO] Type checking passed.
% 4.49/1.90 % [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 ...
% 11.03/3.54 % External prover 'e' found a proof!
% 11.03/3.54 % [INFO] Killing All external provers ...
% 11.03/3.54 % Time passed: 3023ms (effective reasoning time: 2372ms)
% 11.03/3.54 % Solved by 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)>
% 11.03/3.55 % Axioms used in derivation (848): clsrel_Ring__and__Field_Osemiring__1__cancel_9, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19, clsrel_OrderedGroup_Ocancel__semigroup__add_1, cls_Finite__Set_Ofinite__Union_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13, 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, cls_List_Olistrel__Cons1_0, clsrel_Ring__and__Field_Opordered__comm__semiring_14, cls_Message_Omsg_Oinject__7__iff1_0, cls_Finite__Set_Ofinite__converse__iff1_0, clsrel_Ring__and__Field_Oordered__semiring__strict_5, cls_Message_Oanalz_OInj_0, 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, 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_Opordered__semiring_6, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7, cls_Datatype__Universe_OuprodI_0, clsrel_Ring__and__Field_Oordered__semidom_16, cls_List_Oappend__in__lists__conv__iff2_0, clsrel_Ring__and__Field_Osemiring__0__cancel_9, clsarity_nat_32, clsarity_nat_26, cls_Message_Oanalz__analzD__dest_0, cls_Set_OsubsetI_1, 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, cls_Datatype__Universe_Odsum__In0I_0, clsrel_Ring__and__Field_Ocomm__semiring__0_2, cls_List_Olength__remdups__eq__iff2_0, cls_List_Oset__empty2__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14, clsrel_Ring__and__Field_Opordered__cancel__semiring_6, cls_List_Olists_ONil_0, cls_Set_OInterD_0, cls_Shared_OSpy__knows__Spy__bad_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, cls_List_Olistrel__Cons2_1, cls_Divides_Omod__eq__0D__dest_0, cls_SetInterval_OatLeast__subset__iff__iff2_0, clsrel_Ring__and__Field_Ocomm__semiring__1_3, clsrel_Orderings_Olinorder_0, clsrel_Ring__and__Field_Ocomm__semiring_4, cls_Sum__Type_OInr__not__Inl__iff1_0, cls_Message_OMPair__eq__HPair__iff1_1, clsarity_nat_21, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22, cls_List_ONil__is__append__conv__iff2_0, clsrel_Power_Orecpower_14, clsrel_OrderedGroup_Ocomm__monoid__mult_0, clsrel_OrderedGroup_Omonoid__mult_2, clsarity_IntDef__Oint_24, clsrel_OrderedGroup_Osemigroup__add_0, cls_Message_Osynth_OAgent_0, 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, cls_SetInterval_OgreaterThan__iff__iff2_0, clsarity_nat_7, clsrel_Ring__and__Field_Oordered__semidom_9, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1, cls_Sum__Type_OInr__eq__iff1_0, clsrel_OrderedGroup_Ocomm__monoid__add_2, clsrel_Ring__and__Field_Oordered__semidom_39, clsarity_IntDef__Oint_13, 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, clsrel_Power_Orecpower_21, clsrel_Wellfounded__Recursion_Owellorder_4, clsrel_Power_Orecpower_6, clsarity_nat_10, cls_Set_OemptyE_0, clsrel_Ring__and__Field_Oordered__semidom_28, 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clsarity_nat_40, clsrel_Power_Orecpower_5, clsarity_IntDef__Oint_6, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13, clsrel_Orderings_Olinorder_4, clsrel_Power_Orecpower_0, clsrel_Ring__and__Field_Osemiring__1__cancel_3, clsrel_Ring__and__Field_Oordered__semiring__strict_9, clsarity_nat_25, cls_Set_OUnionE_1, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8, cls_Nat_Oadd__is__0__iff1_1, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6, clsarity_IntDef__Oint_56, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7, cls_Message_OHPair__neqs__3__iff1_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21, cls_IntDiv_Ozminus__dvd__iff__iff1_0, clsrel_Ring__and__Field_Opordered__comm__semiring_3, clsrel_Wellfounded__Recursion_Owellorder_0, cls_Finite__Set_OFinites_OinsertI_0, cls_Wellfounded__Relations_Owf__lex__prod_0, clsarity_nat_14, cls_Nat_Oless__irrefl_0, clsarity_set_2, cls_Message_Omsg__Nonce__supply_0, cls_List_Olistrel__Nil1_0, clsrel_Ring__and__Field_Ocomm__semiring__1_4, clsarity_nat_3, clsrel_Power_Orecpower_24, 