%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV342-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:59:03 AM UTC 2026
% Result : Unsatisfiable 108.14s 25.34s
% Output : Refutation 106.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 464
% Syntax : Number of formulae : 1040 ( 539 unt; 0 typ; 0 def)
% Number of atoms : 1756 (1009 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 9215 ( 745 ~; 632 |; 0 &;7838 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 105 ( 102 usr; 27 con; 0-4 aty)
% Number of variables : 2451 ( 0 ^;2451 !; 0 ?;2451 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_A_decl,type,
v_A: $i ).
thf(c_Event_Obad_decl,type,
c_Event_Obad: $i ).
thf(tc_Message_Oagent_decl,type,
tc_Message_Oagent: $i ).
thf(v_B_decl,type,
v_B: $i ).
thf(c_Event_Oevent_ONotes_decl,type,
c_Event_Oevent_ONotes: $i > $i > $i ).
thf(c_Message_Oagent_OSpy_decl,type,
c_Message_Oagent_OSpy: $i ).
thf(c_Message_Omsg_OMPair_decl,type,
c_Message_Omsg_OMPair: $i > $i > $i ).
thf(v_na_decl,type,
v_na: $i ).
thf(v_nb_decl,type,
v_nb: $i ).
thf(c_Message_Omsg_OKey_decl,type,
c_Message_Omsg_OKey: $i > $i ).
thf(v_K_decl,type,
v_K: $i ).
thf(c_List_Oset_decl,type,
c_List_Oset: $i > $i > $i ).
thf(v_evs3_decl,type,
v_evs3: $i ).
thf(tc_Event_Oevent_decl,type,
tc_Event_Oevent: $i ).
thf(c_Yahalom_Oyahalom_decl,type,
c_Yahalom_Oyahalom: $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(c_Event_Oused_decl,type,
c_Event_Oused: $i > $i ).
thf(tc_Message_Omsg_decl,type,
tc_Message_Omsg: $i ).
thf(c_Message_OsymKeys_decl,type,
c_Message_OsymKeys: $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_Event_Oevent_OGets_decl,type,
c_Event_Oevent_OGets: $i > $i > $i ).
thf(c_Message_Oagent_OServer_decl,type,
c_Message_Oagent_OServer: $i ).
thf(c_Message_Omsg_OAgent_decl,type,
c_Message_Omsg_OAgent: $i > $i ).
thf(v_Ba_decl,type,
v_Ba: $i ).
thf(c_Message_Omsg_OCrypt_decl,type,
c_Message_Omsg_OCrypt: $i > $i > $i ).
thf(c_Public_OshrK_decl,type,
c_Public_OshrK: $i > $i ).
thf(v_Aa_decl,type,
v_Aa: $i ).
thf(c_Message_Omsg_ONonce_decl,type,
c_Message_Omsg_ONonce: $i > $i ).
thf(v_NA_decl,type,
v_NA: $i ).
thf(v_NB_decl,type,
v_NB: $i ).
thf(c_Message_Oanalz_decl,type,
c_Message_Oanalz: $i > $i ).
thf(c_Event_Oknows_decl,type,
c_Event_Oknows: $i > $i > $i ).
thf(c_Event_Oevent_OSays_decl,type,
c_Event_Oevent_OSays: $i > $i > $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_List_Odrop_decl,type,
c_List_Odrop: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i ).
thf(c_Nat_Osize_decl,type,
c_Nat_Osize: $i > $i > $i ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
thf(c_List_Ohd_decl,type,
c_List_Ohd: $i > $i > $i ).
thf(c_List_Oreplicate_decl,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(c_Wellfounded__Recursion_Owf_decl,type,
c_Wellfounded__Recursion_Owf: $i > $i > $o ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(c_List_Oupt_decl,type,
c_List_Oupt: $i > $i > $i ).
thf(c_List_Otake_decl,type,
c_List_Otake: $i > $i > $i > $i ).
thf(c_Divides_Oop_Amod_decl,type,
c_Divides_Oop_Amod: $i > $i > $i > $i ).
thf(c_Numeral_Onumber__of_decl,type,
c_Numeral_Onumber__of: $i > $i > $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_List_Obutlast_decl,type,
c_List_Obutlast: $i > $i > $i ).
