TSTP Solution File: SWV338-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV338-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 12:15:14 EDT 2023
% Result : Unsatisfiable 44.09s 9.46s
% Output : Refutation 44.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 797
% Syntax : Number of formulae : 1461 ( 565 unt; 134 typ; 0 def)
% Number of atoms : 2423 (1014 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 14630 (1068 ~;1096 |; 0 &;12466 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 266 ( 266 >; 0 *; 0 +; 0 <<)
% Number of symbols : 136 ( 134 usr; 21 con; 0-5 aty)
% Number of variables : 3608 ( 0 ^;3608 !; 0 ?;3608 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_K_type,type,
v_K: $i ).
thf(c_Message_OsymKeys_type,type,
c_Message_OsymKeys: $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(v_evsf_type,type,
v_evsf: $i ).
thf(c_Yahalom_Oyahalom_type,type,
c_Yahalom_Oyahalom: $i ).
thf(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
thf(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
thf(v_X_type,type,
v_X: $i ).
thf(c_Message_Osynth_type,type,
c_Message_Osynth: $i > $i ).
thf(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
thf(c_Event_Oknows_type,type,
c_Event_Oknows: $i > $i > $i ).
thf(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
thf(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
thf(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i > $i ).
thf(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
thf(c_insert_type,type,
c_insert: $i > $i > $i > $i ).
thf(c_emptyset_type,type,
c_emptyset: $i ).
thf(c_Event_Oused_type,type,
c_Event_Oused: $i > $i ).
thf(c_Message_OkeysFor_type,type,
c_Message_OkeysFor: $i > $i ).
thf(c_less_type,type,
c_less: $i > $i > $i > $o ).
thf(c_Nat_Osize_type,type,
c_Nat_Osize: $i > $i > $i ).
thf(c_List_Onth_type,type,
c_List_Onth: $i > $i > $i > $i ).
thf(c_List_Oset_type,type,
c_List_Oset: $i > $i > $i ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_0_type,type,
c_0: $i ).
thf(c_append_type,type,
c_append: $i > $i > $i > $i ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(c_List_Oreplicate_type,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(c_plus_type,type,
c_plus: $i > $i > $i > $i ).
thf(c_List_Oremdups_type,type,
c_List_Oremdups: $i > $i > $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $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_Relation_Oconverse_type,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_Finite__Set_OFinites_type,type,
c_Finite__Set_OFinites: $i ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_SetInterval_OatLeastLessThan_type,type,
c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_List_Olast_type,type,
c_List_Olast: $i > $i > $i ).
thf(c_List_Odistinct_type,type,
c_List_Odistinct: $i > $i > $o ).
thf(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_List_Orev_type,type,
c_List_Orev: $i > $i > $i ).
thf(c_Finite__Set_OMin_type,type,
c_Finite__Set_OMin: $i > $i > $i ).
thf(c_List_Oconcat_type,type,
c_List_Oconcat: $i > $i > $i ).
thf(c_Orderings_Omin_type,type,
c_Orderings_Omin: $i > $i > $i > $i ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(c_List_Olex_type,type,
c_List_Olex: $i > $i > $i ).
thf(c_Orderings_Omax_type,type,
c_Orderings_Omax: $i > $i > $i > $i ).
thf(c_union_type,type,
c_union: $i > $i > $i > $i ).
thf(c_List_Ohd_type,type,
c_List_Ohd: $i > $i > $i ).
thf(c_List_Olist__inter_type,type,
c_List_Olist__inter: $i > $i > $i > $i ).
thf(c_Relation_Orel__comp_type,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OMax__le__iff__1_type,type,
c_Main_OMax__le__iff__1: $i > $i > $i > $i ).
thf(c_Finite__Set_OMax_type,type,
c_Finite__Set_OMax: $i > $i > $i ).
thf(c_List_Ozip_type,type,
c_List_Ozip: $i > $i > $i > $i > $i ).
thf(c_Wellfounded__Recursion_Oacyclic_type,type,
c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).
thf(c_inter_type,type,
c_inter: $i > $i > $i > $i ).
thf(c_Relation_Odiag_type,type,
c_Relation_Odiag: $i > $i > $i ).
thf(c_List_Osublist_type,type,
c_List_Osublist: $i > $i > $i > $i ).
thf(c_Main_OMax__less__iff__1_type,type,
c_Main_OMax__less__iff__1: $i > $i > $i > $i ).
thf(c_Message_Omsg_OHash_type,type,
c_Message_Omsg_OHash: $i > $i ).
thf(c_List_Obutlast_type,type,
c_List_Obutlast: $i > $i > $i ).
thf(c_Main_OMin__gr__iff__1_type,type,
c_Main_OMin__gr__iff__1: $i > $i > $i > $i ).
thf(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(c_Inter_type,type,
c_Inter: $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_Main_Oempty__Union__conv__1_type,type,
c_Main_Oempty__Union__conv__1: $i > $i > $i ).
thf(c_Main_OUnion__iff__1_type,type,
c_Main_OUnion__iff__1: $i > $i > $i > $i ).
thf(c_Wellfounded__Recursion_Owf_type,type,
c_Wellfounded__Recursion_Owf: $i > $i > $o ).
thf(c_Message_Omsg_OCrypt_type,type,
c_Message_Omsg_OCrypt: $i > $i > $i ).
thf(c_Main_OMin__ge__iff__1_type,type,
c_Main_OMin__ge__iff__1: $i > $i > $i > $i ).
thf(c_Message_Omsg_OMPair_type,type,
c_Message_Omsg_OMPair: $i > $i > $i ).
thf(c_Main_OUnion__empty__conv__1_type,type,
c_Main_OUnion__empty__conv__1: $i > $i > $i ).
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_Message_Omsg_OAgent_type,type,
c_Message_Omsg_OAgent: $i > $i ).
thf(c_Message_OHPair_type,type,
c_Message_OHPair: $i > $i > $i ).
thf(c_Wellfounded__Relations_Oless__than_type,type,
c_Wellfounded__Relations_Oless__than: $i ).
thf(c_SetInterval_OatLeastAtMost_type,type,
c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_Event_Oevent_OGets_type,type,
c_Event_Oevent_OGets: $i > $i > $i ).
thf(c_List_Olexord_type,type,
c_List_Olexord: $i > $i > $i ).
thf(c_Event_Oevent_OSays_type,type,
c_Event_Oevent_OSays: $i > $i > $i > $i ).
thf(c_Wellfounded__Relations_Olex__prod_type,type,
c_Wellfounded__Relations_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_Message_Omsg_ONumber_type,type,
c_Message_Omsg_ONumber: $i > $i ).
thf(class_Nat_Opower_type,type,
class_Nat_Opower: $i > $o ).
thf(c_List_Olistrel_type,type,
c_List_Olistrel: $i > $i > $i ).
thf(c_Main_Olistrel__Cons1__1_type,type,
c_Main_Olistrel__Cons1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Message_Oagent_OFriend_type,type,
c_Message_Oagent_OFriend: $i > $i ).
thf(tc_Message_Oagent_type,type,
tc_Message_Oagent: $i ).
thf(c_Message_OinvKey_type,type,
c_Message_OinvKey: $i > $i ).
thf(c_SetInterval_OatMost_type,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(c_Event_Oevent_ONotes_type,type,
c_Event_Oevent_ONotes: $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_type,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Pow_type,type,
c_Pow: $i > $i > $i ).
thf(class_Wellfounded__Recursion_Owellorder_type,type,
class_Wellfounded__Recursion_Owellorder: $i > $o ).
thf(c_Main_Olexord__Nil__left__1_type,type,
c_Main_Olexord__Nil__left__1: $i > $i > $i ).
thf(c_Main_Olexord__Nil__left__2_type,type,
c_Main_Olexord__Nil__left__2: $i > $i > $i ).
thf(c_Public_OshrK_type,type,
c_Public_OshrK: $i > $i ).
thf(c_Public_OpublicKey_type,type,
c_Public_OpublicKey: $i > $i > $i ).
thf(c_Message_Omsg_ONonce_type,type,
c_Message_Omsg_ONonce: $i > $i ).
thf(c_Message_Oagent_OServer_type,type,
c_Message_Oagent_OServer: $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_List_Olists_type,type,
c_List_Olists: $i > $i > $i ).
thf(c_Main_Oin__listsI__1_type,type,
c_Main_Oin__listsI__1: $i > $i > $i > $i ).
thf(c_Datatype_Oo2s_type,type,
c_Datatype_Oo2s: $i > $i > $i ).
thf(c_Datatype_Ooption_OSome_type,type,
c_Datatype_Ooption_OSome: $i > $i > $i ).
thf(c_Public_Okeymode_OEncryption_type,type,
c_Public_Okeymode_OEncryption: $i ).
thf(c_IntDef_Ointrel_type,type,
c_IntDef_Ointrel: $i ).
thf(c_Main_OdiagE__1_type,type,
c_Main_OdiagE__1: $i > $i > $i > $i ).
thf(c_List_Olistset_type,type,
c_List_Olistset: $i > $i > $i ).
thf(c_List_Oset__Cons_type,type,
c_List_Oset__Cons: $i > $i > $i > $i ).
thf(c_Relation_ODomain_type,type,
c_Relation_ODomain: $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_Relation_Otrans_type,type,
c_Relation_Otrans: $i > $i > $o ).
thf(c_Event_OinitState_type,type,
c_Event_OinitState: $i > $i ).
thf(c_Main_ODomainE__1_type,type,
c_Main_ODomainE__1: $i > $i > $i > $i > $i ).
thf(c_IntDef_OInteg_type,type,
c_IntDef_OInteg: $i ).
thf(c_Event_Obad_type,type,
c_Event_Obad: $i ).
thf(v_sko__uhi_type,type,
v_sko__uhi: $i > $i > $i ).
thf(c_Infinite__Set_Oatmost__one_type,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_Equiv__Relations_Oquotient_type,type,
c_Equiv__Relations_Oquotient: $i > $i > $i > $i ).
thf(class_Parity_Oeven__odd_type,type,
class_Parity_Oeven__odd: $i > $o ).
thf(c_Main_Oall__not__in__conv__1_type,type,
c_Main_Oall__not__in__conv__1: $i > $i > $i ).
thf(c_List_Olexn_type,type,
c_List_Olexn: $i > $i > $i > $i ).
thf(c_List_Olenlex_type,type,
c_List_Olenlex: $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_Divides_Odiv_type,type,
class_Divides_Odiv: $i > $o ).
thf(c_Set_Ocontents_type,type,
c_Set_Ocontents: $i > $i > $i ).
thf(106,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( ( c_Nat_Osize @ E @ ( tc_List_Olist @ C ) )
!= ( c_Nat_Osize @ F @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ E @ C ) @ ( c_List_Olist_OCons @ B @ F @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_4) ).
thf(892,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( ( c_Nat_Osize @ E @ ( tc_List_Olist @ C ) )
!= ( c_Nat_Osize @ F @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ E @ C ) @ ( c_List_Olist_OCons @ B @ F @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(357,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_OUnion__empty__conv__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( ( c_Union @ A @ B )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_1) ).
thf(1501,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_OUnion__empty__conv__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( ( c_Union @ A @ B )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
thf(1024,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(486,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OFake__parts__insert__in__Un__dest_0) ).
thf(1823,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(602,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONumber__synth_0) ).
thf(2072,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)],[602]) ).
thf(567,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Oanalz__spies__pubK_0) ).
thf(1995,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(201,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
thf(1105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ~ ( c_List_Odistinct @ A @ B )
| ( c_List_Odistinct @ ( c_List_Orev @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rev_1) ).
thf(909,plain,
! [B: $i,A: $i] :
( ~ ( c_List_Odistinct @ A @ B )
| ( c_List_Odistinct @ ( c_List_Orev @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(495,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Crypt_0) ).
thf(1840,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(137,axiom,
! [A: $i] :
( ( c_Orderings_Omin @ A @ c_0 @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0R_0) ).
thf(962,plain,
! [A: $i] :
( ( c_Orderings_Omin @ A @ c_0 @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
thf(777,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)],[53]) ).
thf(548,axiom,
! [A: $i] : ( c_in @ ( c_Public_OshrK @ A ) @ c_Message_OsymKeys @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK_AX1_A_58_AsymKeys_A_61_61_ATrue_0) ).
thf(1950,plain,
! [A: $i] : ( c_in @ ( c_Public_OshrK @ A ) @ c_Message_OsymKeys @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(429,axiom,
! [A: $i] :
( ( c_Nat_Osize @ ( c_Message_Omsg_ONumber @ A ) @ tc_Message_Omsg )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__2_0) ).
thf(1686,plain,
! [A: $i] :
( ( c_Nat_Osize @ ( c_Message_Omsg_ONumber @ A ) @ tc_Message_Omsg )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(621,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__into__used_0) ).
thf(2109,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(632,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ B ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__see__shrK_0) ).
thf(2131,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ B ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(256,axiom,
! [A: $i] :
( ( c_Nat_Osize @ ( c_Message_Oagent_OFriend @ A ) @ tc_Message_Oagent )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__2_0) ).
thf(1237,plain,
! [A: $i] :
( ( c_Nat_Osize @ ( c_Message_Oagent_OFriend @ A ) @ tc_Message_Oagent )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(85,axiom,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
thf(846,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(288,axiom,
! [A: $i] :
( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_2) ).
thf(1315,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)],[288]) ).
thf(501,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONonce__synth__eq_1) ).
thf(1850,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(6,negated_conjecture,
c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_insert @ v_X @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) @ tc_Message_Omsg ) ) ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(666,plain,
c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_insert @ v_X @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) @ tc_Message_Omsg ) ) ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(280,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).
thf(1295,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)],[280]) ).
thf(377,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_2) ).
thf(1554,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)],[377]) ).
thf(203,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_1) ).
thf(1110,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)],[203]) ).
thf(605,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C ) )
| ( c_emptyset
= ( c_inter @ B @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_1) ).
thf(2077,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C ) )
| ( c_emptyset
= ( c_inter @ B @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(224,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ( c_lessequals @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
thf(1158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ( c_lessequals @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(598,axiom,
! [A: $i] :
( ( c_SetInterval_OatLeastLessThan @ A @ ( c_Suc @ A ) @ tc_nat )
= ( c_insert @ A @ c_emptyset @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
thf(2062,plain,
! [A: $i] :
( ( c_SetInterval_OatLeastLessThan @ A @ ( c_Suc @ A ) @ tc_nat )
= ( c_insert @ A @ c_emptyset @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(335,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__2_0) ).
thf(1443,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(577,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OKey @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AKey_AK2_A_61_61_AFalse_0) ).
thf(2014,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)],[577]) ).
thf(616,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_union @ ( c_Message_Oparts @ ( c_insert @ B @ c_emptyset @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oused__Notes_0) ).
thf(2099,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_union @ ( c_Message_Oparts @ ( c_insert @ B @ c_emptyset @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(624,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Number_0) ).
thf(2114,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(473,axiom,
! [A: $i] :
( ( c_Pow @ c_emptyset @ A )
= ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
thf(1793,plain,
! [A: $i] :
( ( c_Pow @ c_emptyset @ A )
= ( c_insert @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ C @ A )
| ( ( c_SetInterval_OatLeastAtMost @ C @ B @ A )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
thf(1437,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ C @ A )
| ( ( c_SetInterval_OatLeastAtMost @ C @ B @ A )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__1_0) ).
thf(1173,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)],[230]) ).
thf(455,axiom,
! [A: $i] :
( ( c_Message_OinvKey @ ( c_Public_OshrK @ A ) )
= ( c_Public_OshrK @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OinvKey__shrK_0) ).
thf(1750,plain,
! [A: $i] :
( ( c_Message_OinvKey @ ( c_Public_OshrK @ A ) )
= ( c_Public_OshrK @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ A @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
thf(977,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ A @ C @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ D @ C @ A )
| ( c_less @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_2) ).
thf(730,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ D @ C @ A )
| ( c_less @ ( c_Orderings_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(278,axiom,
! [A: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ A )
| ( class_Orderings_Olinorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).
thf(1290,plain,
! [A: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ A )
| ( class_Orderings_Olinorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(516,axiom,
! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(1882,plain,
! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(384,axiom,
! [B: $i,A: $i] :
( ( c_inter @ A @ c_emptyset @ B )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__empty__right_0) ).
thf(1569,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ c_emptyset @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(543,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ c_emptyset @ A @ B )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).
thf(1939,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ c_emptyset @ A @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(38,axiom,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
thf(741,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ B @ A @ C ) @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Obutlast @ A @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_1) ).
thf(1073,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ B @ A @ C ) @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Obutlast @ A @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(424,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Public_OpublicKey @ A @ B )
!= ( c_Message_OinvKey @ ( c_Public_OpublicKey @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__neq__privateKey_0) ).
thf(1671,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Public_OpublicKey @ A @ B )
!= ( c_Message_OinvKey @ ( c_Public_OpublicKey @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(400,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( B = c_emptyset )
| ( ( c_Finite__Set_OMax @ ( c_insert @ C @ B @ A ) @ A )
= ( c_Orderings_Omax @ C @ ( c_Finite__Set_OMax @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__insert_0) ).
thf(1608,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( B = c_emptyset )
| ( ( c_Finite__Set_OMax @ ( c_insert @ C @ B @ A ) @ A )
= ( c_Orderings_Omax @ C @ ( c_Finite__Set_OMax @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(448,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_0) ).