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, cls_Nat_Oless__one__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10, cls_Set_OComplI_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8, clsrel_Ring__and__Field_Opordered__comm__semiring_8, cls_Finite__Set_Ofinite__Int_0, clsrel_Power_Orecpower_1, cls_Datatype__Universe_OIn1__eq__iff1_0, cls_Nat_Oadd__gr__0__iff2_0, cls_SetInterval_Ofinite__atLeastLessThan__int_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25, cls_Message_OMPair__synth__analz__iff1_1, clsarity_nat_29, clsarity_IntDef__Oint_27, clsrel_Ring__and__Field_Opordered__cancel__semiring_3, 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, cls_Message_OHash__synth_0, cls_Relation_OconverseE_1, cls_Message_OHPair__eq__iff1_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_Ring__and__Field_Ocomm__semiring__1_8, clsrel_Ring__and__Field_Opordered__comm__semiring_10, cls_List_ONil__is__append__conv__iff1_0, cls_Message_OHash_91X_93_AY_A_61_AAgent_AA_A_61_61_62_AR_0, 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, clsarity_IntDef__Oint_38, cls_Message_OMPair__eq__HPair__iff1_0, clsrel_OrderedGroup_Oab__semigroup__mult_0, cls_Set_OpsubsetI_0, cls_Relation_Oconverse__iff__iff2_0, clsrel_Ring__and__Field_Opordered__semiring_2, 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clsarity_nat_45, cls_Set_ODiffE_0, cls_SetInterval_OgreaterThan__eq__iff__iff1_0, clsrel_Ring__and__Field_Osemiring__1_2, clsrel_Ring__and__Field_Oordered__semidom_7, cls_Sum__Type_OInl__not__Inr__iff1_0, clsrel_Ring__and__Field_Opordered__comm__semiring_12, cls_Infinite__Set_Oatmost__one__unique_0, clsrel_OrderedGroup_Ocomm__monoid__mult_2, clsrel_Ring__and__Field_Opordered__comm__semiring_5, clsarity_set_1, cls_Datatype__Universe_OdprodE_2, cls_Nat_Oadd__leE_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4, cls_Wellfounded__Relations_Otrans__less__than_0, cls_Relation_ORangeI_0, cls_List_Oset__empty__iff1_0, cls_Message_Omsg_Oinject__1__iff1_0, cls_Nat_OSuc__le__mono__iff1_0, clsrel_Ring__and__Field_Oordered__semidom_36, cls_Message_OMPair__analz_1, cls_Message_OHPair__neqs__6__iff1_0, clsarity_nat_17, 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, 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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, clsarity_nat_23, cls_Equiv__Relations_Oquotient__is__empty__iff1_0, clsrel_LOrder_Olorder_2, clsrel_Ring__and__Field_Oordered__semiring__strict_10, clsrel_Ring__and__Field_Opordered__semiring_8, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8, cls_IntDef_Oint__int__eq__iff1_0, cls_IntDiv_Ozdvd__0__left__iff1_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6, cls_Wellfounded__Relations_Oless__than__iff__iff2_0, clsrel_Power_Orecpower_12, cls_Message_Omsg_Oinject__6__iff1_0, 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, cls_Divides_Odvd__0__right_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22, cls_IntDiv_Odvd__zminus__iff__iff1_0, clsrel_Ring__and__Field_Oordered__semidom_18, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5, clsrel_Ring__and__Field_Osemiring__0__cancel_7, clsrel_Ring__and__Field_Oordered__semidom_0, cls_Finite__Set_Ofinite__Diff__insert__iff2_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2, clsrel_Ring__and__Field_Osemiring__1__cancel_1, clsrel_Ring__and__Field_Osemiring__1__cancel_2, cls_Wellfounded__Recursion_Owf__empty_0, cls_Message_OMPair__synth__analz__iff1_0, clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1, cls_Wellfounded__Relations_Owf__less__than_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15, cls_List_Olist_Odistinct__2__iff1_0, clsrel_Power_Orecpower_15, cls_Transitive__Closure_Or__into__rtrancl_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, cls_Message_Osynth_OCrypt_0, cls_Datatype__Universe_OdprodI_0, cls_Shared_Oanalz__Decrypt_H__dest_0, cls_Message_Oagent_Odistinct__4__iff1_0, cls_SetInterval_Ofinite__greaterThanLessThan_0, clsarity_IntDef__Oint_32, cls_Message_OMPair__parts_1, cls_Message_Osynth__synthD__dest_0, cls_List_Olistrel__Cons1_2, cls_List_OlistsE_1, cls_List_Oappend__self__conv2__iff2_0, clsarity_nat_12, cls_List_Oappend__self__conv__iff2_0, clsarity_IntDef__Oint_22, cls_SetInterval_OgreaterThan__iff__iff1_0, cls_List_Oappend__same__eq__iff1_0, clsrel_Wellfounded__Recursion_Owellorder_2, cls_Equiv__Relations_Oquotient__is__empty2__iff1_0, clsarity_IntDef__Oint_5, cls_Set_ODiffI_0, clsrel_OrderedGroup_Oab__semigroup__add_0, 