thf(c_List_Onth_decl,type,
c_List_Onth: $i > $i > $i > $i ).
thf(c_List_Olist__update_decl,type,
c_List_Olist__update: $i > $i > $i > $i > $i ).
thf(c_append_decl,type,
c_append: $i > $i > $i > $i ).
thf(c_List_Ozip_decl,type,
c_List_Ozip: $i > $i > $i > $i > $i ).
thf(c_List_Otl_decl,type,
c_List_Otl: $i > $i > $i ).
thf(c_List_Orev_decl,type,
c_List_Orev: $i > $i > $i ).
thf(c_List_Olast_decl,type,
c_List_Olast: $i > $i > $i ).
thf(c_Wellfounded__Relations_Oless__than_decl,type,
c_Wellfounded__Relations_Oless__than: $i ).
thf(c_List_Olists_decl,type,
c_List_Olists: $i > $i > $i ).
thf(c_List_Oremdups_decl,type,
c_List_Oremdups: $i > $i > $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(c_Message_Oparts_decl,type,
c_Message_Oparts: $i > $i ).
thf(c_Message_OHPair_decl,type,
c_Message_OHPair: $i > $i > $i ).
thf(c_Message_Omsg_OHash_decl,type,
c_Message_Omsg_OHash: $i > $i ).
thf(c_Message_Osynth_decl,type,
c_Message_Osynth: $i > $i ).
thf(c_List_Oremove1_decl,type,
c_List_Oremove1: $i > $i > $i > $i ).
thf(c_Message_OkeysFor_decl,type,
c_Message_OkeysFor: $i > $i ).
thf(c_Message_OinvKey_decl,type,
c_Message_OinvKey: $i > $i ).
thf(v_sko__uhi_decl,type,
v_sko__uhi: $i > $i > $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_List_Oconcat_decl,type,
c_List_Oconcat: $i > $i > $i ).
thf(c_Message_Omsg_ONumber_decl,type,
c_Message_Omsg_ONumber: $i > $i ).
thf(c_List_Orotate_decl,type,
c_List_Orotate: $i > $i > $i > $i ).
thf(c_List_Osublist_decl,type,
c_List_Osublist: $i > $i > $i > $i ).
thf(c_Message_Oagent_OFriend_decl,type,
c_Message_Oagent_OFriend: $i > $i ).
thf(c_Event_OinitState_decl,type,
c_Event_OinitState: $i > $i ).
thf(c_List_Olist__inter_decl,type,
c_List_Olist__inter: $i > $i > $i > $i ).
thf(c_List_Orotate1_decl,type,
c_List_Orotate1: $i > $i > $i ).
thf(c_Public_OpublicKey_decl,type,
c_Public_OpublicKey: $i > $i > $i ).
thf(c_Public_Okeymode_OEncryption_decl,type,
c_Public_Okeymode_OEncryption: $i ).
thf(c_Main_ONil__eq__concat__conv__1_decl,type,
c_Main_ONil__eq__concat__conv__1: $i > $i > $i ).
thf(c_SetInterval_OatMost_decl,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(c_Datatype_Ooption_ONone_decl,type,
c_Datatype_Ooption_ONone: $i ).
thf(tc_Datatype_Ooption_decl,type,
tc_Datatype_Ooption: $i > $i ).
thf(c_List_Olexn_decl,type,
c_List_Olexn: $i > $i > $i > $i ).
thf(c_Set_Ocontents_decl,type,
c_Set_Ocontents: $i > $i > $i ).
thf(c_List_Olistset_decl,type,
c_List_Olistset: $i > $i > $i ).
thf(c_Main_Oconcat__eq__Nil__conv__1_decl,type,
c_Main_Oconcat__eq__Nil__conv__1: $i > $i > $i ).
thf(c_Map_Omap__of_decl,type,
c_Map_Omap__of: $i > $i > $i > $i > $i ).
thf(c_Main_Oin__listsI__1_decl,type,
c_Main_Oin__listsI__1: $i > $i > $i > $i ).
thf(class_Nat_Opower_decl,type,
class_Nat_Opower: $i > $o ).