thf(1735,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)],[448]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Pow @ ( c_inter @ A @ B @ C ) @ C )
= ( c_inter @ ( c_Pow @ A @ C ) @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__Int__eq_0) ).
thf(1275,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Pow @ ( c_inter @ A @ B @ C ) @ C )
= ( c_inter @ ( c_Pow @ A @ C ) @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(292,axiom,
! [B: $i,A: $i] :
( A
= ( c_append @ A @ c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv_1) ).
thf(1327,plain,
! [B: $i,A: $i] :
( A
= ( c_append @ A @ c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Oreplicate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).
thf(913,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Oreplicate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(412,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair_1) ).
thf(1640,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)],[412]) ).
thf(550,axiom,
! [A: $i] :
( c_Message_Oagent_OSpy
!= ( c_Message_Oagent_OFriend @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__6_0) ).
thf(1954,plain,
! [A: $i] :
( c_Message_Oagent_OSpy
!= ( c_Message_Oagent_OFriend @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(359,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/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_0) ).
thf(1507,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)],[359]) ).
thf(341,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( C = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_2) ).
thf(1458,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( C = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(4,negated_conjecture,
~ ( c_in @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Oparts @ ( c_insert @ v_X @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(670,plain,
~ ( c_in @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Oparts @ ( c_insert @ v_X @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(356,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Public_OpublicKey @ A @ B )
!= ( c_Public_OpublicKey @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject_0) ).
thf(1497,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Public_OpublicKey @ A @ B )
!= ( c_Public_OpublicKey @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(663,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_emptyset )
| ( c_in @ D @ A @ C )
| ( ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_2) ).
thf(2195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_emptyset )
| ( c_in @ D @ A @ C )
| ( ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(437,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_2) ).
thf(1705,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)],[437]) ).
thf(509,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).
thf(1867,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)],[509]) ).
thf(658,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Key_0) ).
thf(2184,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(569,axiom,
class_Parity_Oeven__odd @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_47) ).
thf(1999,plain,
class_Parity_Oeven__odd @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
thf(797,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(651,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(2168,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OAgent @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AAgent_AA2_A_61_61_AFalse_0) ).
thf(1260,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)],[266]) ).
thf(533,axiom,
! [B: $i,A: $i] :
( c_emptyset
= ( c_Equiv__Relations_Oquotient @ c_emptyset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2_1) ).
thf(1919,plain,
! [B: $i,A: $i] :
( c_emptyset
= ( c_Equiv__Relations_Oquotient @ c_emptyset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(564,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Notes_1) ).
thf(1988,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(301,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
thf(1354,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)],[301]) ).
thf(639,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_1) ).
thf(2146,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)],[639]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_Message_Omsg_OCrypt @ A @ B ) @ tc_Message_Omsg )
= ( c_plus @ ( c_Nat_Osize @ B @ tc_Message_Omsg ) @ ( c_Suc @ c_0 ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__7_0) ).
thf(1095,plain,
! [B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_Message_Omsg_OCrypt @ A @ B ) @ tc_Message_Omsg )
= ( c_plus @ ( c_Nat_Osize @ B @ tc_Message_Omsg ) @ ( c_Suc @ c_0 ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(453,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_1) ).
thf(1746,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)],[453]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ ( c_Orderings_Omax @ B @ C @ A ) @ A )
= ( c_Orderings_Omax @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).
thf(1001,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ ( c_Orderings_Omax @ B @ C @ A ) @ A )
= ( c_Orderings_Omax @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(468,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).
thf(1782,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)],[468]) ).
thf(316,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_List_Odistinct @ ( c_append @ A @ B @ C ) @ C )
| ( ( c_inter @ ( c_List_Oset @ A @ C ) @ ( c_List_Oset @ B @ C ) @ C )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_2) ).
thf(1391,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_List_Odistinct @ ( c_append @ A @ B @ C ) @ C )
| ( ( c_inter @ ( c_List_Oset @ A @ C ) @ ( c_List_Oset @ B @ C ) @ C )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ C @ A )
| ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_2) ).
thf(782,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ C @ A )
| ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(709,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(579,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ~ ( c_in @ B @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__see__shrK_1) ).
thf(2020,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ~ ( c_in @ B @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
thf(973,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(402,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_OHPair @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__6_0) ).
thf(1613,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)],[402]) ).
thf(541,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_OHPair @ A @ B ) @ ( c_insert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__HPair_0) ).
thf(1935,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_OHPair @ A @ B ) @ ( c_insert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(303,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_insert @ B @ C @ D ) @ D )
= ( c_insert @ B @ ( c_union @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
thf(1359,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_insert @ B @ C @ D ) @ D )
= ( c_insert @ B @ ( c_union @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(397,axiom,
! [A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ tc_nat )
= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
thf(1601,plain,
! [A: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ tc_nat )
= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(444,axiom,
! [A: $i] :
( c_0
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc_0) ).
thf(1724,plain,
! [A: $i] :
( c_0
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(600,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ c_emptyset @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(2067,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)],[600]) ).
thf(519,axiom,
! [A: $i] :
~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ c_List_Olist_ONil ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_ONonce__notin__used__empty_0) ).
thf(1887,plain,
! [A: $i] :
~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ c_List_Olist_ONil ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(416,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2_0) ).
thf(1650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(414,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
thf(1645,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)],[414]) ).
thf(534,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_OinitState @ C ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__in__initState_0) ).
thf(1921,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_OinitState @ C ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(634,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ C @ A ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_OHPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_2) ).
thf(2136,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ C @ A ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_OHPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(527,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oanalz @ B ) ) @ tc_nat )
| ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Key_0) ).
thf(1904,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oanalz @ B ) ) @ tc_nat )
| ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_append @ A @ B @ C ) @ C )
= ( c_union @ ( c_List_Oset @ A @ C ) @ ( c_List_Oset @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__append_0) ).
thf(1703,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_append @ A @ B @ C ) @ C )
= ( c_union @ ( c_List_Oset @ A @ C ) @ ( c_List_Oset @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(252,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
thf(1228,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)],[252]) ).
thf(262,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_0) ).
thf(1254,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)],[262]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B )
!= ( c_List_Orev @ C @ B ) )
| ( C
= ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osingleton__rev__conv_0) ).
thf(724,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B )
!= ( c_List_Orev @ C @ B ) )
| ( C
= ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(439,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Oagent_OFriend @ A )
!= ( c_Message_Oagent_OFriend @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Oinject_0) ).
thf(1709,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Oagent_OFriend @ A )
!= ( c_Message_Oagent_OFriend @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(588,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/sandbox2/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).
thf(2039,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)],[588]) ).
thf(420,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ c_0 @ A @ tc_nat )
| ( ( c_List_Osublist @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ A @ C )
= ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_0) ).
thf(1660,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ c_0 @ A @ tc_nat )
| ( ( c_List_Osublist @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ A @ C )
= ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
thf(785,plain,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(511,axiom,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) )
= ( c_union @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__synth_0) ).
thf(1871,plain,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) )
= ( c_union @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(528,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
thf(1907,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)],[528]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ~ ( c_List_Odistinct @ ( c_List_Orev @ A @ B ) @ B )
| ( c_List_Odistinct @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rev_0) ).
thf(838,plain,
! [B: $i,A: $i] :
( ~ ( c_List_Odistinct @ ( c_List_Orev @ A @ B ) @ B )
| ( c_List_Odistinct @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(65,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ C @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_2) ).
thf(802,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ C @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(342,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_1) ).
thf(1462,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)],[342]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( ( c_Finite__Set_Ocard @ A @ B )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__infinite_0) ).
thf(949,plain,
! [B: $i,A: $i] :
( ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( ( c_Finite__Set_Ocard @ A @ B )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_1) ).
thf(1511,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)],[360]) ).
thf(42,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
thf(751,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)],[42]) ).
thf(387,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Odiag @ A @ B ) @ B @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).
thf(1577,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Odiag @ A @ B ) @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(340,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
thf(1455,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)],[340]) ).
thf(491,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OMPair__used_0) ).
thf(1832,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(125,axiom,
! [A: $i] :
( ( c_Finite__Set_Ocard @ c_emptyset @ A )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__empty_0) ).
thf(934,plain,
! [A: $i] :
( ( c_Finite__Set_Ocard @ c_emptyset @ A )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(374,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
| ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_0) ).
thf(1545,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
| ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(476,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/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OMPair_0) ).
thf(1800,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)],[476]) ).
thf(521,axiom,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Public_OpublicKey @ A @ B ) @ c_Message_OsymKeys @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__pubK_0) ).
thf(1892,plain,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Public_OpublicKey @ A @ B ) @ c_Message_OsymKeys @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(593,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ C ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Crypt_0) ).
thf(2049,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ C ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(95,axiom,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
thf(870,plain,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(100,axiom,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(881,plain,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(646,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_0) ).
thf(2158,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)],[646]) ).
thf(513,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ B @ C )
!= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
thf(1875,plain,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ B @ C )
!= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(254,axiom,
! [B: $i,A: $i] :
( ( c_inter @ A @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).
thf(1232,plain,
! [B: $i,A: $i] :
( ( c_inter @ A @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(499,axiom,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__parts_0) ).
thf(1847,plain,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(535,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ B @ C ) )
| ( c_in @ D @ A @ C )
| ( c_emptyset
= ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_2) ).
thf(1922,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ B @ C ) )
| ( c_in @ D @ A @ C )
| ( c_emptyset
= ( c_inter @ A @ ( c_insert @ D @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_inter @ B @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ A @ B @ ( tc_set @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_0) ).
thf(902,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_inter @ B @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ A @ B @ ( tc_set @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_List_Orev @ A @ B ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_0) ).
thf(1087,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_List_Orev @ A @ B ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(361,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
| ( ( c_List_Oremdups @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oremdups @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_1) ).
thf(1514,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
| ( ( c_List_Oremdups @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oremdups @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(140,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_1) ).
thf(969,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)],[140]) ).
thf(299,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).
thf(1347,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)],[299]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_Finite__Set_OMin @ C @ A ) @ B @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__le_0) ).
thf(1013,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_Finite__Set_OMin @ C @ A ) @ B @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( c_List_Olast @ ( c_append @ B @ A @ C ) @ C )
= ( c_List_Olast @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__appendR_0) ).
thf(770,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( c_List_Olast @ ( c_append @ B @ A @ C ) @ C )
= ( c_List_Olast @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(655,axiom,
( ( c_Message_Oparts @ c_emptyset )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__empty_0) ).
thf(2178,plain,
( ( c_Message_Oparts @ c_emptyset )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(353,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/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_1) ).
thf(1489,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)],[353]) ).
thf(121,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
thf(924,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)],[121]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ c_List_Olist_ONil @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_1) ).
thf(1302,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ c_List_Olist_ONil @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(59,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).
thf(789,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)],[59]) ).
thf(530,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat )
| ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
| ( c_in @ ( c_Message_Omsg_OKey @ ( v_sko__uhi @ B @ A ) ) @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_0) ).
thf(1911,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat )
| ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
| ( c_in @ ( c_Message_Omsg_OKey @ ( v_sko__uhi @ B @ A ) ) @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
thf(1040,plain,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(325,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_Finite__Set_OMin @ B @ A ) @ ( c_Finite__Set_OMax @ B @ A ) @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).
thf(1418,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ ( c_Finite__Set_OMin @ B @ A ) @ ( c_Finite__Set_OMax @ B @ A ) @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(295,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Public_OpublicKey @ A @ B )
!= ( c_Public_OpublicKey @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject_1) ).
thf(1334,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Public_OpublicKey @ A @ B )
!= ( c_Public_OpublicKey @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
thf(834,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(489,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/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__analzD__dest_0) ).
thf(1828,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)],[489]) ).
thf(389,axiom,
! [B: $i,A: $i] :
( ( c_Union @ ( c_Pow @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).
thf(1581,plain,
! [B: $i,A: $i] :
( ( c_Union @ ( c_Pow @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(603,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/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).
thf(2073,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)],[603]) ).
thf(73,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).
thf(821,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)],[73]) ).
thf(578,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__3_0) ).
thf(2017,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(546,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_2) ).
thf(1946,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)],[546]) ).
thf(343,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
thf(1465,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)],[343]) ).
thf(619,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Hash_0) ).
thf(2105,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(481,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat )
| ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
| ( A
= ( c_Message_OinvKey @ ( v_sko__uhi @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_1) ).
thf(1811,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat )
| ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
| ( A
= ( c_Message_OinvKey @ ( v_sko__uhi @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(505,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(1858,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)],[505]) ).
thf(507,axiom,
class_Nat_Opower @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_12) ).
thf(1864,plain,
class_Nat_Opower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(628,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_1) ).
thf(2122,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)],[628]) ).
thf(426,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
thf(1677,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)],[426]) ).
thf(585,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Agent_0) ).
thf(2034,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(552,axiom,
! [B: $i,A: $i] :
( ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ A @ B ) @ B )
= ( c_insert @ A @ c_emptyset @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s_Osimps__2_0) ).
thf(1960,plain,
! [B: $i,A: $i] :
( ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ A @ B ) @ B )
= ( c_insert @ A @ c_emptyset @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd_Osimps_0) ).
thf(806,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(310,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ A @ B ) @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_1) ).
thf(1377,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)],[310]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_List_Odistinct @ ( c_append @ A @ B @ C ) @ C )
| ( c_List_Odistinct @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_1) ).
thf(734,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_List_Odistinct @ ( c_append @ A @ B @ C ) @ C )
| ( c_List_Odistinct @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(186,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
thf(1072,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)],[186]) ).
thf(405,axiom,
! [B: $i,A: $i] :
( ( c_union @ c_emptyset @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
thf(1622,plain,
! [B: $i,A: $i] :
( ( c_union @ c_emptyset @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(317,axiom,
! [B: $i,A: $i] :
( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption @ A ) )
!= ( c_Public_OshrK @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpriEK__noteq__shrK_0) ).
thf(1394,plain,
! [B: $i,A: $i] :
( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption @ A ) )
!= ( c_Public_OshrK @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(571,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__shrK_0) ).
thf(2002,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(618,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
| ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_2) ).
thf(2103,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
| ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_1) ).
thf(849,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(364,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Inter @ ( c_insert @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_inter @ A @ ( c_Inter @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__insert_0) ).
thf(1521,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Inter @ ( c_insert @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_inter @ A @ ( c_Inter @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(433,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).
thf(1696,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)],[433]) ).
thf(228,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
thf(1169,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)],[228]) ).
thf(14,axiom,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_1) ).
thf(687,plain,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(523,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Hash_0) ).
thf(1896,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(98,axiom,
! [A: $i] :
( ~ ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( ( c_Finite__Set_Ocard @ c_emptyset @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_1) ).
thf(877,plain,
! [A: $i] :
( ~ ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( ( c_Finite__Set_Ocard @ c_emptyset @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(545,axiom,
! [B: $i,A: $i] :
( ( ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ A @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) )
!= ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ B @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( c_in @ ( c_Pair @ A @ B @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_Ointrel @ ( tc_prod @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_0) ).
thf(1943,plain,
! [B: $i,A: $i] :
( ( ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ A @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) )
!= ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ B @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( c_in @ ( c_Pair @ A @ B @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_Ointrel @ ( tc_prod @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oconcat @ ( c_List_Olist_OCons @ A @ B @ ( tc_List_Olist @ C ) ) @ C )
= ( c_append @ A @ ( c_List_Oconcat @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__2_0) ).
thf(1201,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oconcat @ ( c_List_Olist_OCons @ A @ B @ ( tc_List_Olist @ C ) ) @ C )
= ( c_append @ A @ ( c_List_Oconcat @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(576,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ( ( c_Message_Oparts @ ( c_insert @ A @ B @ tc_Message_Omsg ) )
= ( c_Message_Oparts @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__cut__eq_0) ).
thf(2011,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
| ( ( c_Message_Oparts @ ( c_insert @ A @ B @ tc_Message_Omsg ) )
= ( c_Message_Oparts @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(243,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ F @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ E @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_1) ).
thf(1206,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ F @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ E @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(119,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_less @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_0) ).
thf(920,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_less @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(129,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_1) ).
thf(942,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)],[129]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_append @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ D ) ) @ D )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length_0) ).
thf(678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_append @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ D ) ) @ D )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(431,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__5_0) ).
thf(1691,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(285,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_Olexord @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A
= ( c_List_Olist_OCons @ ( c_Main_Olexord__Nil__left__1 @ A @ B ) @ ( c_Main_Olexord__Nil__left__2 @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_0) ).
thf(1306,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_Olexord @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A
= ( c_List_Olist_OCons @ ( c_Main_Olexord__Nil__left__1 @ A @ B ) @ ( c_Main_Olexord__Nil__left__2 @ A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(626,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/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
thf(2118,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)],[626]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_union @ B @ A @ C ) @ C )
= ( c_union @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Ostrange__Un__eq_0) ).
thf(1338,plain,
! [C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_union @ B @ A @ C ) @ C )
= ( c_union @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(592,axiom,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oanalz @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__idem_0) ).
thf(2047,plain,
! [A: $i] :
( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oanalz @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(570,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__conj__parts_0) ).
thf(2000,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(240,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_Olexord @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__right_0) ).
thf(1199,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_Olexord @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(649,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Key_0) ).
thf(2164,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(222,axiom,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_List_Oremdups @ A @ B ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_0) ).