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_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, clsarity_IntDef__Oint_62, cls_Set_OUn__empty__iff2_0, cls_Set_OCompl__subset__Compl__iff__iff1_0, clsarity_nat_20, cls_Orderings_Oorder__less__irrefl__iff1_0, clsrel_Power_Orecpower_22, 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_Message_ONonce__synth_0, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7, cls_Datatype__Universe_OuprodE_1, cls_Shared_OshrK__in__initState_0, cls_Set_OpsubsetE_0, clsrel_Ring__and__Field_Opordered__semiring_0, clsrel_Ring__and__Field_Opordered__comm__semiring_6, clsarity_IntDef__Oint_43, clsrel_Ring__and__Field_Oordered__semidom_11, clsrel_Ring__and__Field_Osemiring__1_9, cls_List_Olistrel__Nil2_0, 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, clsrel_Ring__and__Field_Osemiring__0_5, cls_Set_OUnionI_0, clsrel_Ring__and__Field_Ocomm__semiring__0_5, clsrel_OrderedGroup_Opordered__ab__semigroup__add_2, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3, cls_Datatype__Universe_OScons__Scons__eq__iff1_1, 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, cls_Message_OHPair__neqs__5__iff1_0, clsrel_Ring__and__Field_Osemiring_3, clsrel_Ring__and__Field_Opordered__semiring_11, clsarity_nat_31, cls_Datatype__Universe_OIn0__eq__iff1_0, clsrel_OrderedGroup_Ocomm__monoid__add_3, 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_Power_Orecpower_8, cls_Relation_OdiagE_1, 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, cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0, clsrel_Ring__and__Field_Osemiring__1_6, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23, cls_Message_OMPair__synth__analz__iff2_0, clsarity_nat_9, cls_Wellfounded__Relations_Otrans__lex__prod_0, 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_Ring__and__Field_Ocomm__semiring__1_9, clsarity_IntDef__Oint_33, clsrel_Ring__and__Field_Oordered__semiring__strict_6, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9, cls_Message_OHPair__eq__MPair__iff1_1, clsrel_Ring__and__Field_Oordered__semidom_15, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14, clsarity_nat_46, cls_List_Oself__append__conv2__iff1_0, clsrel_Ring__and__Field_Oordered__semidom_5, clsrel_Ring__and__Field_Ocomm__semiring__0_1, clsrel_Ring__and__Field_Oordered__semidom_6, clsarity_IntDef__Oint_44, cls_Nat_Oneq0__conv__iff1_0, cls_Message_OMPair__synth_1, clsrel_Power_Orecpower_2, cls_List_Olist_Odistinct__1__iff1_0, clsrel_Ring__and__Field_Oordered__semiring__strict_23, cls_Message_OHash_91X_93_AY_A_61_ANonce_AN_A_61_61_62_AR_0, cls_List_Olistrel__Cons1_1, clsrel_Ring__and__Field_Oordered__semiring__strict_4, clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2, clsrel_Ring__and__Field_Ocomm__semiring__0_0, clsrel_Ring__and__Field_Oordered__semidom_22, clsrel_Ring__and__Field_Opordered__cancel__semiring_0, cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0, cls_Nat_Oadd__is__0__iff1_0, cls_Set_OInterI_0, cls_List_Olistrel__Cons2_2, 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_Power_Orecpower_9, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7, cls_Message_Osynth_OInj_0, clsrel_Ring__and__Field_Opordered__comm__semiring_11, 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, cls_Message_OMPair__analz_0, clsarity_nat_8, cls_Sum__Type_OPlusE_1, clsrel_Ring__and__Field_Oordered__semidom_29, cls_Set_OUnionE_0, clsrel_Ring__and__Field_Oordered__semidom_19, clsrel_Ring__and__Field_Osemiring__1__cancel_15, clsrel_Ring__and__Field_Osemiring__1_1, 