thf(class_Wellfounded__Recursion_Owellorder_decl,type,
class_Wellfounded__Recursion_Owellorder: $i > $o ).
thf(c_Infinite__Set_Oatmost__one_decl,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(class_Parity_Oeven__odd_decl,type,
class_Parity_Oeven__odd: $i > $o ).
thf(c_Relation_Otrans_decl,type,
c_Relation_Otrans: $i > $i > $o ).
thf(c_Main_Oall__not__in__conv__1_decl,type,
c_Main_Oall__not__in__conv__1: $i > $i > $i ).
thf(c_List_Olenlex_decl,type,
c_List_Olenlex: $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__mult_decl,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_Divides_Odiv_decl,type,
class_Divides_Odiv: $i > $o ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ c_List_Otake ) ) )
= A )
| ~ ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__all_0) ).
thf(645,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ c_List_Otake ) ) )
= A )
| ~ ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(351,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__1_0) ).
thf(1322,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(234,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( E @ ( A @ ( C @ ( D @ ( A @ ( B @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( E @ ( A @ ( B @ c_List_Olist__update ) ) ) ) )
| ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__overwrite_0) ).
thf(1036,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( E @ ( A @ ( C @ ( D @ ( A @ ( B @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( C @ ( E @ ( A @ ( B @ c_List_Olist__update ) ) ) ) )
| ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(355,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( C @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Says_0) ).
thf(1337,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( C @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(408,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Nonce_0) ).
thf(1469,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(368,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate1_0) ).
thf(1369,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(5,negated_conjecture,
~ ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(465,plain,
~ ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(479,plain,
~ ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[465]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_append ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev_Osimps__2_0) ).
thf(893,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(6,negated_conjecture,
tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(468,plain,
tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).
thf(555,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(447,axiom,
tc_nat @ class_Divides_Odiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_44) ).
thf(1554,plain,
tc_nat @ class_Divides_Odiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(12,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
thf(481,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(317,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__remdups_0) ).
thf(1237,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Osublist ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__nil_0) ).
thf(846,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Osublist ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ c_List_Onth ) ) )
= ( D @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( C @ c_List_Onth ) ) ) )
| ~ ( tc_nat @ ( D @ tc_List_Olist @ ( C @ c_Nat_Osize ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__drop_0) ).
thf(628,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ c_List_Onth ) ) )
= ( D @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( C @ c_List_Onth ) ) ) )
| ~ ( tc_nat @ ( D @ tc_List_Olist @ ( C @ c_Nat_Osize ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Ohd ) )
= ( C @ ( A @ c_List_Ohd ) ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__append2_0) ).
thf(1031,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Ohd ) )
= ( C @ ( A @ c_List_Ohd ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Ozip ) ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).
thf(977,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Ozip ) ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).
thf(1211,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_0) ).
thf(523,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(442,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).
thf(1544,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(462,axiom,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OServer_A_58_Abad_A_61_61_AFalse_0) ).
thf(1591,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(330,axiom,
! [A: $i] :
( ( ( A @ c_Message_OinvKey )
= A )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OinvKey__K_0) ).
thf(1269,plain,
! [A: $i] :
( ( ( A @ c_Message_OinvKey )
= A )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(1682,plain,
( ( ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[468,479]) ).
thf(1683,plain,
( ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[1682]) ).
thf(1692,plain,
( ( tc_nat != tc_Message_Omsg )
| ( ( v_evs3 @ c_Event_Oused )
!= c_Message_OsymKeys )
| ( ( v_K @ c_Message_Omsg_OKey )
!= v_K ) ),
inference(simp,[status(thm)],[1683]) ).
thf(342,axiom,
! [A: $i] :
( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff_1) ).
thf(1305,plain,
! [A: $i] :
( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(394,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONonce ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_ANonce_AN2_A_61_61_AFalse_0) ).
thf(1437,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONonce ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(236,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).
thf(1041,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( D @ ( A @ ( B @ c_List_Olist__update ) ) ) @ c_List_Onth ) ) )
= D )
| ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__list__update__eq_0) ).
thf(873,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( D @ ( A @ ( B @ c_List_Olist__update ) ) ) @ c_List_Onth ) ) )
= D )
| ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(301,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__analzD__dest_0) ).