thf(1153,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_List_Oremdups @ A @ B ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(46,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(761,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)],[46]) ).
thf(345,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
thf(1470,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)],[345]) ).
thf(612,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Gets_0) ).
thf(2093,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(607,axiom,
! [A: $i] :
( ( c_Relation_Odiag @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).
thf(2083,plain,
! [A: $i] :
( ( c_Relation_Odiag @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= c_List_Olist_ONil )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_0) ).
thf(1067,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= c_List_Olist_ONil )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(462,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ C @ D @ tc_nat ) )
| ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ tc_nat @ tc_nat ) @ ( c_Pair @ C @ B @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_Ointrel @ ( tc_prod @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_1) ).
thf(1768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ C @ D @ tc_nat ) )
| ( c_in @ ( c_Pair @ ( c_Pair @ A @ D @ tc_nat @ tc_nat ) @ ( c_Pair @ C @ B @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_Ointrel @ ( tc_prod @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq_0) ).
thf(714,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)],[27]) ).
thf(173,axiom,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(1047,plain,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(446,axiom,
! [A: $i] :
( ( c_Event_Oknows @ A @ c_List_Olist_ONil )
= ( c_Event_OinitState @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows_Oknows__Nil_0) ).
thf(1730,plain,
! [A: $i] :
( ( c_Event_Oknows @ A @ c_List_Olist_ONil )
= ( c_Event_OinitState @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(226,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize @ C @ ( tc_List_Olist @ B ) ) )
| ( ( c_append @ D @ A @ B )
!= ( c_append @ E @ C @ B ) )
| ( D = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_2) ).
thf(1163,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize @ C @ ( tc_List_Olist @ B ) ) )
| ( ( c_append @ D @ A @ B )
!= ( c_append @ E @ C @ B ) )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(525,axiom,
class_Wellfounded__Recursion_Owellorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_8) ).
thf(1900,plain,
class_Wellfounded__Recursion_Owellorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).
thf(957,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(194,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ozip @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Oreplicate @ D @ E @ F ) @ C @ F )
= ( c_List_Oreplicate @ ( c_Orderings_Omin @ A @ D @ tc_nat ) @ ( c_Pair @ B @ E @ C @ F ) @ ( tc_prod @ C @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__replicate_0) ).
thf(1091,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ozip @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Oreplicate @ D @ E @ F ) @ C @ F )
= ( c_List_Oreplicate @ ( c_Orderings_Omin @ A @ D @ tc_nat ) @ ( c_Pair @ B @ E @ C @ F ) @ ( tc_prod @ C @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
| ( c_less @ D @ B @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_0) ).
thf(952,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
| ( c_less @ D @ B @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(363,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).
thf(1519,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)],[363]) ).
thf(633,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_OMax @ ( c_insert @ B @ c_emptyset @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__singleton_0) ).
thf(2133,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_OMax @ ( c_insert @ B @ c_emptyset @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(422,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
| ( ( c_List_Olist__inter @ ( c_List_Olist_OCons @ A @ D @ C ) @ B @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist__inter @ D @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_0) ).
thf(1666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
| ( ( c_List_Olist__inter @ ( c_List_Olist_OCons @ A @ D @ C ) @ B @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist__inter @ D @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(352,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
thf(1487,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)],[352]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_0) ).
thf(693,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)],[17]) ).
thf(584,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_union @ ( c_Message_Osynth @ A ) @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_Oanalz @ ( c_union @ A @ B @ tc_Message_Omsg ) ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__synth__Un_0) ).
thf(2032,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_union @ ( c_Message_Osynth @ A ) @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_Oanalz @ ( c_union @ A @ B @ tc_Message_Omsg ) ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(517,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) ) @ tc_nat )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_union @ C @ D @ tc_Message_Omsg ) ) ) @ tc_nat )
| ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oparts @ D ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__parts__insert__dest_0) ).
thf(1883,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) ) @ tc_nat )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_union @ C @ D @ tc_Message_Omsg ) ) ) @ tc_nat )
| ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oparts @ D ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(162,axiom,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= c_0 )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_0) ).
thf(1021,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)],[162]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( c_plus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__Suc__right_0) ).
thf(778,plain,
! [B: $i,A: $i] :
( ( c_plus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(58,axiom,
! [A: $i] : ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
thf(788,plain,
! [A: $i] : ( c_less @ c_0 @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(308,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/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).
thf(1370,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)],[308]) ).
thf(327,axiom,
! [A: $i] :
( ( c_Nat_Osize @ ( c_Message_Omsg_ONonce @ A ) @ tc_Message_Omsg )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__3_0) ).
thf(1423,plain,
! [A: $i] :
( ( c_Nat_Osize @ ( c_Message_Omsg_ONonce @ A ) @ tc_Message_Omsg )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osublist @ B @ C @ D ) @ D ) @ D )
| ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onotin__set__sublistI_0) ).
thf(916,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osublist @ B @ C @ D ) @ D ) @ D )
| ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(306,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
thf(1365,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)],[306]) ).
thf(556,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OMPair__used_1) ).
thf(1968,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(87,axiom,
! [A: $i] :
( ( c_Nat_Osize @ ( c_Message_Omsg_OHash @ A ) @ tc_Message_Omsg )
= ( c_plus @ ( c_Nat_Osize @ A @ tc_Message_Omsg ) @ ( c_Suc @ c_0 ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__5_0) ).
thf(852,plain,
! [A: $i] :
( ( c_Nat_Osize @ ( c_Message_Omsg_OHash @ A ) @ tc_Message_Omsg )
= ( c_plus @ ( c_Nat_Osize @ A @ tc_Message_Omsg ) @ ( c_Suc @ c_0 ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(232,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair_2) ).
thf(1178,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)],[232]) ).
thf(549,axiom,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__4_0) ).
thf(1951,plain,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(1,negated_conjecture,
c_in @ v_K @ c_Message_OsymKeys @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(665,plain,
c_in @ v_K @ c_Message_OsymKeys @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ A @ D @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
thf(830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ A @ D @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(211,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_Message_Omsg_OMPair @ A @ B ) @ tc_Message_Omsg )
= ( c_plus @ ( c_plus @ ( c_Nat_Osize @ A @ tc_Message_Omsg ) @ ( c_Nat_Osize @ B @ tc_Message_Omsg ) @ tc_nat ) @ ( c_Suc @ c_0 ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__6_0) ).
thf(1128,plain,
! [B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_Message_Omsg_OMPair @ A @ B ) @ tc_Message_Omsg )
= ( c_plus @ ( c_plus @ ( c_Nat_Osize @ A @ tc_Message_Omsg ) @ ( c_Nat_Osize @ B @ tc_Message_Omsg ) @ tc_nat ) @ ( c_Suc @ c_0 ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(410,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Public_OpublicKey @ A @ B )
!= ( c_Public_OshrK @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__neq__pubK_0) ).
thf(1634,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Public_OpublicKey @ A @ B )
!= ( c_Public_OshrK @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(623,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_3) ).
thf(2112,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(386,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq_1) ).
thf(1573,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)],[386]) ).
thf(484,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ C @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OSays__imp__analz__Spy__dest_0) ).
thf(1819,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ C @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C ) @ C )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast__snoc_0) ).
thf(1624,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C ) @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(493,axiom,
! [A: $i] :
~ ( c_in @ A @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__emptyE_0) ).
thf(1836,plain,
! [A: $i] :
~ ( c_in @ A @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(470,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ ( c_insert @ A @ B @ C ) @ C )
= ( c_insert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
thf(1787,plain,
! [C: $i,B: $i,A: $i] :
( ( c_insert @ A @ ( c_insert @ A @ B @ C ) @ C )
= ( c_insert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ C @ B @ tc_nat ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
thf(1079,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ C @ B @ tc_nat ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ C @ A @ B )
| ( ( c_Finite__Set_Ocard @ ( c_insert @ C @ A @ B ) @ B )
= ( c_Suc @ ( c_Finite__Set_Ocard @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).
thf(1027,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ C @ A @ B )
| ( ( c_Finite__Set_Ocard @ ( c_insert @ C @ A @ B ) @ B )
= ( c_Suc @ ( c_Finite__Set_Ocard @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( ( c_List_Onth @ ( c_List_Oreplicate @ B @ C @ D ) @ A @ D )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__replicate_0) ).
thf(682,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( ( c_List_Onth @ ( c_List_Oreplicate @ B @ C @ D ) @ A @ D )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq_0) ).
thf(1195,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(321,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_0) ).
thf(1407,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)],[321]) ).
thf(450,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
thf(1740,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(83,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_1) ).
thf(842,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)],[83]) ).
thf(300,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OAgent @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1_0) ).
thf(1350,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)],[300]) ).
thf(394,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Oset @ B @ ( tc_List_Olist @ C ) ) @ ( tc_List_Olist @ C ) )
| ( ( c_List_Oconcat @ B @ C )
!= c_List_Olist_ONil )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_0) ).
thf(1592,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Oset @ B @ ( tc_List_Olist @ C ) ) @ ( tc_List_Olist @ C ) )
| ( ( c_List_Oconcat @ B @ C )
!= c_List_Olist_ONil )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMin__ge__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_lessequals @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_1) ).
thf(1143,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMin__ge__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_lessequals @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(460,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff_0) ).
thf(1762,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)],[460]) ).
thf(369,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ F @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ E @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_1) ).
thf(1534,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ F @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ E @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(478,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_insert @ B @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Notes_0) ).
thf(1804,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_insert @ B @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( C = c_emptyset )
| ( ( c_Orderings_Omax @ B @ ( c_Finite__Set_OMin @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) ).
thf(1121,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( C = c_emptyset )
| ( ( c_Orderings_Omax @ B @ ( c_Finite__Set_OMin @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(182,axiom,
! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(1064,plain,
! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(504,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ B @ A ) ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__privateKey_0) ).
thf(1856,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ B @ A ) ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(328,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ ( c_Pair @ C @ D @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_Ointrel @ ( tc_prod @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( ( c_plus @ A @ D @ tc_nat )
= ( c_plus @ C @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_0) ).
thf(1425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ ( c_Pair @ C @ D @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_Ointrel @ ( tc_prod @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( ( c_plus @ A @ D @ tc_nat )
= ( c_plus @ C @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(155,axiom,
! [B: $i,A: $i] :
( ( ( c_Main_Oempty__Union__conv__1 @ A @ B )
!= c_emptyset )
| ( c_emptyset
= ( c_Union @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).
thf(1006,plain,
! [B: $i,A: $i] :
( ( ( c_Main_Oempty__Union__conv__1 @ A @ B )
!= c_emptyset )
| ( c_emptyset
= ( c_Union @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(514,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_0) ).
thf(1878,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)],[514]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ C @ ( c_Main_OMin__ge__iff__1 @ B @ C @ A ) @ A )
| ( c_lessequals @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_2) ).
thf(1118,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ C @ ( c_Main_OMin__ge__iff__1 @ B @ C @ A ) @ A )
| ( c_lessequals @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__6_0) ).
thf(1397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(19,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ E @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ E @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ ( tc_set @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_3) ).
thf(697,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ E @ A )
| ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ E @ B @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ C @ A ) @ ( tc_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(255,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ c_0 @ A @ tc_nat )
| ( ( c_List_Osublist @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ A @ C )
= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_1) ).
thf(1234,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ c_0 @ A @ tc_nat )
| ( ( c_List_Osublist @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ A @ C )
= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(372,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_append @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_append @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_A_64_Oappend__Cons_0) ).
thf(1541,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_append @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_append @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(270,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ORange @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).
thf(1270,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ORange @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(464,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_Odiag @ A @ B ) @ B @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).
thf(1772,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_Odiag @ A @ B ) @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(265,axiom,
c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
thf(1259,plain,
c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(557,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).
thf(1970,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)],[557]) ).
thf(251,axiom,
! [A: $i] : ( class_Nat_Opower @ ( tc_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_4) ).
thf(1227,plain,
! [A: $i] : ( class_Nat_Opower @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(145,axiom,
! [A: $i] :
( ~ ( c_less @ A @ ( c_Suc @ c_0 ) @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_0) ).
thf(980,plain,
! [A: $i] :
( ~ ( c_less @ A @ ( c_Suc @ c_0 ) @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(392,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Finite__Set_OMin @ B @ A ) @ B @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__in_0) ).
thf(1587,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Finite__Set_OMin @ B @ A ) @ B @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(215,axiom,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(1138,plain,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_0) ).
thf(1719,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)],[442]) ).
thf(383,axiom,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_2) ).
thf(1567,plain,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(225,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_1) ).
thf(1160,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)],[225]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_inter @ B @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ A @ C @ ( tc_set @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_1) ).
thf(1082,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_inter @ B @ C @ D ) @ ( tc_set @ D ) )
| ( c_lessequals @ A @ C @ ( tc_set @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ ( c_Main_OUnion__iff__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_0) ).
thf(1361,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ ( c_Main_OUnion__iff__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(279,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
thf(1292,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)],[279]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__subset__iff_1) ).
thf(753,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(234,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_OCons @ C @ D @ B ) )
| ( A
= ( c_append @ ( c_List_Orev @ D @ B ) @ ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_0) ).
thf(1182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_OCons @ C @ D @ B ) )
| ( A
= ( c_append @ ( c_List_Orev @ D @ B ) @ ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(3,negated_conjecture,
c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) ) @ tc_Message_Omsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(669,plain,
c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) ) @ tc_Message_Omsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(606,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OKey @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__4_0) ).
thf(2080,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)],[606]) ).
thf(472,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).
thf(1791,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)],[472]) ).
thf(336,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_1) ).
thf(1446,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)],[336]) ).
thf(520,axiom,
! [A: $i] :
( ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
| ( ( c_Message_OinvKey @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OinvKey__K_0) ).
thf(1889,plain,
! [A: $i] :
( ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
| ( ( c_Message_OinvKey @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(452,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_append @ ( c_List_Orev @ A @ B ) @ ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Olist_OCons @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_1) ).
thf(1744,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_append @ ( c_List_Orev @ A @ B ) @ ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Olist_OCons @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(354,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
thf(1493,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)],[354]) ).
thf(428,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__4_0) ).
thf(1683,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(102,axiom,
! [A: $i] :
( ( c_plus @ c_0 @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
thf(884,plain,
! [A: $i] :
( ( c_plus @ c_0 @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(293,axiom,
( ( c_Nat_Osize @ c_Message_Oagent_OSpy @ tc_Message_Oagent )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__3_0) ).
thf(1329,plain,
( ( c_Nat_Osize @ c_Message_Oagent_OSpy @ tc_Message_Oagent )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(554,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ~ ( c_in @ B @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__analz__shrK_1) ).
thf(1964,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ~ ( c_in @ B @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(419,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).
thf(1659,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(324,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/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_0) ).
thf(1414,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)],[324]) ).
thf(496,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ c_emptyset @ A @ B )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).
thf(1842,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ c_emptyset @ A @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(435,axiom,
! [A: $i] :
( c_Message_Oagent_OServer
!= ( c_Message_Oagent_OFriend @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__1_0) ).
thf(1700,plain,
! [A: $i] :
( c_Message_Oagent_OServer
!= ( c_Message_Oagent_OFriend @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(542,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__analz__shrK_0) ).
thf(1937,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(159,axiom,
! [A: $i] :
( c_List_Olist_ONil
= ( c_List_Orev @ c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_1) ).
thf(1016,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( c_List_Orev @ c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(608,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).
thf(2085,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)],[608]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_List_Odistinct @ ( c_append @ A @ B @ C ) @ C )
| ( c_List_Odistinct @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_0) ).
thf(701,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_List_Odistinct @ ( c_append @ A @ B @ C ) @ C )
| ( c_List_Odistinct @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(281,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).
thf(1297,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)],[281]) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
thf(911,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)],[114]) ).
thf(573,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_union @ A @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_OkeysFor @ A ) @ ( c_Message_OkeysFor @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__Un_0) ).
thf(2006,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_union @ A @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_OkeysFor @ A ) @ ( c_Message_OkeysFor @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(562,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Nonce_0) ).
thf(1984,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(502,axiom,
! [A: $i] :
( ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Event_OinitState @ A ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OkeysFor__parts__initState_0) ).
thf(1852,plain,
! [A: $i] :
( ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Event_OinitState @ A ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(330,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_append @ ( c_List_Orev @ B @ C ) @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev_Osimps__2_0) ).
thf(1429,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_append @ ( c_List_Orev @ B @ C ) @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(396,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_1) ).
thf(1599,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)],[396]) ).
thf(441,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq_0) ).
thf(1715,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)],[441]) ).
thf(560,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/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OCrypt_0) ).
thf(1979,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)],[560]) ).
thf(636,axiom,
! [A: $i] :
( ( c_Message_Oagent_OFriend @ A )
!= c_Message_Oagent_OSpy ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__5_0) ).
thf(2140,plain,
! [A: $i] :
( ( c_Message_Oagent_OFriend @ A )
!= c_Message_Oagent_OSpy ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(366,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_ONotes @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__3_0) ).
thf(1525,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_ONotes @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(487,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/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).
thf(1825,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)],[487]) ).
thf(205,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_2) ).
thf(1114,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)],[205]) ).
thf(466,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3_1) ).
thf(1776,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
thf(1263,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)],[267]) ).
thf(198,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_1) ).
thf(1099,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)],[198]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(985,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)],[147]) ).