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_List_Oin__listsI_0, cls_Divides_Odvd__1__left_0, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10, clsarity_IntDef__Oint_39, cls_IntDef_Onegative__zle_0, clsarity_nat_13, cls_SetInterval_OatLeast__iff__iff1_0, cls_Wellfounded__Recursion_Owf__insert__iff1_1, cls_Message_Omsg_Oinject__6__iff1_1, cls_Message_Oagent_Odistinct__3__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14, clsrel_OrderedGroup_Omonoid__mult_1, clsrel_Power_Orecpower_20, clsrel_Ring__and__Field_Oordered__semidom_1, clsrel_Ring__and__Field_Osemiring_0, clsrel_Ring__and__Field_Osemiring__0__cancel_5, clsrel_Ring__and__Field_Oordered__semidom_33, cls_Message_OHPair__neqs__2__iff1_0, clsrel_Ring__and__Field_Oordered__semiring__strict_0, cls_List_Oappend1__eq__conv__iff1_0, clsrel_Ring__and__Field_Ocomm__semiring__1_0, clsrel_Ring__and__Field_Opordered__cancel__semiring_10, clsrel_OrderedGroup_Ocomm__monoid__mult_1, 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, cls_Message_OHash_91X_93_AY_A_61_ANumber_AN_A_61_61_62_AR_0, clsarity_IntDef__Oint_41, clsarity_nat_24, cls_Message_OHPair__eq__iff1_1, cls_Message_OKey__synth_0, clsarity_nat_1, clsrel_Power_Orecpower_11, clsrel_LOrder_Omeet__semilorder_1, clsarity_set_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, cls_Nat_Ole0_0, clsarity_IntDef__Oint_63, cls_Event_OSpy_A_58_Abad_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_0, clsarity_nat_4, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3, clsrel_Wellfounded__Recursion_Owellorder_1, clsrel_OrderedGroup_Oab__semigroup__mult_1, cls_Nat_Oless__one__iff2_0, 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_Message_OMPair__parts_0, cls_Relation_OImage__singleton__iff__iff2_0, 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_Ring__and__Field_Ocomm__semiring__0_8, clsrel_LOrder_Olorder_3, cls_List_Olength__0__conv__iff1_0, clsrel_Ring__and__Field_Opordered__semiring_5, clsrel_Ring__and__Field_Ocomm__semiring__1_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_Oordered__comm__semiring__strict_28, clsarity_nat_2, cls_Message_Oparts__emptyE_0, clsrel_Ring__and__Field_Osemiring__0__cancel_8, clsrel_Power_Orecpower_16, cls_Set_OpsubsetE_1, clsrel_Ring__and__Field_Osemiring__0__cancel_1, clsarity_IntDef__Oint_61, clsrel_Ring__and__Field_Oordered__semiring__strict_7, clsrel_Ring__and__Field_Ocomm__semiring__1_1, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20, clsrel_Ring__and__Field_Osemiring__0_3, cls_List_Owf__lenlex_0, clsrel_Ring__and__Field_Ocomm__semiring__1_13, clsrel_Ring__and__Field_Opordered__comm__semiring_7, clsrel_Ring__and__Field_Oordered__semidom_14, cls_Nat_OlessI_0, cls_SetInterval_Ofinite__atMost_0, cls_Equiv__Relations_Oquotient__is__empty2__iff2_0, cls_Set_OIntE_0, clsarity_nat_30, clsarity_set_4, clsarity_nat_41, cls_List_Oappend__is__Nil__conv__iff1_1, cls_Finite__Set_Ofinite__Un__iff2_0, clsrel_Ring__and__Field_Osemiring__0__cancel_0, cls_Shared_O_91_124_AshrK_Ax_A_61_AshrK_Ay_59_Ax_A_61_Ay_A_61_61_62_AP_A_124_93_A_61_61_62_AP_0, cls_Relation_Orel__compE_1, cls_List_Olength__remdups__eq__iff1_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7, cls_Message_OMPair__synth_0, clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24, cls_Set_OinsertCI_1, clsrel_Power_Orecpower_23, cls_Set_ODiffE_1, cls_IntDef_Onegative__zless_0, cls_List_ONil__is__append__conv__iff1_1, cls_Transitive__Closure_Otrancl__into__rtrancl_0, clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13, clsrel_Power_Orecpower_19, cls_List_Oappend__self__conv__iff1_0, cls_IntDiv_Ozminus__dvd__iff__iff2_0, clsarity_IntDef__Oint_9, 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_Oordered__comm__semiring__strict_13, clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6, cls_Event_OServer_A_58_Abad_A_61_61_62_AR_0, clsrel_Ring__and__Field_Oordered__semiring__strict_18
% 11.03/3.55 % No. of inferences in proof: 1703
% 11.03/3.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3023 ms resp. 2372 ms w/o parsing
% 12.02/3.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.02/3.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------