thf(1205,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(173,axiom,
! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
thf(878,plain,
! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(85,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oremdups ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_1) ).
thf(654,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oremdups ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(655,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oremdups ) )
= c_List_Olist_ONil ),
inference(lifteq,[status(thm)],[654]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
thf(511,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OMPair_0) ).
thf(1173,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(417,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpriK__in__initState_0) ).
thf(1486,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(390,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OKey ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AKey_AK2_A_61_61_AFalse_0) ).
thf(1426,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OKey ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(348,axiom,
tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OSpy_A_58_Abad_A_61_61_ATrue_0) ).
thf(1317,plain,
tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(1,negated_conjecture,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(467,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(477,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[467]) ).
thf(1664,plain,
( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1317,477]) ).
thf(1665,plain,
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1664]) ).
thf(1668,plain,
( ( tc_Message_Oagent != tc_Message_Oagent )
| ( c_Event_Obad != c_Event_Obad )
| ( c_Message_Oagent_OSpy != v_A ) ),
inference(simp,[status(thm)],[1665]) ).
thf(1671,plain,
c_Message_Oagent_OSpy != v_A,
inference(simp,[status(thm)],[1668]) ).
thf(273,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oconcat ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__1_0) ).
thf(1137,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oconcat ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_0 @ c_List_Otake ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__eq__Nil_1) ).
thf(500,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_0 @ c_List_Otake ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(141,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
thf(797,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv_0) ).
thf(715,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(3,negated_conjecture,
~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_nb @ c_Message_Omsg_OMPair ) @ ( v_na @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_10) ).
thf(472,plain,
~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_nb @ c_Message_Omsg_OMPair ) @ ( v_na @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(315,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__privateKey_0) ).
thf(1233,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_Nat_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate_0) ).
thf(814,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_Nat_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(327,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_ONonce ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3_0) ).
thf(1260,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_ONonce ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_1) ).
thf(747,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(10,negated_conjecture,
tc_Message_Oagent @ ( c_Event_Obad @ ( v_Aa @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_8) ).
thf(466,plain,
tc_Message_Oagent @ ( c_Event_Obad @ ( v_Aa @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1592,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[1591]) ).
thf(1632,plain,
( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Aa @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[466,1592]) ).
thf(1633,plain,
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Aa @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
inference(simp,[status(thm)],[1632]) ).
thf(1638,plain,
( ( tc_Message_Oagent != tc_Message_Oagent )
| ( c_Event_Obad != c_Event_Obad )
| ( v_Aa != c_Message_Oagent_OServer ) ),
inference(simp,[status(thm)],[1633]) ).
thf(1640,plain,
v_Aa != c_Message_Oagent_OServer,
inference(simp,[status(thm)],[1638]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) )
| ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__drop_0) ).
thf(1063,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) )
| ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(362,axiom,
! [A: $i] :
( c_Message_Oagent_OSpy
!= ( A @ c_Message_Oagent_OFriend ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__6_0) ).
thf(1354,plain,
! [A: $i] :
( c_Message_Oagent_OSpy
!= ( A @ c_Message_Oagent_OFriend ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(403,axiom,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
= ( A @ c_Message_Oanalz ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__idem_0) ).
thf(1458,plain,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
= ( A @ c_Message_Oanalz ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(257,axiom,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Message_Omsg_ONumber @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__2_0) ).
thf(1095,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Message_Omsg_ONumber @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).
thf(709,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(2,negated_conjecture,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(470,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(478,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[470]) ).
thf(1609,plain,
( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Aa @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[466,478]) ).
thf(1610,plain,
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Aa @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) ),
inference(simp,[status(thm)],[1609]) ).
thf(1612,plain,
( ( tc_Message_Oagent != tc_Message_Oagent )
| ( c_Event_Obad != c_Event_Obad )
| ( v_Aa != v_B ) ),
inference(simp,[status(thm)],[1610]) ).
thf(1613,plain,
v_Aa != v_B,
inference(simp,[status(thm)],[1612]) ).
thf(4,negated_conjecture,
tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs3 @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(475,plain,
tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs3 @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1646,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs3 @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[475,477]) ).