thf(221,axiom,
! [B: $i,A: $i] :
( ( ( c_Main_OUnion__empty__conv__1 @ A @ B )
!= c_emptyset )
| ( ( c_Union @ A @ B )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_2) ).
thf(1150,plain,
! [B: $i,A: $i] :
( ( ( c_Main_OUnion__empty__conv__1 @ A @ B )
!= c_emptyset )
| ( ( c_Union @ A @ B )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(349,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
thf(1478,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)],[349]) ).
thf(371,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_0) ).
thf(1539,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)],[371]) ).
thf(313,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ~ ( c_in @ ( c_Pair @ C @ C @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).
thf(1382,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ~ ( c_in @ ( c_Pair @ C @ C @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(268,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_Event_Oevent_ONotes @ A @ B ) @ tc_Event_Oevent )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__3_0) ).
thf(1266,plain,
! [B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_Event_Oevent_ONotes @ A @ B ) @ tc_Event_Oevent )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(643,axiom,
! [A: $i] :
( ( c_Transitive__Closure_Otrancl @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).
thf(2153,plain,
! [A: $i] :
( ( c_Transitive__Closure_Otrancl @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(180,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/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
thf(1060,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)],[180]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= ( c_plus @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ ( c_Suc @ c_0 ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Osize__2_0) ).
thf(1050,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= ( c_plus @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ ( c_Suc @ c_0 ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(565,axiom,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) @ c_Message_OsymKeys @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__priK_0) ).
thf(1991,plain,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) @ c_Message_OsymKeys @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(258,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__same__eq_0) ).
thf(1241,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)],[258]) ).
thf(590,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_OHPair @ 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 )
| ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_1) ).
thf(2043,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_OHPair @ 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 )
| ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(381,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
thf(1563,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)],[381]) ).
thf(168,axiom,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
thf(1035,plain,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
| ( c_in @ ( c_List_Onth @ B @ A @ C ) @ ( c_List_Oset @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__mem_0) ).
thf(674,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
| ( c_in @ ( c_List_Onth @ B @ A @ C ) @ ( c_List_Oset @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(164,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_List_Oset @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
thf(1026,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)],[164]) ).
thf(403,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/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).
thf(1616,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)],[403]) ).
thf(235,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_List_Ohd @ A @ B ) @ ( c_List_Oset @ A @ B ) @ B )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__in__set_0) ).
thf(1185,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_List_Ohd @ A @ B ) @ ( c_List_Oset @ A @ B ) @ B )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(104,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_0) ).
thf(888,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)],[104]) ).
thf(447,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_List_Olast @ A @ B ) @ ( c_List_Oset @ A @ B ) @ B )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__in__set_0) ).
thf(1732,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_List_Olast @ A @ B ) @ ( c_List_Oset @ A @ B ) @ B )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(926,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)],[122]) ).
thf(482,axiom,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oparts @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__analz_0) ).
thf(1814,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oparts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ( c_Orderings_Omin @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Omin @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__Suc__Suc_0) ).
thf(938,plain,
! [B: $i,A: $i] :
( ( c_Orderings_Omin @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Omin @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp__self__comp_0) ).
thf(765,plain,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(177,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_0) ).
thf(1054,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(421,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OGets @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__1_0) ).
thf(1663,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OGets @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(610,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Number_0) ).
thf(2089,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Oremdups @ A @ B ) @ B )
= ( c_List_Oset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__remdups_0) ).
thf(773,plain,
! [B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Oremdups @ A @ B ) @ B )
= ( c_List_Oset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(61,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize @ C @ ( tc_List_Olist @ B ) ) )
| ( ( c_append @ A @ D @ B )
!= ( c_append @ C @ E @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_0) ).
thf(794,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize @ C @ ( tc_List_Olist @ B ) ) )
| ( ( c_append @ A @ D @ B )
!= ( c_append @ C @ E @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(568,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D ) )
| ( c_emptyset
= ( c_inter @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_1) ).
thf(1996,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D ) )
| ( c_emptyset
= ( c_inter @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
| ( c_lessequals @ B @ D @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_0) ).
thf(1135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
| ( c_lessequals @ B @ D @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= A )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_0) ).
thf(1251,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)],[261]) ).
thf(654,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Number_0) ).
thf(2176,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(641,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_OHPair @ A @ B ) @ ( c_insert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__HPair_0) ).
thf(2149,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_OHPair @ A @ B ) @ ( c_insert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(537,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__HPair_0) ).
thf(1927,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(89,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).
thf(856,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)],[89]) ).
thf(15,axiom,
! [A: $i] :
( ( c_List_Oremdups @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_1) ).
thf(689,plain,
! [A: $i] :
( ( c_List_Oremdups @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(309,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__5_0) ).
thf(1374,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)],[309]) ).
thf(409,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).
thf(1631,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(638,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).
thf(2144,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)],[638]) ).
thf(112,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize @ C @ ( tc_List_Olist @ B ) ) )
| ( ( c_append @ A @ D @ B )
!= ( c_append @ C @ E @ B ) )
| ( D = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_1) ).
thf(906,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize @ C @ ( tc_List_Olist @ B ) ) )
| ( ( c_append @ A @ D @ B )
!= ( c_append @ C @ E @ B ) )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(41,axiom,
c_lessequals @ c_0 @ c_0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_1) ).
thf(750,plain,
c_lessequals @ c_0 @ c_0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(445,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv_0) ).
thf(1727,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)],[445]) ).
thf(219,axiom,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
thf(1146,plain,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(457,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair_0) ).
thf(1754,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)],[457]) ).
thf(434,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
thf(1698,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)],[434]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ( c_lessequals @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).
thf(1103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ( c_lessequals @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(582,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/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
thf(2028,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)],[582]) ).
thf(395,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
thf(1595,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)],[395]) ).
thf(532,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D )
!= c_emptyset )
| ( ( c_inter @ A @ C @ D )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_1) ).
thf(1916,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ ( c_insert @ B @ C @ D ) @ D )
!= c_emptyset )
| ( ( c_inter @ A @ C @ D )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__iff_1) ).
thf(732,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(660,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_0) ).
thf(2188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(404,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
thf(1620,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)],[404]) ).
thf(456,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair_2) ).
thf(1752,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)],[456]) ).
thf(538,axiom,
c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OSpy_A_58_Abad_A_61_61_ATrue_0) ).
thf(1929,plain,
c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(315,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_ONumber @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_ANumber_AN2_A_61_61_AFalse_0) ).
thf(1388,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)],[315]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3_0) ).
thf(1403,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(474,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ ( c_insert @ A @ ( c_insert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__MPair_0) ).
thf(1795,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ ( c_insert @ A @ ( c_insert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(209,axiom,
! [A: $i] :
( ( c_List_Oconcat @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__1_0) ).
thf(1124,plain,
! [A: $i] :
( ( c_List_Oconcat @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(263,axiom,
! [A: $i] :
( ( c_Message_OinvKey @ ( c_Message_OinvKey @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
thf(1256,plain,
! [A: $i] :
( ( c_Message_OinvKey @ ( c_Message_OinvKey @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_append @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= ( c_plus @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__append_0) ).
thf(904,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_append @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= ( c_plus @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(143,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_union @ D @ A @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
thf(975,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_union @ D @ A @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ A ) @ B @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__Suc_0) ).
thf(875,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ A ) @ B @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(75,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
thf(826,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= c_List_Olist_ONil )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv_0) ).
thf(711,plain,
! [B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= c_List_Olist_ONil )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(216,axiom,
! [A: $i] :
( ( c_Orderings_Omin @ c_0 @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0L_0) ).
thf(1139,plain,
! [A: $i] :
( ( c_Orderings_Omin @ c_0 @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(126,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_1) ).
thf(936,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(438,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Union @ ( c_union @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_union @ ( c_Union @ A @ C ) @ ( c_Union @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Un__distrib_0) ).
thf(1707,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Union @ ( c_union @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_union @ ( c_Union @ A @ C ) @ ( c_Union @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Public_OshrK @ A )
!= ( c_Public_OpublicKey @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpubK__neq__shrK_0) ).
thf(1312,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Public_OshrK @ A )
!= ( c_Public_OpublicKey @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(508,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OHash @ ( 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 )
| ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth__analz_0) ).
thf(1865,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OHash @ ( 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 )
| ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(257,axiom,
! [A: $i] :
( c_emptyset
= ( c_List_Oset @ c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2_1) ).
thf(1239,plain,
! [A: $i] :
( c_emptyset
= ( c_List_Oset @ c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_2) ).
thf(804,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)],[66]) ).
thf(264,axiom,
! [A: $i] : ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
thf(1258,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)],[264]) ).
thf(131,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ E @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_1) ).
thf(947,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ C @ E @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).
thf(1224,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(640,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).
thf(2148,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(329,axiom,
! [B: $i,A: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ A @ B ) @ ( tc_List_Olist @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
thf(1428,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)],[329]) ).
thf(648,axiom,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( c_insert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
thf(2161,plain,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( c_insert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(662,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).
thf(2193,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)],[662]) ).
thf(423,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ODomain @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).
thf(1669,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ODomain @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(179,axiom,
! [A: $i] :
( ( c_Orderings_Omax @ c_0 @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0L_0) ).
thf(1058,plain,
! [A: $i] :
( ( c_Orderings_Omax @ c_0 @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(202,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(1107,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)],[202]) ).
thf(650,axiom,
! [B: $i,A: $i] :
( ( c_Set_Ocontents @ ( c_insert @ A @ c_emptyset @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
thf(2166,plain,
! [B: $i,A: $i] :
( ( c_Set_Ocontents @ ( c_insert @ A @ c_emptyset @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(461,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Oset @ B @ ( tc_List_Olist @ C ) ) @ ( tc_List_Olist @ C ) )
| ( c_List_Olist_ONil
!= ( c_List_Oconcat @ B @ C ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_0) ).
thf(1765,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Oset @ B @ ( tc_List_Olist @ C ) ) @ ( tc_List_Olist @ C ) )
| ( c_List_Olist_ONil
!= ( c_List_Oconcat @ B @ C ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(193,axiom,
! [A: $i] : ( c_lessequals @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_1) ).
thf(1090,plain,
! [A: $i] : ( c_lessequals @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(245,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_0) ).
thf(1209,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(275,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_0 )
| ( ( c_List_Oset @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
= ( c_insert @ B @ c_emptyset @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__replicate_0) ).
thf(1282,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_0 )
| ( ( c_List_Oset @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
= ( c_insert @ B @ c_emptyset @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(642,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth__eq_0) ).
thf(2151,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)],[642]) ).
thf(522,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_0) ).
thf(1894,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)],[522]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( ( c_List_Olast @ ( c_append @ A @ c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olast @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__appendL_0) ).
thf(1011,plain,
! [B: $i,A: $i] :
( ( c_List_Olast @ ( c_append @ A @ c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olast @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_0) ).
thf(736,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(614,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OprivateKey__into__used_0) ).
thf(2097,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(398,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).
thf(1603,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)],[398]) ).
thf(443,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
thf(1722,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)],[443]) ).
thf(625,axiom,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__idem_0) ).
thf(2116,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
= ( c_Message_Oparts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(463,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_OInteg @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel_A_96_96_A_123_Ix1_M_Ay1_J_125_A_58_AInteg_A_61_61_ATrue_0) ).
thf(1771,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_OInteg @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(385,axiom,
( ( c_Nat_Osize @ c_Message_Oagent_OServer @ tc_Message_Oagent )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__1_0) ).
thf(1571,plain,
( ( c_Nat_Osize @ c_Message_Oagent_OServer @ tc_Message_Oagent )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(92,axiom,
! [A: $i] :
( ( c_Nat_Osize @ ( c_Message_Omsg_OKey @ A ) @ tc_Message_Omsg )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__4_0) ).
thf(863,plain,
! [A: $i] :
( ( c_Nat_Osize @ ( c_Message_Omsg_OKey @ A ) @ tc_Message_Omsg )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ c_emptyset @ ( tc_set @ B ) )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
thf(990,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ c_emptyset @ ( tc_set @ B ) )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(151,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(996,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)],[151]) ).
thf(540,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_2) ).
thf(1933,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)],[540]) ).
thf(99,axiom,
! [A: $i] : ( c_List_Odistinct @ c_List_Olist_ONil @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__1_0) ).
thf(880,plain,
! [A: $i] : ( c_List_Odistinct @ c_List_Olist_ONil @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(171,axiom,
! [B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_1) ).
thf(1043,plain,
! [B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(581,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
thf(2025,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)],[581]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_0 )
| ( ( c_List_Ohd @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__replicate_0) ).
thf(758,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_0 )
| ( ( c_List_Ohd @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(90,axiom,
! [A: $i] :
( ( c_plus @ A @ c_0 @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(858,plain,
! [A: $i] :
( ( c_plus @ A @ c_0 @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(631,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ c_emptyset @ B @ C )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).
thf(2129,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ c_emptyset @ B @ C )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__rev__ident_0) ).
thf(816,plain,
! [B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(566,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Agent_0) ).
thf(1993,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(485,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/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OHash_0) ).
thf(1821,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)],[485]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
| ( c_List_Odistinct @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_1) ).
thf(895,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
| ( c_List_Odistinct @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__ge_0) ).
thf(964,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_lessequals @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(116,axiom,
! [B: $i,A: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).
thf(915,plain,
! [B: $i,A: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(298,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair_0) ).
thf(1344,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)],[298]) ).
thf(378,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_union @ ( c_insert @ A @ B @ C ) @ D @ C )
= ( c_insert @ A @ ( c_union @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
thf(1556,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_union @ ( c_insert @ A @ B @ C ) @ D @ C )
= ( c_insert @ A @ ( c_union @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(7,negated_conjecture,
( ~ ( c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) ) @ tc_nat )
| ( c_in @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Event_Oused @ v_evsf ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(668,plain,
( ~ ( c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) ) @ tc_nat )
| ( c_in @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Event_Oused @ v_evsf ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(105,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_0) ).
thf(890,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)],[105]) ).
thf(656,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ ( c_insert @ A @ ( c_insert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__MPair_0) ).
thf(2180,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ ( c_insert @ A @ ( c_insert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ A @ D @ ( tc_set @ C ) )
| ( c_lessequals @ A @ ( c_inter @ D @ B @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_2) ).
thf(811,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ A @ D @ ( tc_set @ C ) )
| ( c_lessequals @ A @ ( c_inter @ D @ B @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(657,axiom,
! [A: $i] :
( ( c_List_Olistset @ c_List_Olist_ONil @ A )
= ( c_insert @ c_List_Olist_ONil @ c_emptyset @ ( tc_List_Olist @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).
thf(2182,plain,
! [A: $i] :
( ( c_List_Olistset @ c_List_Olist_ONil @ A )
= ( c_insert @ c_List_Olist_ONil @ c_emptyset @ ( tc_List_Olist @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( c_Orderings_Omax @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Omax @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__Suc__Suc_0) ).
thf(799,plain,
! [B: $i,A: $i] :
( ( c_Orderings_Omax @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Omax @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(529,axiom,
! [A: $i] :
( ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
| ( c_in @ ( c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff_1) ).
thf(1909,plain,
! [A: $i] :
( ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
| ( c_in @ ( c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(494,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).
thf(1838,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)],[494]) ).
thf(291,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_0) ).
thf(1325,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)],[291]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_append @ A @ B @ C ) @ C )
= ( c_append @ ( c_List_Orev @ B @ C ) @ ( c_List_Orev @ A @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__append_0) ).
thf(1112,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_append @ A @ B @ C ) @ C )
= ( c_append @ ( c_List_Orev @ B @ C ) @ ( c_List_Orev @ A @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(430,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) )
!= ( c_Public_OshrK @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__neq__priK_0) ).
thf(1688,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) )
!= ( c_Public_OshrK @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(347,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
thf(1474,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)],[347]) ).
thf(136,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ B @ E @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) )
= ( c_Nat_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_3) ).
thf(959,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ B @ E @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) )
= ( c_Nat_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
| ( ( c_List_Oremdups @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Oremdups @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_0) ).
thf(1213,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
| ( ( c_List_Oremdups @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Oremdups @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(367,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( B = c_emptyset )
| ( ( c_Finite__Set_OMin @ ( c_insert @ C @ B @ A ) @ A )
= ( c_Orderings_Omin @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__insert_0) ).
thf(1528,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( B = c_emptyset )
| ( ( c_Finite__Set_OMin @ ( c_insert @ C @ B @ A ) @ A )
= ( c_Orderings_Omin @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(599,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_OatLeastAtMost @ B @ B @ A )
= ( c_insert @ B @ c_emptyset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).
thf(2064,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_OatLeastAtMost @ B @ B @ A )
= ( c_insert @ B @ c_emptyset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(231,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_1) ).
thf(1176,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)],[231]) ).
thf(332,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_insert @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps__2_0) ).
thf(1435,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_insert @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(580,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_Oall__not__in__conv__1 @ A @ B ) @ A @ B )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
thf(2022,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_Oall__not__in__conv__1 @ A @ B ) @ A @ B )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(617,axiom,
! [B: $i,A: $i] :
( ( c_List_Olexn @ A @ c_0 @ B )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
thf(2101,plain,
! [B: $i,A: $i] :
( ( c_List_Olexn @ A @ c_0 @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(645,axiom,
! [A: $i] :
( ~ ( c_in @ ( c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat )
| ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff_0) ).