thf(1647,plain,
( ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs3 @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1646]) ).
thf(1650,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Oagent )
| ( c_Yahalom_Oyahalom != c_Event_Obad )
| ( v_evs3 != v_A ) ),
inference(simp,[status(thm)],[1647]) ).
thf(320,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth__analz_0) ).
thf(1243,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_insert ) ) @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__HPair_0) ).
thf(1127,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_insert ) ) @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(177,axiom,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ c_List_Oremdups ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_1) ).
thf(885,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ c_List_Oremdups ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(238,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
thf(1046,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(48,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( C @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ozip ) ) ) )
= ( F @ ( C @ tc_prod ) @ ( F @ ( C @ ( E @ ( B @ c_List_Ozip ) ) ) @ ( F @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Cons__Cons_0) ).
thf(565,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( C @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ozip ) ) ) )
= ( F @ ( C @ tc_prod ) @ ( F @ ( C @ ( E @ ( B @ c_List_Ozip ) ) ) @ ( F @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(367,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__2_0) ).
thf(1366,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(430,axiom,
! [B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( c_List_Olist_ONil @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OCrypt__notin__used__empty_0) ).
thf(1518,plain,
! [B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( c_List_Olist_ONil @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(328,axiom,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__synth_0) ).
thf(1265,plain,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(313,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
thf(1228,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(414,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__in__knows_0) ).
thf(1482,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
thf(504,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(402,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J = E )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( L @ ( K @ ( J @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( G @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_2) ).
thf(1455,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J = E )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( L @ ( K @ ( J @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( G @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
= ( tc_Message_Omsg @ ( D @ c_Event_Oused @ ( tc_Message_Omsg @ ( c_emptyset @ ( C @ c_insert ) ) @ c_Message_Oparts @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oused__Says_0) ).
thf(949,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
= ( tc_Message_Omsg @ ( D @ c_Event_Oused @ ( tc_Message_Omsg @ ( c_emptyset @ ( C @ c_insert ) ) @ c_Message_Oparts @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_0) ).
thf(917,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OHash_0) ).
thf(702,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(405,axiom,
( ( tc_Message_Oagent @ ( c_Message_Oagent_OServer @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__1_0) ).
thf(1462,plain,
( ( tc_Message_Oagent @ ( c_Message_Oagent_OServer @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv_0) ).
thf(1132,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(443,axiom,
! [A: $i] :
( c_Message_Oagent_OServer
!= ( A @ c_Message_Oagent_OFriend ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__1_0) ).
thf(1545,plain,
! [A: $i] :
( c_Message_Oagent_OServer
!= ( A @ c_Message_Oagent_OFriend ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
thf(902,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(45,axiom,
! [A: $i] :
( ( c_0 @ ( A @ c_List_Oupt ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_1) ).
thf(559,plain,
! [A: $i] :
( ( c_0 @ ( A @ c_List_Oupt ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(255,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) )
!= ( D @ ( C @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__neq__privateKey_0) ).
thf(1087,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) )
!= ( D @ ( C @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_append ) ) @ c_List_Orev ) )
= ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_1) ).
thf(1147,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_append ) ) @ c_List_Orev ) )
= ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(413,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OKey )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__4_0) ).
thf(1479,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OKey )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(1013,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(175,axiom,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Message_Omsg_ONonce @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__3_0) ).
thf(881,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Message_Omsg_ONonce @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(453,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OKey )
!= ( B @ c_Message_Omsg_OKey ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4_0) ).
thf(1568,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OKey )
!= ( B @ c_Message_Omsg_OKey ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(9,negated_conjecture,
tc_Message_Oagent @ ( c_Event_Obad @ ( v_Ba @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_7) ).
thf(469,plain,
tc_Message_Oagent @ ( c_Event_Obad @ ( v_Ba @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1634,plain,
( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Ba @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[469,1592]) ).
thf(1635,plain,
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Ba @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
inference(simp,[status(thm)],[1634]) ).
thf(1639,plain,
( ( tc_Message_Oagent != tc_Message_Oagent )
| ( c_Event_Obad != c_Event_Obad )
| ( v_Ba != c_Message_Oagent_OServer ) ),
inference(simp,[status(thm)],[1635]) ).
thf(1641,plain,
v_Ba != c_Message_Oagent_OServer,
inference(simp,[status(thm)],[1639]) ).
thf(365,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).
thf(1362,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Ozip ) ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).
thf(1100,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Ozip ) ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(208,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Obutlast ) @ c_append ) ) )
= A )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__butlast__last__id_0) ).
thf(969,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Obutlast ) @ c_append ) ) )
= A )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Oset ) )
= ( C @ ( B @ c_List_Oset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate_0) ).
thf(1347,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Oset ) )
= ( C @ ( B @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(386,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_0) ).
thf(1415,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Olist__inter ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__1_0) ).
thf(756,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Olist__inter ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A = c_0 )
| ( ( C @ ( B @ ( A @ c_List_Otake ) ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__eq__Nil_0) ).
thf(591,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A = c_0 )
| ( ( C @ ( B @ ( A @ c_List_Otake ) ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(263,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Oset ) )
= ( C @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( A @ c_List_Oset ) @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__append_0) ).
thf(1109,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Oset ) )
= ( C @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( A @ c_List_Oset ) @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(280,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_List_Oconcat ) )
= c_List_Olist_ONil )
| ( ( B @ ( A @ c_Main_Oconcat__eq__Nil__conv__1 ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_2) ).
thf(1151,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_List_Oconcat ) )
= c_List_Olist_ONil )
| ( ( B @ ( A @ c_Main_Oconcat__eq__Nil__conv__1 ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(228,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_0) ).
thf(1020,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(207,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
thf(966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(292,axiom,
! [B: $i,A: $i] :
( ( tc_Event_Oevent @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__2_0) ).
thf(1183,plain,
! [B: $i,A: $i] :
( ( tc_Event_Oevent @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(150,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__rev__ident_0) ).
thf(821,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(112,axiom,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__emptyE_0) ).
thf(725,plain,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(726,plain,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[725]) ).
thf(277,axiom,
( ( c_emptyset @ c_Message_Oparts )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__empty_0) ).
thf(1145,plain,
( ( c_emptyset @ c_Message_Oparts )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(1146,plain,
( ( c_emptyset @ c_Message_Oparts )
= c_emptyset ),
inference(lifteq,[status(thm)],[1145]) ).
thf(2075,plain,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(rewrite,[status(thm)],[726,1146]) ).
thf(2076,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[468,2075]) ).
thf(2077,plain,
! [A: $i] :
( ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[2076]) ).
thf(2093,plain,
! [A: $i] :
( ( tc_nat != tc_Message_Omsg )
| ( c_emptyset != c_Message_OsymKeys )
| ( v_K != A ) ),
inference(simp,[status(thm)],[2077]) ).
thf(2105,plain,
( ( tc_nat != tc_Message_Omsg )
| ( c_emptyset != c_Message_OsymKeys ) ),
inference(simp,[status(thm)],[2093]) ).
thf(400,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__2_0) ).
thf(1450,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_0) ).
thf(485,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(156,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OHash ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AHash_AZ2_A_61_61_AFalse_0) ).
thf(834,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OHash ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( D @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osame__append__eq_0) ).
thf(905,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( D @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(8,negated_conjecture,
~ ( tc_Message_Omsg @ ( v_evs3 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(474,plain,
~ ( tc_Message_Omsg @ ( v_evs3 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(480,plain,
~ ( tc_Message_Omsg @ ( v_evs3 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[474]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
thf(602,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Oset ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty_0) ).
thf(687,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Oset ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_List_Olist @ ( B @ ( A @ c_append ) ) @ c_List_Oconcat ) )
= ( C @ ( C @ ( B @ c_List_Oconcat ) @ ( C @ ( A @ c_List_Oconcat ) @ c_append ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__append_0) ).
thf(692,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_List_Olist @ ( B @ ( A @ c_append ) ) @ c_List_Oconcat ) )
= ( C @ ( C @ ( B @ c_List_Oconcat ) @ ( C @ ( A @ c_List_Oconcat ) @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( B @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__same__eq_0) ).
thf(734,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( B @ ( D @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
= ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair_2) ).