thf(2156,plain,
! [A: $i] :
( ~ ( c_in @ ( c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat )
| ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(558,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C )
!= c_emptyset )
| ( ( c_inter @ B @ D @ C )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_1) ).
thf(1973,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ ( c_insert @ A @ B @ C ) @ D @ C )
!= c_emptyset )
| ( ( c_inter @ B @ D @ C )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_append @ A @ B @ C ) @ ( c_plus @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ tc_nat ) @ C )
= ( c_List_Onth @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length__plus_0) ).
thf(685,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_append @ A @ B @ C ) @ ( c_plus @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ tc_nat ) @ C )
= ( c_List_Onth @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(229,axiom,
! [B: $i,A: $i] :
( ( c_union @ A @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
thf(1171,plain,
! [B: $i,A: $i] :
( ( c_union @ A @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ( c_plus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__Suc_0) ).
thf(983,plain,
! [B: $i,A: $i] :
( ( c_plus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_plus @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(604,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OKey__synth__eq_1) ).
thf(2075,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(594,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_emptyset )
| ( c_in @ D @ B @ C )
| ( ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_2) ).
thf(2051,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_inter @ A @ B @ C )
!= c_emptyset )
| ( c_in @ D @ B @ C )
| ( ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__converse_0) ).
thf(695,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(259,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair_1) ).
thf(1245,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)],[259]) ).
thf(55,axiom,
( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_2) ).
thf(780,plain,
( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(413,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).
thf(1643,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)],[413]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olast @ ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C ) @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__snoc_0) ).
thf(1694,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olast @ ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C ) @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
thf(922,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(188,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq_1) ).
thf(1076,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)],[188]) ).
thf(407,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Finite__Set_OMax @ B @ A ) @ B @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__in_0) ).
thf(1626,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Finite__Set_OMax @ B @ A ) @ B @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(390,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ozip @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ F ) @ C @ F )
= ( c_List_Olist_OCons @ ( c_Pair @ A @ D @ C @ F ) @ ( c_List_Ozip @ B @ E @ C @ F ) @ ( tc_prod @ C @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Cons__Cons_0) ).
thf(1583,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ozip @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ F ) @ C @ F )
= ( c_List_Olist_OCons @ ( c_Pair @ A @ D @ C @ F ) @ ( c_List_Ozip @ B @ E @ C @ F ) @ ( tc_prod @ C @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(480,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Agent_0) ).
thf(1809,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(512,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_OHPair @ 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 )
| ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_0) ).
thf(1873,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_OHPair @ 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 )
| ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(130,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( c_append @ ( c_List_Obutlast @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ A @ B ) @ c_List_Olist_ONil @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__butlast__last__id_0) ).
thf(944,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( c_append @ ( c_List_Obutlast @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ A @ B ) @ c_List_Olist_ONil @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(344,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_0) ).
thf(1467,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)],[344]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_Suc @ D ) @ C )
= ( c_List_Onth @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__Suc_0) ).
thf(680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_Suc @ D ) @ C )
= ( c_List_Onth @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(587,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/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__synthD__dest_0) ).
thf(2037,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)],[587]) ).
thf(297,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/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_1) ).
thf(1340,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)],[297]) ).
thf(346,axiom,
! [B: $i,A: $i] :
( ( c_append @ c_List_Olist_ONil @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2_1) ).
thf(1472,plain,
! [B: $i,A: $i] :
( ( c_append @ c_List_Olist_ONil @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(160,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(1018,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( C = c_emptyset )
| ( ( c_Orderings_Omin @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) ).
thf(823,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( C = c_emptyset )
| ( ( c_Orderings_Omin @ B @ ( c_Finite__Set_OMax @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_0) ).
thf(836,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)],[80]) ).
thf(174,axiom,
! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
thf(1049,plain,
! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(595,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth__analz_1) ).
thf(2054,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).
thf(722,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Omin @ C @ D @ A ) @ A )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(547,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_union @ A @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__Un_0) ).
thf(1948,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_union @ A @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(459,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Datatype_Ooption_OSome @ A @ B )
!= ( c_Datatype_Ooption_OSome @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject_0) ).
thf(1758,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)],[459]) ).
thf(227,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omin @ B @ ( c_Orderings_Omin @ B @ C @ A ) @ A )
= ( c_Orderings_Omin @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).
thf(1166,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omin @ B @ ( c_Orderings_Omin @ B @ C @ A ) @ A )
= ( c_Orderings_Omin @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(620,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__MPair_0) ).
thf(2107,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(242,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oset @ A @ B )
!= c_emptyset )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty_0) ).
thf(1203,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)],[242]) ).
thf(244,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
thf(1208,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)],[244]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_SetInterval_OatLeastLessThan @ C @ B @ A )
= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
thf(1277,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( ( c_SetInterval_OatLeastLessThan @ C @ B @ A )
= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(629,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_insert @ A @ B @ tc_Message_Omsg ) ) )
= ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OFake__analz__eq_0) ).
thf(2124,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_insert @ A @ B @ tc_Message_Omsg ) ) )
= ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(498,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/sandbox2/benchmark/theBenchmark.p',cls_Message_ONonce__synth__eq_0) ).
thf(1845,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)],[498]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Orev @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rev_0) ).
thf(971,plain,
! [B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Orev @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(637,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OAgent__synth_0) ).
thf(2143,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)],[637]) ).
thf(399,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= B )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2_0) ).
thf(1605,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)],[399]) ).
thf(415,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) )
!= ( c_Public_OpublicKey @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OprivateKey_Ab1_AA1_A_61_ApublicKey_Ac1_AA_H1_A_61_61_AFalse_0) ).
thf(1647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) )
!= ( c_Public_OpublicKey @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(544,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_insert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Says_0) ).
thf(1941,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_insert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(37,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(739,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)],[37]) ).
thf(467,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
thf(1780,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)],[467]) ).
thf(368,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/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_0) ).
thf(1531,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)],[368]) ).
thf(150,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_2) ).
thf(993,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)],[150]) ).
thf(375,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_ONonce @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_ANonce_AN2_A_61_61_AFalse_0) ).
thf(1547,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)],[375]) ).
thf(454,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ E @ A @ C ) @ ( c_List_Olist_OCons @ E @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_3) ).
thf(1748,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ E @ A @ C ) @ ( c_List_Olist_OCons @ E @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(185,axiom,
! [A: $i] :
( ( c_List_Obutlast @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__1_0) ).
thf(1070,plain,
! [A: $i] :
( ( c_List_Obutlast @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omin @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).
thf(872,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omin @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(23,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
thf(705,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)],[23]) ).
thf(401,axiom,
! [A: $i] :
( ( c_Nat_Osize @ ( c_Message_Omsg_OAgent @ A ) @ tc_Message_Omsg )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__1_0) ).
thf(1611,plain,
! [A: $i] :
( ( c_Nat_Osize @ ( c_Message_Omsg_OAgent @ A ) @ tc_Message_Omsg )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(223,axiom,
! [B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Orev @ A @ B ) @ B )
= ( c_List_Oset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rev_0) ).
thf(1156,plain,
! [B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Orev @ A @ B ) @ B )
= ( c_List_Oset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(319,axiom,
! [B: $i,A: $i] :
( ( c_emptyset
!= ( c_List_Oset @ A @ B ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2_0) ).
thf(1400,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)],[319]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp_0) ).
thf(707,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(253,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).
thf(1230,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)],[253]) ).
thf(351,axiom,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1_0) ).
thf(1484,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)],[351]) ).
thf(647,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(2160,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(60,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
| ~ ( c_less @ A @ ( c_Nat_Osize @ D @ ( tc_List_Olist @ E ) ) @ tc_nat )
| ( ( c_List_Onth @ ( c_List_Ozip @ D @ B @ E @ C ) @ A @ ( tc_prod @ E @ C ) )
= ( c_Pair @ ( c_List_Onth @ D @ A @ E ) @ ( c_List_Onth @ B @ A @ C ) @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__zip_0) ).
thf(791,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
| ~ ( c_less @ A @ ( c_Nat_Osize @ D @ ( tc_List_Olist @ E ) ) @ tc_nat )
| ( ( c_List_Onth @ ( c_List_Ozip @ D @ B @ E @ C ) @ A @ ( tc_prod @ E @ C ) )
= ( c_Pair @ ( c_List_Onth @ D @ A @ E ) @ ( c_List_Onth @ B @ A @ C ) @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(236,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
thf(1188,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)],[236]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
| ( c_lessequals @ D @ B @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_0) ).
thf(717,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_lessequals @ D @ ( c_Finite__Set_OMin @ C @ A ) @ A )
| ( c_lessequals @ D @ B @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(510,axiom,
! [B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_List_Olistrel @ A @ B ) @ ( c_insert @ c_List_Olist_ONil @ c_emptyset @ ( tc_List_Olist @ B ) ) @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) )
= ( c_insert @ c_List_Olist_ONil @ c_emptyset @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil_0) ).
thf(1869,plain,
! [B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_List_Olistrel @ A @ B ) @ ( c_insert @ c_List_Olist_ONil @ c_emptyset @ ( tc_List_Olist @ B ) ) @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) )
= ( c_insert @ c_List_Olist_ONil @ c_emptyset @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(526,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/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(1901,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)],[526]) ).
thf(68,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ( ( c_Nat_Osize @ E @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize @ F @ ( tc_List_Olist @ D ) ) )
| ( ( c_List_Ozip @ ( c_append @ E @ A @ B ) @ ( c_append @ F @ C @ D ) @ B @ D )
= ( c_append @ ( c_List_Ozip @ E @ F @ B @ D ) @ ( c_List_Ozip @ A @ C @ B @ D ) @ ( tc_prod @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__append_0) ).
thf(808,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ( ( c_Nat_Osize @ E @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize @ F @ ( tc_List_Olist @ D ) ) )
| ( ( c_List_Ozip @ ( c_append @ E @ A @ B ) @ ( c_append @ F @ C @ D ) @ B @ D )
= ( c_append @ ( c_List_Ozip @ E @ F @ B @ D ) @ ( c_List_Ozip @ A @ C @ B @ D ) @ ( tc_prod @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(427,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONumber @ A )
!= ( c_Message_Omsg_ONumber @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2_0) ).
thf(1679,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)],[427]) ).
thf(338,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).
thf(1452,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(411,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero_0) ).
thf(1637,plain,
! [A: $i] :
( ( c_Suc @ A )
!= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(82,axiom,
! [A: $i] :
( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_1) ).
thf(840,plain,
! [A: $i] :
( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(469,axiom,
! [F: $i,E: $i,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 @ ( c_List_Olist_OCons @ A @ E @ C ) @ ( c_List_Olist_OCons @ B @ F @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_2) ).
thf(1785,plain,
! [F: $i,E: $i,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 @ ( c_List_Olist_OCons @ A @ E @ C ) @ ( c_List_Olist_OCons @ B @ F @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(289,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_ONonce @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3_0) ).
thf(1317,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)],[289]) ).
thf(490,axiom,
( ( c_Message_Oanalz @ c_emptyset )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__empty_0) ).
thf(1830,plain,
( ( c_Message_Oanalz @ c_emptyset )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_0 )
| ( ( c_List_Olast @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__replicate_0) ).
thf(1130,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_0 )
| ( ( c_List_Olast @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(388,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
thf(1579,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)],[388]) ).
thf(276,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( ( c_Union @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_0) ).
thf(1285,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( ( c_Union @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_ONumber @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__3_0) ).
thf(1218,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)],[248]) ).
thf(596,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Equiv__Relations_Oquotient @ A @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty_0) ).
thf(2056,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)],[596]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Orev @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv_0) ).
thf(744,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Orev @ C @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olistset @ ( c_List_Olist_OCons @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_List_Oset__Cons @ A @ ( c_List_Olistset @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__2_0) ).
thf(1543,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olistset @ ( c_List_Olist_OCons @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_List_Oset__Cons @ A @ ( c_List_Olistset @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
thf(703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(477,axiom,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
= ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__synth_0) ).
thf(1802,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
= ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(249,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
| ( ( c_List_Olist__inter @ ( c_List_Olist_OCons @ A @ D @ C ) @ B @ C )
= ( c_List_Olist__inter @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_1) ).
thf(1221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
| ( ( c_List_Olist__inter @ ( c_List_Olist_OCons @ A @ D @ C ) @ B @ C )
= ( c_List_Olist__inter @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ A @ ( c_Main_OUnion__iff__1 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_1) ).
thf(1052,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ A @ ( c_Main_OUnion__iff__1 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(391,axiom,
! [B: $i,A: $i] :
( A
= ( c_append @ c_List_Olist_ONil @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2_1) ).
thf(1585,plain,
! [B: $i,A: $i] :
( A
= ( c_append @ c_List_Olist_ONil @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(475,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_0) ).
thf(1797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(583,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth__eq_1) ).
thf(2030,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(271,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_ACrypt_AK2_AX_H2_A_61_61_AFalse_0) ).
thf(1272,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)],[271]) ).
thf(524,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
thf(1898,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)],[524]) ).
thf(500,axiom,
! [A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_OinitState @ A ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__in__initState_0) ).
thf(1849,plain,
! [A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_OinitState @ A ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(217,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_Pair @ A @ B @ C @ D ) @ ( tc_prod @ C @ D ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oprod_Osize_0) ).
thf(1141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_Pair @ A @ B @ C @ D ) @ ( tc_prod @ C @ D ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(370,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_1) ).
thf(1536,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)],[370]) ).
thf(561,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_OMin @ ( c_insert @ B @ c_emptyset @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__singleton_0) ).
thf(1981,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_OMin @ ( c_insert @ B @ c_emptyset @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(358,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ C @ B )
| ( ( c_inter @ ( c_List_Oset @ C @ B ) @ ( c_List_Oset @ A @ B ) @ B )
!= c_emptyset )
| ( c_List_Odistinct @ ( c_append @ C @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_3) ).
thf(1504,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ C @ B )
| ( ( c_inter @ ( c_List_Oset @ C @ B ) @ ( c_List_Oset @ A @ B ) @ B )
!= c_emptyset )
| ( c_List_Odistinct @ ( c_append @ C @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(32,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( A = D )
| ( ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) )
= ( c_Nat_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_2) ).
thf(727,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( A = D )
| ( ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) )
= ( c_Nat_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(326,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ E @ A @ C ) @ ( c_List_Olist_OCons @ E @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_5) ).
thf(1421,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ E @ A @ C ) @ ( c_List_Olist_OCons @ E @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ D @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(191,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_2) ).
thf(1084,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)],[191]) ).
thf(609,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ A @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__in__knows_0) ).
thf(2088,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ A @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(591,axiom,
( ( c_SetInterval_OatMost @ c_0 @ tc_nat )
= ( c_insert @ c_0 @ c_emptyset @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__0_0) ).
thf(2045,plain,
( ( c_SetInterval_OatMost @ c_0 @ tc_nat )
= ( c_insert @ c_0 @ c_emptyset @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Relation_Odiag @ A @ B ) @ C @ B @ B )
= ( c_inter @ A @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
thf(1180,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Relation_Odiag @ A @ B ) @ C @ B @ B )
= ( c_inter @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(555,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).
thf(1966,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)],[555]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( ( c_Finite__Set_Ocard @ A @ B )
!= c_0 )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_0) ).
thf(931,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( ( c_Finite__Set_Ocard @ A @ B )
!= c_0 )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(497,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__in__used_0) ).
thf(1844,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_insert @ A @ B @ C ) @ ( c_insert @ A @ D @ C ) @ C )
= ( c_insert @ A @ ( c_inter @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__inter__insert_0) ).
thf(1517,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_inter @ ( c_insert @ A @ B @ C ) @ ( c_insert @ A @ D @ C ) @ C )
= ( c_insert @ A @ ( c_inter @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(247,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
thf(1216,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)],[247]) ).
thf(210,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).
thf(1126,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_less @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(622,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/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).
thf(2110,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)],[622]) ).
thf(479,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OKey__synth__eq_0) ).
thf(1807,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)],[479]) ).
thf(290,axiom,
! [B: $i,A: $i] :
( ( ( c_Public_OshrK @ A )
!= ( c_Public_OshrK @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__injective_0) ).
thf(1321,plain,
! [B: $i,A: $i] :
( ( ( c_Public_OshrK @ A )
!= ( c_Public_OshrK @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(492,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OBody__dest_0) ).
thf(1834,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ 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)],[492]) ).
thf(531,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_1) ).
thf(1913,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(417,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( c_emptyset
!= ( c_Union @ B @ C ) )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_0) ).
thf(1654,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( c_emptyset
!= ( c_Union @ B @ C ) )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(323,axiom,
! [B: $i,A: $i] :
( ( c_union @ A @ c_emptyset @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
thf(1412,plain,
! [B: $i,A: $i] :
( ( c_union @ A @ c_emptyset @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ A @ D @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osame__append__eq_0) ).
thf(1448,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)],[337]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OHash @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5_0) ).
thf(1189,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)],[237]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ( c_List_Osublist @ c_List_Olist_ONil @ A @ B )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__nil_0) ).
thf(844,plain,
! [B: $i,A: $i] :
( ( c_List_Osublist @ c_List_Olist_ONil @ A @ B )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(339,axiom,
! [B: $i,A: $i] :
( ( c_append @ A @ c_List_Olist_ONil @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_1) ).