thf(660,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
= ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(216,axiom,
( ( tc_nat @ ( c_0 @ c_SetInterval_OatMost ) )
= ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__0_0) ).
thf(988,plain,
( ( tc_nat @ ( c_0 @ c_SetInterval_OatMost ) )
= ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(382,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I = C )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( L @ ( K @ ( J @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( G @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_1) ).
thf(1405,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I = C )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( L @ ( K @ ( J @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( G @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(261,axiom,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__idem_0) ).
thf(1104,plain,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).
thf(507,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( C @ ( A @ c_List_Oupt ) @ c_List_Onth ) ) )
= ( tc_nat @ ( B @ ( A @ c_plus ) ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__upt_0) ).
thf(527,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( C @ ( A @ c_List_Oupt ) @ c_List_Onth ) ) )
= ( tc_nat @ ( B @ ( A @ c_plus ) ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1680,plain,
( ( ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1317,479]) ).
thf(1681,plain,
( ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
inference(simp,[status(thm)],[1680]) ).
thf(1696,plain,
( ( tc_Message_Omsg != tc_Message_Oagent )
| ( ( v_evs3 @ c_Event_Oused )
!= c_Event_Obad )
| ( ( v_K @ c_Message_Omsg_OKey )
!= c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[1681]) ).
thf(306,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONonce__synth__eq_0) ).
thf(1215,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( C @ ( A @ c_List_Olist__update ) ) ) )
= A )
| ~ ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__beyond_0) ).
thf(634,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( C @ ( A @ c_List_Olist__update ) ) ) )
= A )
| ~ ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(250,axiom,
! [B: $i,A: $i] :
( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq_1) ).
thf(1074,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(189,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_1) ).
thf(920,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_List_Oremdups ) )
= A )
| ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq_0) ).
thf(678,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_List_Oremdups ) )
= A )
| ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
= A )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).
thf(546,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
= A )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_append ) ) @ c_Nat_Osize ) )
= ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ c_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__append_0) ).
thf(925,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_append ) ) @ c_Nat_Osize ) )
= ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ c_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(298,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
= ( C @ ( B @ ( D @ c_List_Olist__inter ) ) ) )
| ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_1) ).
thf(1199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
= ( C @ ( B @ ( D @ c_List_Olist__inter ) ) ) )
| ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(761,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Hash_0) ).
thf(810,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(332,axiom,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OServer ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__2_0) ).
thf(1274,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OServer ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(310,axiom,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oanalz )
= ( A @ c_Message_Oparts ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__parts_0) ).
thf(1223,plain,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oanalz )
= ( A @ c_Message_Oparts ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(358,axiom,
! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK_AX1_A_58_AsymKeys_A_61_61_ATrue_0) ).
thf(1343,plain,
! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(133,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( E @ tc_prod ) @ ( A @ ( C @ ( E @ ( B @ ( D @ c_List_Ozip ) ) ) @ c_List_Onth ) ) )
= ( C @ ( E @ ( C @ ( A @ ( B @ c_List_Onth ) ) @ ( E @ ( A @ ( D @ c_List_Onth ) ) @ c_Pair ) ) ) ) )
| ~ ( tc_nat @ ( E @ tc_List_Olist @ ( D @ c_Nat_Osize ) @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__zip_0) ).
thf(778,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( E @ tc_prod ) @ ( A @ ( C @ ( E @ ( B @ ( D @ c_List_Ozip ) ) ) @ c_List_Onth ) ) )
= ( C @ ( E @ ( C @ ( A @ ( B @ c_List_Onth ) ) @ ( E @ ( A @ ( D @ c_List_Onth ) ) @ c_Pair ) ) ) ) )
| ~ ( tc_nat @ ( E @ tc_List_Olist @ ( D @ c_Nat_Osize ) @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(457,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ c_List_Oconcat ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_0) ).
thf(1580,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ c_List_Oconcat ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpubK__neq__shrK_0) ).
thf(1255,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_0) ).
thf(1123,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(307,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( B @ c_in ) ) )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Onew__keys__not__used_0) ).
thf(1217,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( B @ c_in ) ) )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(423,axiom,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__into__used_0) ).
thf(1502,plain,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
thf(561,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(418,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) )
!= ( C @ c_Public_OshrK ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__neq__pubK_0) ).