thf(1453,plain,
! [B: $i,A: $i] :
( ( c_append @ A @ c_List_Olist_ONil @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(393,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
thf(1590,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)],[393]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_0) ).
thf(699,plain,
! [B: $i,A: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( c_List_Olast @ ( c_List_Olist_OCons @ B @ A @ C ) @ C )
= ( c_List_Olast @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_1) ).
thf(813,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( c_List_Olast @ ( c_List_Olist_OCons @ B @ A @ C ) @ C )
= ( c_List_Olast @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(425,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_Oempty__Union__conv__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_emptyset
= ( c_Union @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_1) ).
thf(1674,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Main_Oempty__Union__conv__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_emptyset
= ( c_Union @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(181,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ D @ B @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_0) ).
thf(1062,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_SetInterval_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_OatLeastLessThan @ D @ E @ A ) @ ( tc_set @ A ) )
| ( c_lessequals @ D @ B @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(199,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ozip @ A @ c_List_Olist_ONil @ B @ C )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).
thf(1101,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ozip @ A @ c_List_Olist_ONil @ B @ C )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(503,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
thf(1854,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)],[503]) ).
thf(365,axiom,
! [A: $i] :
( ( c_List_Oset @ c_List_Olist_ONil @ A )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty_1) ).
thf(1523,plain,
! [A: $i] :
( ( c_List_Oset @ c_List_Olist_ONil @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__2_0) ).
thf(1558,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)],[379]) ).
thf(653,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).
thf(2174,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)],[653]) ).
thf(348,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_0) ).
thf(1476,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)],[348]) ).
thf(615,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpriK__in__initState_0) ).
thf(2098,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
thf(748,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(408,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Union @ ( c_insert @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_union @ A @ ( c_Union @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__insert_0) ).
thf(1629,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Union @ ( c_insert @ A @ B @ ( tc_set @ C ) ) @ C )
= ( c_union @ A @ ( c_Union @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(572,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/sandbox2/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(2004,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)],[572]) ).
thf(166,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize @ C @ ( tc_List_Olist @ B ) ) )
| ( ( c_append @ D @ A @ B )
!= ( c_append @ E @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_3) ).
thf(1030,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize @ C @ ( tc_List_Olist @ B ) ) )
| ( ( c_append @ D @ A @ B )
!= ( c_append @ E @ C @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(589,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/sandbox2/benchmark/theBenchmark.p',cls_Public_ONonce__notin__initState_0) ).
thf(2041,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)],[589]) ).
thf(2,negated_conjecture,
c_in @ v_evsf @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(667,plain,
c_in @ v_evsf @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(334,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
thf(1440,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)],[334]) ).
thf(238,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_Event_Oevent_OGets @ A @ B ) @ tc_Event_Oevent )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__2_0) ).
thf(1193,plain,
! [B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_Event_Oevent_OGets @ A @ B ) @ tc_Event_Oevent )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( c_List_Olist__inter @ c_List_Olist_ONil @ A @ B )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__1_0) ).
thf(763,plain,
! [B: $i,A: $i] :
( ( c_List_Olist__inter @ c_List_Olist_ONil @ A @ B )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ C @ A )
| ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_2) ).
thf(899,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ ( c_Main_OMax__less__iff__1 @ B @ C @ A ) @ C @ A )
| ( c_less @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(627,axiom,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Event_Oused @ c_List_Olist_ONil ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OCrypt__notin__used__empty_0) ).
thf(2120,plain,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Event_Oused @ c_List_Olist_ONil ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(172,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ B @ D @ A )
| ( c_less @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_2) ).
thf(1045,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ B @ C @ A )
| ~ ( c_less @ B @ D @ A )
| ( c_less @ B @ ( c_Orderings_Omin @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(575,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_union @ ( c_Message_Oparts @ ( c_insert @ C @ c_emptyset @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ D ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oused__Says_0) ).
thf(2009,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_union @ ( c_Message_Oparts @ ( c_insert @ C @ c_emptyset @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ D ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(506,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_emptyset
!= ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_0) ).
thf(1861,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_emptyset
!= ( c_inter @ B @ ( c_insert @ A @ D @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(613,axiom,
! [B: $i,A: $i] :
( ( c_Equiv__Relations_Oquotient @ c_emptyset @ A @ B )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty_1) ).
thf(2095,plain,
! [B: $i,A: $i] :
( ( c_Equiv__Relations_Oquotient @ c_emptyset @ A @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(78,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Odiag @ A @ B ) @ B @ B )
= ( c_Relation_Odiag @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__diag_0) ).
thf(832,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Odiag @ A @ B ) @ B @ B )
= ( c_Relation_Odiag @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(586,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
thf(2036,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Public_OshrK @ A )
!= ( c_Message_OinvKey @ ( c_Public_OpublicKey @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpriK__neq__shrK_0) ).
thf(1309,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Public_OshrK @ A )
!= ( c_Message_OinvKey @ ( c_Public_OpublicKey @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_insert @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).
thf(1116,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_insert @ 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)],[206]) ).
thf(213,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ( c_less @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_0) ).
thf(1133,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)],[213]) ).
thf(152,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
thf(999,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)],[152]) ).
thf(465,axiom,
~ ( c_in @ c_Message_Oagent_OServer @ c_Event_Obad @ tc_Message_Oagent ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OServer_A_58_Abad_A_61_61_AFalse_0) ).
thf(1774,plain,
~ ( c_in @ c_Message_Oagent_OServer @ c_Event_Obad @ tc_Message_Oagent ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(274,axiom,
! [A: $i] :
( c_List_Olist_ONil
= ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_2) ).
thf(1280,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)],[274]) ).
thf(551,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Oanalz @ ( c_insert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_0) ).
thf(1957,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Oanalz @ ( c_insert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(644,axiom,
class_Divides_Odiv @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_44) ).
thf(2155,plain,
class_Divides_Odiv @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ozip @ c_List_Olist_ONil @ A @ B @ C )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).
thf(967,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ozip @ c_List_Olist_ONil @ A @ B @ C )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(197,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(1097,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)],[197]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_1) ).
thf(818,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMax__le__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_lessequals @ ( c_Finite__Set_OMax @ B @ A ) @ C @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ tc_Event_Oevent )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__1_0) ).
thf(1380,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ tc_Event_Oevent )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_List_Odistinct @ A @ B )
| ( c_List_Odistinct @ ( c_List_Osublist @ A @ C @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__sublistI_0) ).
thf(1148,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_List_Odistinct @ A @ B )
| ( c_List_Odistinct @ ( c_List_Osublist @ A @ C @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2_0) ).
thf(1248,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)],[260]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) @ B )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_0) ).
thf(854,plain,
! [B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) @ B )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(563,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Hash_0) ).
thf(1986,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_OkeysFor @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(574,axiom,
c_Relation_Otrans @ c_Wellfounded__Relations_Oless__than @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).
thf(2008,plain,
c_Relation_Otrans @ c_Wellfounded__Relations_Oless__than @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ B @ A @ C ) )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2_0) ).
thf(1303,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)],[284]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_1) ).
thf(867,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ( c_in @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ B @ A )
| ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(458,axiom,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(1757,plain,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ( c_List_Osublist @ A @ c_emptyset @ B )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__empty_0) ).
thf(865,plain,
! [B: $i,A: $i] :
( ( c_List_Osublist @ A @ c_emptyset @ B )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(350,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2_1) ).
thf(1480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(305,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
thf(1363,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)],[305]) ).
thf(418,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).
thf(1657,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)],[418]) ).
thf(659,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Nonce_0) ).
thf(2186,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(601,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Nonce_0) ).
thf(2070,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
= ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(380,axiom,
! [A: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).
thf(1561,plain,
! [A: $i] :
( ~ ( class_Wellfounded__Recursion_Owellorder @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(611,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/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
thf(2091,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)],[611]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_1) ).
thf(828,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_less @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_less @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Ozip @ A @ B @ C @ D ) @ ( tc_List_Olist @ ( tc_prod @ C @ D ) ) )
= ( c_Orderings_Omin @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__zip_0) ).
thf(1065,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Ozip @ A @ B @ C @ D ) @ ( tc_List_Olist @ ( tc_prod @ C @ D ) ) )
= ( c_Orderings_Omin @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oconcat @ ( c_append @ A @ B @ ( tc_List_Olist @ C ) ) @ C )
= ( c_append @ ( c_List_Oconcat @ A @ C ) @ ( c_List_Oconcat @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__append_0) ).
thf(720,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oconcat @ ( c_append @ A @ B @ ( tc_List_Olist @ C ) ) @ C )
= ( c_append @ ( c_List_Oconcat @ A @ C ) @ ( c_List_Oconcat @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(134,axiom,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
thf(955,plain,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__subset__iff_0) ).
thf(918,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(64,axiom,
c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0_1) ).
thf(801,plain,
c_less @ c_0 @ ( c_Suc @ c_0 ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(483,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ B @ C ) )
| ( c_in @ D @ B @ C )
| ( c_emptyset
= ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_2) ).
thf(1816,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_inter @ A @ B @ C ) )
| ( c_in @ D @ B @ C )
| ( c_emptyset
= ( c_inter @ ( c_insert @ D @ A @ C ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(355,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/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex_0) ).
thf(1495,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)],[355]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
thf(897,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
| ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(322,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_append @ ( c_append @ A @ B @ C ) @ D @ C )
= ( c_append @ A @ ( c_append @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__assoc_0) ).
thf(1410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_append @ ( c_append @ A @ B @ C ) @ D @ C )
= ( c_append @ A @ ( c_append @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(49,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_1) ).
thf(767,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)],[49]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
= ( c_List_Oreplicate @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__replicate_0) ).
thf(1056,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
= ( c_List_Oreplicate @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(471,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
thf(1789,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)],[471]) ).
thf(5,negated_conjecture,
~ ( c_in @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Event_Oused @ v_evsf ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(664,plain,
~ ( c_in @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Event_Oused @ v_evsf ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(167,axiom,
! [B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B )
= ( c_List_Orev @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osingleton__rev__conv_1) ).
thf(1033,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B )
= ( c_List_Orev @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(277,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/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex_0) ).
thf(1288,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)],[277]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__iff_0) ).
thf(886,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(451,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
thf(1742,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)],[451]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ C @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ A )
| ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_2) ).
thf(928,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ C @ ( c_Main_OMin__gr__iff__1 @ B @ C @ A ) @ A )
| ( c_less @ C @ ( c_Finite__Set_OMin @ B @ A ) @ A )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(488,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Ospies__pubK_0) ).
thf(1827,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_List_Odistinct @ A @ B )
| ( c_List_Odistinct @ ( c_List_Olist_OCons @ C @ A @ B ) @ B )
| ( c_in @ C @ ( c_List_Oset @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_2) ).
thf(1268,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_List_Odistinct @ A @ B )
| ( c_List_Odistinct @ ( c_List_Olist_OCons @ C @ A @ B ) @ B )
| ( c_in @ C @ ( c_List_Oset @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
| ( c_less @ B @ D @ A )
| ( C = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_0) ).
thf(860,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ A ) )
| ~ ( c_less @ ( c_Finite__Set_OMax @ C @ A ) @ D @ A )
| ( c_less @ B @ D @ A )
| ( C = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(314,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_1) ).
thf(1384,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olists @ ( c_inter @ A @ B @ C ) @ C )
= ( c_inter @ ( c_List_Olists @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists__Int__eq_0) ).
thf(1378,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olists @ ( c_inter @ A @ B @ C ) @ C )
= ( c_inter @ ( c_List_Olists @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(161,axiom,
! [A: $i] :
( ( c_List_Orev @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv_1) ).
thf(1019,plain,
! [A: $i] :
( ( c_List_Orev @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(302,axiom,
! [B: $i,A: $i] :
( ( c_inter @ c_emptyset @ A @ B )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).
thf(1357,plain,
! [B: $i,A: $i] :
( ( c_inter @ c_emptyset @ A @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(536,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_union @ ( c_Message_Oanalz @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ ( c_union @ A @ B @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__analz__Un_0) ).
thf(1925,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_union @ ( c_Message_Oanalz @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ ( c_union @ A @ B @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(440,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/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).
thf(1713,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)],[440]) ).
thf(282,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ F @ ( tc_prod @ C @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_0) ).
thf(1299,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olexord @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ F @ ( tc_prod @ C @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
thf(691,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)],[16]) ).
thf(518,axiom,
! [A: $i] :
( ( c_Union @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
thf(1885,plain,
! [A: $i] :
( ( c_Union @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(635,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/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__partsD__dest_0) ).
thf(2138,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)],[635]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_0) ).
thf(1093,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(539,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_Ointrel @ ( tc_prod @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ A @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ B @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_1) ).
thf(1930,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ c_IntDef_Ointrel @ ( tc_prod @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ A @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_Relation_OImage @ c_IntDef_Ointrel @ ( c_insert @ B @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(148,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
thf(987,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Omax @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(630,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 @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).
thf(2127,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 @ ( c_Message_OinvKey @ 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)],[630]) ).
thf(559,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( c_Equiv__Relations_Oquotient @ A @ B @ C ) )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2_0) ).
thf(1976,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)],[559]) ).
thf(376,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
thf(1550,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)],[376]) ).
thf(154,axiom,
! [A: $i] :
~ ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_0) ).
thf(1004,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)],[154]) ).
thf(515,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ B @ C ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ C @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OGets__imp__analz__Spy__dest_0) ).
thf(1880,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ B @ C ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ C @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(331,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_OinvKey @ A )
!= ( c_Message_OinvKey @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OinvKey__eq_0) ).
thf(1431,plain,
! [B: $i,A: $i] :
( ( ( c_Message_OinvKey @ A )
!= ( c_Message_OinvKey @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(294,axiom,
! [A: $i] :
( ( c_Message_Oagent_OFriend @ A )
!= c_Message_Oagent_OServer ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__2_0) ).
thf(1331,plain,
! [A: $i] :
( ( c_Message_Oagent_OFriend @ A )
!= c_Message_Oagent_OServer ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(553,axiom,
( ( c_Message_OkeysFor @ c_emptyset )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__empty_0) ).
thf(1962,plain,
( ( c_Message_OkeysFor @ c_emptyset )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(156,axiom,
! [B: $i,A: $i] :
( ( c_List_Oreplicate @ c_0 @ A @ B )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__0_0) ).
thf(1009,plain,
! [B: $i,A: $i] :
( ( c_List_Oreplicate @ c_0 @ A @ B )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(449,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ F @ ( tc_prod @ C @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_0) ).
thf(1737,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olex @ F @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ F @ ( tc_prod @ C @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(382,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/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).
thf(1565,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)],[382]) ).
thf(597,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_emptyset
!= ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_0) ).
thf(2059,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_emptyset
!= ( c_inter @ ( c_insert @ A @ D @ C ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(652,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OKey @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4_0) ).
thf(2170,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)],[652]) ).
thf(661,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oused @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oused__Gets_0) ).
thf(2191,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oused @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(101,axiom,
! [A: $i] :
( c_List_Olist_ONil
= ( c_List_Oremdups @ c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_1) ).
thf(882,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( c_List_Oremdups @ c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OHash @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AHash_AZ2_A_61_61_AFalse_0) ).
thf(1367,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)],[307]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_1) ).
thf(940,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( c_List_Ohd @ ( c_append @ A @ B @ C ) @ C )
= ( c_List_Ohd @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__append2_0) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( c_List_Ohd @ ( c_append @ A @ B @ C ) @ C )
= ( c_List_Ohd @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(52,axiom,
! [A: $i] :
( ( c_Orderings_Omax @ A @ c_0 @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0R_0) ).
thf(775,plain,
! [A: $i] :
( ( c_Orderings_Omax @ A @ c_0 @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_1) ).
thf(755,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)],[44]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ c_0 @ C )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__0_0) ).
thf(676,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ c_0 @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11646,plain,
$false,
inference(e,[status(thm)],[892,1501,1024,1823,2072,1995,1105,909,1840,962,777,1950,1686,2109,2131,1237,846,1315,1850,666,1295,1554,1110,2077,1158,2062,1443,2014,2099,2114,1793,1437,1173,1750,977,730,1290,1882,1569,1939,741,1073,1671,1608,1735,1275,1327,913,1640,1954,1507,1458,670,1497,2195,1705,1867,2184,1999,797,2168,1260,1919,1988,1354,2146,1095,1746,1001,1782,1391,782,709,2020,973,1613,1935,1359,1601,1724,2067,1887,1650,1645,1921,2136,1904,1703,1228,1254,724,1709,2039,1660,785,1871,1907,838,802,1462,949,1511,751,1577,1455,1832,934,1545,1800,1892,2049,870,881,2158,1875,1232,1847,1922,902,1087,1514,969,1347,1013,770,2178,1489,924,1302,789,1911,1040,1418,1334,834,1828,1581,2073,821,2017,1946,1465,2105,1811,1858,1864,2122,1677,2034,1960,806,1377,734,1072,1622,1394,2002,2103,849,1521,1696,1169,687,1896,877,1943,1201,2011,1206,920,942,678,1691,1306,2118,1338,2047,2000,1199,2164,1153,761,1470,2093,2083,1067,1768,714,1047,1730,1163,1900,957,1091,952,1519,2133,1666,1487,693,2032,1883,1021,778,788,1370,1423,916,1365,1968,852,1178,1951,665,830,1128,1634,2112,1573,1819,1624,1836,1787,1079,1027,682,1195,1407,1740,842,1350,1592,1143,1762,1534,1804,1121,1064,1856,1425,1006,1878,1118,1397,697,1234,1541,1270,1772,1259,1970,1227,980,1587,1138,1719,1567,1160,1082,1361,1292,753,1182,669,2080,1791,1446,1889,1744,1493,1683,884,1329,1964,1659,1414,1842,1700,1937,1016,2085,701,1297,911,2006,1984,1852,1429,1599,1715,1979,2140,1525,1825,1114,1776,1263,1099,985,1150,1478,1539,1382,1266,2153,1060,1050,1991,1241,2043,1563,1035,674,1026,1616,1185,888,1732,926,1814,938,765,1054,1663,2089,773,794,1996,1135,1251,2176,2149,1927,856,689,1374,1631,2144,906,750,1727,1146,1754,1698,1103,2028,1595,1916,732,2188,1620,1752,1929,1388,1403,1795,1124,1256,904,975,875,826,711,1139,936,1707,1312,1865,1239,804,1258,947,1224,2148,1428,2161,2193,1669,1058,1107,2166,1765,1090,1209,1282,2151,1894,1011,736,2097,1603,1722,2116,1771,1571,863,990,996,1933,880,1043,2025,758,858,2129,816,1993,1821,895,964,915,1344,1556,668,890,2180,811,2182,799,1909,1838,1325,1112,1688,1474,959,1213,1528,2064,1176,1435,2022,2101,2156,1973,685,1171,983,2075,2051,695,1245,780,1643,1694,922,1076,1626,1583,1809,1873,944,1467,680,2037,1340,1472,1018,823,836,1049,2054,722,1948,1758,1166,2107,1203,1208,1277,2124,1845,971,2143,1605,1647,1941,739,1780,1531,993,1547,1748,1070,872,705,1611,1156,1400,707,1230,1484,2160,791,1188,717,1869,1901,808,1679,1452,1637,840,1785,1317,1830,1130,1579,1285,1218,2056,744,1543,703,1802,1221,1052,1585,1797,2030,1272,1898,1849,1141,1536,1981,1504,727,1421,1084,2088,2045,1180,1966,931,1844,1517,1216,1126,2110,1807,1321,1834,1913,1654,1412,1448,1189,844,1453,1590,699,813,1674,1062,1101,1854,1523,1558,2174,1476,2098,748,1629,2004,1030,2041,667,1440,1193,763,899,2120,1045,2009,1861,2095,832,2036,1309,1116,1133,999,1774,1280,1957,2155,967,1097,818,1380,1148,1248,854,1986,2008,1303,867,1757,865,1480,1363,1657,2186,2070,1561,2091,828,1065,720,955,918,801,1816,1495,897,1410,767,1056,1789,664,1033,1288,886,1742,928,1827,1268,860,1384,1378,1019,1357,1925,1713,1299,691,1885,2138,1093,1930,987,2127,1976,1550,1004,1880,1431,1331,1962,1009,1737,1565,2059,2170,2191,882,1367,940,1037,775,755,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV338-1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n025.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 19 02:34:05 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.08/1.20 % [INFO] Parsing done (334ms).
% 2.08/1.21 % [INFO] Running in sequential loop mode.
% 2.82/1.46 % [INFO] eprover registered as external prover.
% 2.82/1.46 % [INFO] cvc4 registered as external prover.
% 2.82/1.47 % [INFO] Scanning for conjecture ...
% 3.59/1.66 % [INFO] Found a conjecture and 2941 axioms. Running axiom selection ...
% 4.79/1.98 % [INFO] Axiom selection finished. Selected 656 axioms (removed 2285 axioms).
% 5.55/2.18 % [INFO] Problem is propositional (TPTP CNF).
% 5.55/2.20 % [INFO] Type checking passed.
% 5.55/2.20 % [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 ...
% 43.85/9.46 % External prover 'e' found a proof!
% 43.85/9.46 % [INFO] Killing All external provers ...
% 44.09/9.46 % Time passed: 8928ms (effective reasoning time: 8243ms)
% 44.09/9.46 % 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)>
% 44.09/9.46 % Axioms used in derivation (656): cls_Message_Oanalz__synth__Un_0, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0, cls_Relation_ODomain__empty_0, cls_List_Oself__append__conv2_0, cls_Set_OPow__iff_1, cls_Set_Oempty__Union__conv_1, cls_Transitive__Closure_Otrancl__range_0, cls_Set_Oinsert__disjoint__1_1, cls_Equiv__Relations_Oquotient__is__empty2_0, cls_Finite__Set_OMin__gr__iff_2, cls_Event_Oevent_Oinject__3_0, cls_List_Olistrel__Cons1_0, cls_Nat_Onot__gr0_0, cls_Message_Oanalz_OInj_0, cls_Nat_Onot__less0_0, cls_List_Ofinite__set_0, cls_Nat_Onat__add__left__cancel__less_1, cls_Set_Osingleton__insert__inj__eq_0, cls_Message_Oagent_Osize__3_0, cls_Event_OSays__imp__analz__Spy__dest_0, cls_SetInterval_OatMost__0_0, cls_List_Onth__zip_0, cls_Relation_OImageI_0, cls_List_Oremdups__eq__nil__iff_1, cls_Set_OInt__iff_2, cls_Relation_ODomain__diag_0, cls_Message_Oparts__Un_0, cls_List_Olists_ONil_0, cls_Message_OHPair__neqs__2_0, cls_Public_OpublicKey__into__used_0, cls_Finite__Set_OMin__insert_0, cls_Message_Omsg_Osize__7_0, cls_List_Olistrel__Cons2_1, cls_List_Oappend__eq__append__conv_1, cls_Event_OkeysFor__synth_H_0, cls_List_OCons__in__lex_1, cls_Message_Oanalz__analzD__dest_0, cls_Message_OCrypt__synth__eq_0, cls_Message_Omsg_Osize__2_0, cls_Relation_ORange__diag_0, cls_List_Olength__append_0, cls_List_Olexord__cons__cons_2, cls_List_Onth__append__length_0, cls_Nat_Onat__add__right__cancel_0, cls_Event_Oused__Gets_0, cls_Message_Oparts__insert__Crypt_0, cls_List_Olength__remdups__eq_1, cls_Wellfounded__Recursion_Owf__insert_0, cls_Message_Oanalz__synth_0, cls_IntDef_Ointrel_A_96_96_A_123_Ix1_M_Ay1_J_125_A_58_AInteg_A_61_61_ATrue_0, cls_Message_OkeysFor__Un_0, clsarity_nat_7, cls_List_Olast__snoc_0, cls_Finite__Set_OMin__singleton_0, cls_Finite__Set_Ocard__infinite_0, cls_List_Orev__is__Nil__conv_0, cls_Message_Oparts__empty_0, cls_Set_Oinsert__disjoint__2_2, cls_Transitive__Closure_Otrancl_Or__into__trancl_0, cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2, cls_Message_OKey__synth__eq_1, cls_List_Oappend__in__lists__conv_2, cls_Finite__Set_OMax__less__iff_2, cls_Message_Oanalz__conj__parts_0, cls_Message_Oanalz__idem_0, cls_Message_OHPair__synth__analz_1, clsrel_Orderings_Olinorder_4, cls_Orderings_Oorder__less__irrefl_0, cls_Public_OpubK__neq__shrK_0, cls_Message_Oagent_Oinject_0, cls_List_Olast_Osimps_0, cls_Finite__Set_OFinites_OemptyI_0, cls_Message_Oanalz__empty_0, cls_Message_Oparts__insert__MPair_0, cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0, cls_Set_Osingleton__inject__dest_0, cls_Message_Oanalz__insert__HPair_0, cls_Relation_OImageE_0, cls_Nat_OSuc__Suc__eq_0, cls_Set_OInt__subset__iff_0, cls_List_Olength__0__conv_1, cls_Public_Onot__symKeys__priK_0, cls_Set_OUnionE_1, cls_List_Olexord__Nil__left_0, cls_Event_Oused__Notes_0, cls_Yahalom_OSpy__see__shrK_0, cls_List_Oappend__same__eq_0, cls_Event_Oevent_Odistinct__6_0, cls_Set_OUn__subset__iff_2, cls_Message_Oparts__insert__Nonce_0, cls_Message_OHPair__neqs__5_0, cls_Message_OHash_91X2_93_AY2_A_61_ACrypt_AK2_AX_H2_A_61_61_AFalse_0, cls_List_Oappend__eq__append__conv_0, cls_Message_Oanalz__Crypt__if_0, cls_Transitive__Closure_Ortrancl__idemp_0, cls_List_Olist_Oinject_1, cls_Finite__Set_OFinites_OinsertI_0, cls_Wellfounded__Relations_Owf__lex__prod_0, cls_Nat_Oless__irrefl_0, cls_Message_Omsg_Oinject__1_0, cls_Nat_Oadd__is__0_0, clsarity_set_2, cls_List_Olistrel__Nil1_0, clsarity_nat_3, cls_List_Odistinct_Osimps__2_2, cls_Event_OkeysFor__synth_H_3, cls_List_Obutlast__snoc_0, cls_Set_OPow__iff_0, cls_List_Olast__in__set_0, cls_Message_OMPair__synth__analz_2, cls_Set_Odisjoint__insert__2_1, cls_Relation_Oconverse__converse_0, cls_Finite__Set_Ofinite__Int_0, cls_Public_OpriK__neq__shrK_0, cls_List_Oself__append__conv_1, cls_Message_OHash__synth_0, cls_Set_Osingleton__insert__inj__eq_H_0, clsarity_nat_47, cls_List_Onth__mem_0, cls_List_Olist_Osize__2_0, cls_Finite__Set_Ocard__0__eq_1, clsrel_Wellfounded__Recursion_Owellorder_5, cls_Finite__Set_Ofinite__Pow__iff_1, cls_Nat_Onat__add__left__cancel__le_0, cls_List_Oappend__eq__append__conv_3, cls_Message_Oparts__insert__Agent_0, cls_Message_Osynth_OHash_0, cls_List_Oconcat_Osimps__2_0, cls_Set_Osubset__refl_0, cls_SetInterval_Oivl__subset_1, cls_Message_OHPair__eq_0, cls_List_Osame__append__eq_0, cls_List_ONil__is__rev__conv_0, cls_List_Olength__remdups__eq_0, cls_Finite__Set_Ofinite__Un_2, cls_Message_Oparts__subset__iff_1, cls_Set_OpsubsetI_0, cls_Set_OInter__iff_0, cls_Event_Oevent_Osize__3_0, cls_List_Olength__replicate_0, cls_Finite__Set_Ocard__insert__disjoint_0, cls_List_OCons__in__lex_0, cls_Public_OCrypt__notin__used__empty_0, cls_List_Orev__rev__ident_0, cls_Message_Oanalz__insert__Agent_0, cls_Message_Omsg_Oinject__6_0, cls_Nat_Onat__add__left__cancel__less_0, cls_Event_Oknows__Spy__Notes_1, cls_List_OCons__in__lex_5, cls_List_Odistinct__append_0, cls_Finite__Set_Ofinite__Un_0, cls_List_Oremdups__eq__nil__iff_0, cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0, cls_Relation_ORangeE_0, cls_Nat_Oadd__gr__0_2, cls_Public_ONonce__notin__initState_0, cls_List_Odistinct__rev_0, cls_List_Olist__inter_Osimps__2_1, cls_List_Oset__empty2_1, cls_Message_Oanalz__insert__Nonce_0, cls_List_Olength__zip_0, cls_Public_OshrK__injective_0, cls_Message_Oagent_Odistinct__1_0, cls_List_Olist__inter_Osimps__2_0, cls_Message_Oparts_OInj_0, cls_Set_OUnion__insert_0, cls_List_Olength__remdups__leq_0, cls_Wellfounded__Recursion_Oacyclic__converse_1, cls_List_Ohd_Osimps_0, cls_Set_Odisjoint__insert__1_1, cls_Orderings_Omax__less__iff__conj_0, cls_Set_Osubset__empty_0, cls_Public_OMPair__used_1, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2, cls_SetInterval_OatLeastAtMost__empty_0, cls_List_Olast__replicate_0, cls_List_Obutlast_Osimps__2_0, cls_Message_OkeysFor__empty_0, cls_Message_Omsg_Oinject__5_0, cls_Relation_OdiagI_0, cls_Message_Oparts__synth_0, clsarity_nat_44, cls_IntDef_Ointrel__iff_1, cls_Message_OCrypt__synth_1, cls_Public_OkeysFor__parts__initState_0, cls_List_Oset__remdups_0, cls_List_OlistsE_0, cls_Message_OHPair__neqs__6_0, cls_List_Osingleton__rev__conv_0, cls_Finite__Set_Ofinite__converse_1, cls_SetInterval_OatLeastAtMost__singleton_0, cls_Finite__Set_OMin__ge__iff_2, cls_Public_OinvKey__K_0, cls_List_Orev__is__rev__conv_0, cls_Finite__Set_OMax__le__iff_2, cls_Message_OHPair__synth__analz_0, cls_Public_OsymKeys__invKey__iff_0, cls_List_Ozip__replicate_0, cls_Nat_Oadd__is__0_1, cls_Set_OUnion__empty__conv_1, cls_Message_Osynth_OMPair_0, cls_List_Olexord__cons__cons_1, cls_Message_ONonce__synth__eq_1, cls_Set_Osingleton__insert__inj__eq_H_1, cls_Event_Oevent_Odistinct__4_0, cls_Set_OUn__iff_0, cls_List_Owf__lex_0, cls_List_Olistrel__Cons2_0, cls_Message_Omsg_Osize__4_0, cls_Message_Oparts__insert__Key_0, cls_Relation_ODomainI_0, cls_Event_OServer_A_58_Abad_A_61_61_AFalse_0, cls_Set_Oinsert__subset_2, cls_Set_OUnion__iff_1, cls_Message_Oparts__insert__HPair_0, cls_Set_OUn__empty_1, cls_List_Oappend1__eq__conv_1, cls_Message_Omsg_Oinject__2_0, cls_Wellfounded__Recursion_Oacyclic__insert_1, cls_Set_Oinsert__disjoint__2_1, cls_List_Oappend__self__conv_0, cls_Orderings_Omin__less__iff__conj_2, cls_Finite__Set_OMin__gr__iff_1, cls_Finite__Set_Ofinite__insert_0, cls_Message_Omsg_Oinject__7_1, cls_Set_Oinsert__iff_2, cls_List_Oremdups__eq__nil__right__iff_0, cls_Message_Oparts__subset__iff_0, cls_Event_Oevent_Oinject__2_0, cls_List_Ozip__append_0, cls_Set_OsingletonD__dest_0, cls_SetInterval_Ofinite__atLeastAtMost_0, cls_Message_Omsg_Osize__5_0, cls_Set_Oinsert__not__empty_0, cls_Event_Oknows__Spy__Says_0, cls_Message_OFake__analz__eq_0, cls_List_ONil2__notin__lex_0, cls_List_Orev__is__Nil__conv_1, cls_List_Odistinct__append_1, cls_Relation_OImageE_1, cls_Relation_OdiagE_0, cls_Message_Oagent_Odistinct__3_0, cls_Nat_Ole__0__eq_0, cls_Event_Oevent_Odistinct__3_0, cls_SetInterval_Ofinite__atLeastLessThan_0, cls_Relation_OImage__singleton__iff_1, cls_Finite__Set_OMax__less__iff_1, cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, cls_Public_OprivateKey_Ab1_AA1_A_61_ApublicKey_Ac1_AA_H1_A_61_61_AFalse_0, cls_Transitive__Closure_Otrancl__empty_0, cls_Set_Oempty__subsetI_0, cls_Finite__Set_Ofinite__Int_1, cls_List_Oappend__in__lists__conv_1, cls_List_ONil__notin__lex_0, cls_Nat_OSuc__le__mono_0, cls_Finite__Set_OMin__le_0, cls_List_Olist_Oinject_0, cls_Nat_OSuc__less__eq_1, cls_Set_Oempty__iff_0, cls_List_Oappend__self__conv_1, cls_List_OCons__in__lex_4, cls_Relation_Oconverse__iff_1, cls_List_Osublist__nil_0, cls_Set_OUnion__iff_0, cls_Set_OUn__subset__iff_0, cls_Wellfounded__Recursion_Owf__not__refl_0, cls_Message_OkeysFor__insert__HPair_0, cls_List_Oreplicate_Oreplicate__0_0, cls_Message_Omsg_Oinject__4_0, cls_Public_OpublicKey__neq__privateKey_0, cls_Event_Oevent_Oinject__3_1, cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0, cls_Event_Oknows__Spy__Notes_0, cls_Message_OAgent__synth_0, cls_Set_OUnion__empty__conv_0, cls_List_Olast_Osimps_1, cls_Set_OsingletonI_0, cls_Event_Oevent_Oinject__1_2, cls_Message_OHPair__eq__MPair_0, cls_Message_Oparts__insert__Hash_0, cls_Set_Osubset__antisym_0, cls_Message_ONumber__synth_0, cls_Set_OsubsetD_0, cls_Event_Oevent_Osize__2_0, cls_Set_OUnion__empty__conv_2, cls_Nat_Ozero__less__Suc_0, cls_List_Oin__listsI_1, cls_Set_Odisjoint__insert__2_2, cls_List_Oremdups_Osimps__2_0, cls_Datatype_Ooption_Oinject_0, cls_Message_Oparts__partsD__dest_0, cls_Finite__Set_OMax__ge_0, cls_List_Ohd__replicate_0, cls_Relation_ORange__empty_0, cls_Message_Omsg_Oinject__6_1, cls_List_Obutlast_Osimps__2_1, cls_Set_OInt__empty__left_0, cls_Nat_Onat__add__left__cancel__le_1, cls_Message_Osynth__subset__iff_1, cls_List_Olist__inter_Osimps__1_0, cls_Nat_Omin__Suc__Suc_0, cls_Message_OkeysFor__insert__Agent_0, cls_Public_OshrK__neq__priK_0, cls_Message_Oparts__insert__Number_0, cls_Message_Oanalz__insert__Key_0, cls_List_Olength__greater__0__conv_1, cls_List_Orev__eq__Cons__iff_1, cls_Message_Oanalz__insert__Hash_0, cls_List_Ozip_Osimps__1_0, cls_List_Oappend__self__conv2_1, cls_Yahalom_OSpy__analz__shrK_1, cls_Message_Oparts_OBody__dest_0, cls_Relation_OImage__empty_0, cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1, cls_List_Olists__Int__eq_0, cls_List_Onth__append__length__plus_0, cls_List_Orev__singleton__conv_1, cls_Event_Oknows_Oknows__Nil_0, cls_Set_OUnion__Un__distrib_0, cls_Set_Oall__not__in__conv_0, cls_Finite__Set_Ofinite__Un_1, cls_Yahalom_OSpy__analz__shrK_0, cls_Public_OshrK__in__used_0, cls_Set_Osingleton__insert__inj__eq_1, cls_Message_OHash__synth__analz_1, cls_Public_OMPair__used_0, cls_List_Obutlast_Osimps__1_0, cls_Public_OshrK__in__initState_0, cls_Nat_Omin__0R_0, cls_Set_Oinsert__iff_1, cls_Public_OpublicKey__inject_0, cls_List_Oset__empty_0, cls_Equiv__Relations_Oquotient__is__empty_0, cls_Finite__Set_OMax__singleton_0, cls_Set_Osubset__empty_1, cls_Finite__Set_Ofinite__converse_0, cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0, cls_Finite__Set_Ofinite__Pow__iff_0, cls_Set_Oinsert__disjoint__1_0, cls_Message_OHash_91X2_93_AY2_A_61_AKey_AK2_A_61_61_AFalse_0, cls_SetInterval_Oivl__subset_0, cls_Set_Odisjoint__insert__1_2, cls_Datatype_Oo2s_Osimps__2_0, cls_Event_OkeysFor__synth_H_2, cls_List_Olength__0__conv_0, cls_List_Oconcat_Osimps__1_0, cls_Set_Oinsert__subset_1, cls_Relation_ORangeI_0, cls_SetInterval_OatLeastLessThan__empty_0, cls_List_Oappend1__eq__conv_0, cls_Message_OMPair__analz_1, cls_Nat_OSuc__le__mono_1, cls_Set_Oempty__Union__conv_0, cls_Public_Onot__symKeys__pubK_0, cls_Infinite__Set_Oatmost__one__unique_0, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0, cls_List_Orev__replicate_0, cls_Relation_Oconverse__diag_0, cls_List_ONil__is__rev__conv_1, cls_Message_Oin__parts__UnE_0, cls_Finite__Set_OMin__ge__iff_1, cls_Wellfounded__Relations_Otrans__less__than_0, cls_IntDef_Ointrel__iff_0, cls_List_Odistinct__remdups_0, cls_Message_OHash_91X2_93_AY2_A_61_AAgent_AA2_A_61_61_AFalse_0, cls_Message_OMPair__eq__HPair_0, cls_List_Oconcat__append_0, cls_Set_Oinsert__disjoint__2_0, cls_List_Oop_A_64_Oappend__Cons_0, cls_List_Oreplicate_Oreplicate__Suc_0, cls_Message_OkeysFor__insert__Nonce_0, cls_Message_OHash_91X2_93_AY2_A_61_ANumber_AN2_A_61_61_AFalse_0, cls_Message_OHPair__eq__MPair_1, cls_List_Olength__greater__0__conv_0, cls_Message_Osynth__subset__iff_0, cls_List_Oself__append__conv_0, cls_Set_OUn__insert__left_0, cls_Finite__Set_OMin__ge__iff_0, cls_Nat_Oadd__gr__0_0, cls_List_Odistinct__sublistI_0, cls_Set_OInt__empty__right_0, cls_Wellfounded__Recursion_Oacyclic__converse_0, cls_List_Oappend__is__Nil__conv_0, cls_Event_OkeysFor__parts__insert__dest_0, cls_Orderings_Omax__less__iff__conj_1, cls_Set_Osingleton__insert__inj__eq_H_2, cls_Wellfounded__Recursion_Owf__insert_2, cls_Nat_Oless__Suc0_0, cls_Datatype_Oelem__o2s_0, cls_List_ONil__is__append__conv_1, cls_Set_OUn__insert__right_0, cls_Nat_Onot__add__less1_0, cls_Message_OkeysFor__insert__Crypt_0, cls_List_Olist_Odistinct__2_0, cls_List_Olistrel__Nil_0, cls_IntDef_Oequiv__intrel__iff_0, cls_Product__Type_OPair__eq_1, cls_Yahalom_OGets__imp__analz__Spy__dest_0, cls_Nat_Oadd__is__0_2, cls_List_Oset__replicate_0, cls_Public_Oanalz__spies__pubK_0, cls_SetInterval_OatLeastLessThan__singleton_0, cls_List_Oappend__self__conv2_0, cls_Wellfounded__Recursion_Owf__empty_0, cls_Message_OHPair__neqs__3_0, cls_Finite__Set_OMax__less__iff_0, cls_Message_Osynth_OCrypt_0, cls_List_OCons__in__lex_3, cls_Event_Oevent_Odistinct__2_0, cls_Relation_Oconverse__iff_0, cls_Finite__Set_OMax__le__iff_0, cls_Message_OMPair__parts_1, cls_List_ONil__is__append__conv_2, cls_Public_OinvKey__shrK_0, cls_List_Odistinct__append_2, cls_Wellfounded__Relations_Owf__less__than_0, cls_Set_OUnion__iff_2, cls_Transitive__Closure_Or__into__rtrancl_0, cls_Message_Omsg_Osize__6_0, cls_List_Orev__append_0, cls_Message_ONonce__synth__eq_0, cls_Message_Osynth__synthD__dest_0, cls_Public_OSpy__spies__bad__shrK_0, cls_List_Onot__Cons__self_0, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0, cls_Set_OUn__iff_1, cls_Finite__Set_OMax__le__iff_1, cls_Message_OkeysFor__insert__Number_0, cls_Event_Oevent_Oinject__2_1, cls_Nat_Oadd__0__right_0, cls_Set_OUnion__empty_0, cls_SetInterval_Oivl__subset_3, cls_Wellfounded__Recursion_Oacyclic__insert_2, cls_Message_Oagent_Odistinct__4_0, cls_Message_Omsg_Osize__1_0, cls_List_Olistrel__Cons1_2, cls_List_Osublist__singleton_1, cls_List_ONil__is__append__conv_0, cls_Message_Omsg_Osize__3_0, cls_List_OlistsE_1, cls_Finite__Set_OMin__gr__iff_0, clsarity_nat_12, cls_Equiv__Relations_Oquotient__is__empty2_1, cls_Message_OkeysFor__insert__Hash_0, cls_Relation_OImage__singleton__iff_0, cls_Nat_Omax__Suc__Suc_0, cls_List_Orev__eq__Cons__iff_0, cls_List_Olast__appendL_0, cls_Message_Oanalz__insert__MPair_0, cls_Message_Oagent_Odistinct__6_0, cls_List_Olist_Odistinct__1_0, cls_Set_Oempty__not__insert_0, cls_Set_OpsubsetE_0, cls_Wellfounded__Relations_Oless__than__iff_1, cls_Nat_Oadd__Suc__right_0, cls_List_Ohd__append2_0, cls_Nat_Onot__gr0_1, cls_Message_OHPair__neqs__1_0, cls_Orderings_Omin__less__iff__conj_0, cls_Set_OInt__subset__iff_2, cls_Nat_Onot__add__less2_0, cls_List_Olistrel__Nil2_0, cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0, cls_Event_Oevent_Oinject__1_1, cls_Relation_Orel__compI_0, cls_List_Onth__Cons__0_0, cls_List_Oset__append_0, cls_Public_OSpy__spies__bad__privateKey_0, cls_List_Onotin__set__sublistI_0, cls_Message_Oagent_Osize__2_0, cls_Set_OInt__iff_0, cls_Transitive__Closure_Otrancl__domain_0, cls_List_Olexord__Nil__right_0, cls_Event_Oused__Says_0, cls_List_Onth__replicate_0, cls_Message_Oagent_Odistinct__2_0, cls_Message_Oanalz__insert__Number_0, cls_Finite__Set_OMax__in_0, cls_Message_OinvKey__eq_0, cls_Relation_OdiagE_1, cls_List_Olength__rev_0, cls_Wellfounded__Relations_Otrans__lex__prod_0, cls_List_Oappend__assoc_0, cls_SetInterval_OatMost__eq__iff_0, cls_List_Ohd__in__set_0, cls_List_Oconcat__eq__Nil__conv_0, cls_List_Oappend__butlast__last__id_0, cls_Public_OshrK_AX1_A_58_AsymKeys_A_61_61_ATrue_0, cls_Message_OHash__synth__analz_0, cls_Set_OInt__iff_1, cls_Set_Oinsert__disjoint__1_2, cls_Relation_Odiag__empty_0, cls_List_Oappend__is__Nil__conv_1, cls_Set_OUn__empty__left_0, cls_Event_Oevent_Odistinct__1_0, cls_Set_OUn__empty__right_0, cls_Message_Oanalz__parts_0, cls_Message_Oanalz__Crypt__if_1, cls_Event_Oevent_Odistinct__5_0, cls_Wellfounded__Recursion_Owf__insert_1, cls_Message_OMPair__synth_1, cls_Set_Oempty__Union__conv_2, cls_Public_OshrK__neq__pubK_0, cls_List_Olast__appendR_0, cls_Message_OCrypt__synth__eq_1, cls_List_Orev__singleton__conv_0, cls_List_Oset__rev_0, cls_Nat_Omax__0L_0, cls_Message_OHash_91X2_93_AY2_A_61_ANonce_AN2_A_61_61_AFalse_0, cls_List_Olistrel__Cons2_2, cls_Public_Ospies__pubK_0, cls_Message_Osynth_OInj_0, cls_Set_OPow__Int__eq_0, cls_List_Olistrel__Cons1_1, cls_List_Oset__empty_1, cls_Set_OInter__insert_0, cls_Orderings_Oorder__class_Oaxioms__1_0, cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0, cls_Nat_Oless__Suc0_1, cls_Set_Ocontents__eq_0, cls_List_Ozip__Nil_0, cls_Message_OkeysFor__insert__MPair_0, cls_List_Osingleton__rev__conv_1, cls_Nat_OSuc__not__Zero_0, cls_Finite__Set_OMin__in_0, cls_Message_Oanalz__subset__iff_1, cls_Relation_ODomainE_0, cls_Public_OprivateKey__into__used_0, cls_List_Oappend__in__lists__conv_0, cls_Message_OMPair__eq__HPair_1, cls_Finite__Set_Ocard__empty_0, cls_Set_OUnionE_0, cls_Public_OpublicKey__inject_1, cls_Datatype_Oelem__o2s_1, cls_Nat_Onat__add__left__cancel_0, cls_Message_Ostrange__Un__eq_0, cls_List_Oin__listsI_0, cls_List_Odistinct_Osimps__2_0, cls_Message_OMPair__analz_0, cls_SetInterval_Ocard__atMost_0, cls_List_Olexord__cons__cons_3, clsarity_nat_8, cls_SetInterval_OatMost__subset__iff_0, cls_Message_OkeysFor__insert__Key_0, cls_Event_OSpy_A_58_Abad_A_61_61_ATrue_0, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0, cls_Message_Oanalz__analz__Un_0, cls_IntDef_Oequiv__intrel__iff_1, cls_Event_OkeysFor__synth_H_1, cls_Equiv__Relations_Oquotient__is__empty_1, cls_List_Odistinct_Osimps__1_0, cls_List_Odistinct__append_3, cls_Message_OFake__parts__insert__in__Un__dest_0, cls_Message_Oparts__cut__eq_0, cls_Public_OpriEK__noteq__shrK_0, cls_Message_OKey__synth__eq_0, cls_Public_OpriK__in__initState_0, clsarity_nat_24, cls_Product__Type_OPair__eq_0, cls_List_Orev_Osimps__2_0, cls_List_Olexn_Osimps__1_0, cls_Message_Oanalz_ODecrypt__dest_0, cls_List_Olexord__Nil__left_1, cls_Message_OHPair__synth__analz_2, cls_List_Oin__listsD__dest_0, cls_List_Oself__append__conv2_1, cls_List_Olistset_Osimps__1_0, cls_List_Oappend__eq__append__conv_2, cls_List_Oset__empty2_0, cls_Message_Oagent_Odistinct__5_0, cls_Public_OpublicKey__in__initState_0, cls_Message_OHPair__eq__MPair_2, cls_List_Osublist__empty_0, cls_Datatype_Oprod_Osize_0, cls_Nat_OSuc__less__eq_0, cls_Event_Oevent_Osize__1_0, cls_List_Olexord__cons__cons_0, cls_List_OCons__in__lex_2, cls_Set_OUn__subset__iff_1, cls_Message_Omsg_Oinject__7_0, cls_Transitive__Closure_Ortrancl__idemp__self__comp_0, cls_List_Oremdups__eq__nil__right__iff_1, cls_Message_OMPair__parts_0, cls_Message_Omsg_Oinject__3_0, cls_List_Odistinct_Osimps__2_1, cls_List_Olistset_Osimps__2_0, cls_Nat_Ole0_0, cls_List_Ozip__Cons__Cons_0, cls_Set_OInt__absorb_0, cls_Message_Oparts__analz_0, cls_List_Oset_Osimps__2_0, cls_Set_OUn__empty_0, cls_Set_Oinsert__iff_0, cls_Wellfounded__Recursion_Oacyclic__insert_0, cls_Set_Oinsert__absorb2_0, cls_Nat_Oop_A_L_Oadd__0_0, cls_Nat_Oadd__gr__0_1, cls_Set_OUnion__Pow__eq_0, cls_Set_Onot__psubset__empty_0, cls_Nat_Omin__0L_0, clsrel_Wellfounded__Recursion_Owellorder_1, cls_List_Onth__Cons__Suc_0, cls_Nat_Ole__0__eq_1, cls_Set_Odisjoint__insert__2_0, cls_Set_OUn__empty_2, cls_Event_Oevent_Oinject__1_0, cls_Message_Oparts__emptyE_0, cls_Set_OUn__iff_2, cls_Nat_Oop_A_L_Oadd__Suc_0, cls_Set_OpsubsetE_1, cls_Message_Oanalz__subset__iff_0, cls_Orderings_Omax__less__iff__conj_2, cls_Set_OPow__empty_0, cls_Message_Oagent_Osize__1_0, cls_Finite__Set_OMax__insert_0, cls_List_Owf__lenlex_0, cls_Set_Osingleton__insert__inj__eq_2, cls_Nat_OZero__not__Suc_0, cls_Set_Oinsert__inter__insert_0, cls_SetInterval_OatMost__subset__iff_1, cls_Yahalom_OSpy__see__shrK_1, cls_Nat_OlessI_0, cls_SetInterval_Ofinite__atMost_0, cls_Finite__Set_Ocard__0__eq_0, clsarity_set_4, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1, cls_Message_OMPair__eq__HPair_2, cls_Message_OMPair__synth__analz_0, cls_Set_Odisjoint__insert__1_0, cls_Public_ONonce__notin__used__empty_0, cls_List_ONil__eq__concat__conv_0, cls_SetInterval_Oivl__subset_2, cls_Public_OsymKeys__invKey__iff_1, cls_Message_Oparts__idem_0, cls_Wellfounded__Relations_Oless__than__iff_0, cls_Set_Oinsert__subset_0, cls_Nat_Omax__0R_0, cls_Message_OHPair__neqs__4_0, cls_List_Odistinct__rev_1, cls_List_Oappend__is__Nil__conv_2, cls_List_Osublist__singleton_0, cls_Event_Oknows__Spy__Gets_0, cls_Public_OshrK__in__knows_0, cls_Message_OHash_91X2_93_AY2_A_61_AHash_AZ2_A_61_61_AFalse_0, cls_Set_OUn__absorb_0, cls_Message_OMPair__synth__analz_1, cls_List_Olists_OCons_0, cls_Relation_OImage__diag_0, cls_Message_OMPair__synth_0, cls_Orderings_Omin__less__iff__conj_1, cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0, cls_List_Oremdups_Osimps__2_1, cls_Set_OInt__subset__iff_1, cls_Transitive__Closure_Otrancl__into__rtrancl_0, cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0, cls_Message_OHPair__eq_1
% 44.09/9.46 % No. of inferences in proof: 1327
% 44.09/9.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8928 ms resp. 8243 ms w/o parsing
% 44.27/9.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 44.27/9.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------