thf(1487,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) )
!= ( C @ c_Public_OshrK ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(137,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= ( C @ ( A @ c_List_Olast ) ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_1) ).
thf(788,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= ( C @ ( A @ c_List_Olast ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ c_List_Onth ) ) )
= C )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__replicate_0) ).
thf(729,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ c_List_Onth ) ) )
= C )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(375,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Agent_0) ).
thf(1387,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_1) ).
thf(910,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(389,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( E @ ( D @ c_Event_Oevent_ONotes ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__3_0) ).
thf(1423,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( E @ ( D @ c_Event_Oevent_ONotes ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(13,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_1) ).
thf(484,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(174,axiom,
( ( c_emptyset @ c_Message_OkeysFor )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__empty_0) ).
thf(879,plain,
( ( c_emptyset @ c_Message_OkeysFor )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(448,axiom,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil
= ( B @ ( A @ c_List_Oconcat ) ) )
| ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_Main_ONil__eq__concat__conv__1 ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_1) ).
thf(1555,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil
= ( B @ ( A @ c_List_Oconcat ) ) )
| ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_Main_ONil__eq__concat__conv__1 ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ c_insert ) ) ) )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Notes_0) ).
thf(1178,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ c_insert ) ) ) )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(154,axiom,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_1) ).
thf(830,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(283,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( B @ ( A @ c_List_Oremdups ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_0) ).
thf(1159,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( B @ ( A @ c_List_Oremdups ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_0) ).
thf(493,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_append ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__take__drop__id_0) ).
thf(551,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_append ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(378,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_1) ).
thf(1392,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(454,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ ( A @ c_insert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__MPair_0) ).
thf(1573,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ ( A @ c_insert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(262,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Orotate1 ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_0) ).
thf(1106,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Orotate1 ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(364,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( B @ c_in ) ) )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__analz__shrK_1) ).
thf(1360,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( B @ c_in ) ) )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(276,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(1143,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(2078,plain,
! [A: $i] :
( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs3 @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[475,2075]) ).
thf(2079,plain,
! [A: $i] :
( ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs3 @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[2078]) ).
thf(2096,plain,
! [A: $i] :
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Omsg )
| ( c_emptyset != c_Yahalom_Oyahalom )
| ( v_evs3 != A ) ),
inference(simp,[status(thm)],[2079]) ).
thf(2100,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Omsg )
| ( c_emptyset != c_Yahalom_Oyahalom ) ),
inference(simp,[status(thm)],[2096]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
thf(650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_append ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__append_0) ).
thf(1111,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(1138,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oconcat ) )
= c_List_Olist_ONil ),
inference(lifteq,[status(thm)],[1137]) ).
thf(169,axiom,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Message_Omsg_OKey @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__4_0) ).
thf(869,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Message_Omsg_OKey @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Otl ) )
= ( C @ ( B @ ( C @ ( A @ c_List_Otl ) @ c_append ) ) ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl__append2_0) ).
thf(610,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Otl ) )
= ( C @ ( B @ ( C @ ( A @ c_List_Otl ) @ c_append ) ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(266,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq_0) ).
thf(1118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(989,plain,
( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) )
= ( tc_nat @ ( c_0 @ c_SetInterval_OatMost ) ) ),
inference(lifteq,[status(thm)],[988]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_0) ).
thf(742,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(54,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).
thf(577,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(578,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(lifteq,[status(thm)],[577]) ).
thf(437,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__partsD__dest_0) ).
thf(1534,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(226,axiom,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_1) ).
thf(1016,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(1017,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
= c_List_Olist_ONil ),
inference(lifteq,[status(thm)],[1016]) ).
thf(212,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_union ) ) )
= ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
thf(980,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_union ) ) )
= ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(460,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rev_0) ).
thf(1587,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(440,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).
thf(1540,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(223,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2_1) ).
thf(1006,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(164,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_0) ).
thf(857,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(379,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__conj__parts_0) ).
thf(1397,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(7,negated_conjecture,
tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_Ba @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_Ba @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OGets ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(471,plain,
tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_Ba @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_Ba @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OGets ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(420,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Hash_0) ).
thf(1493,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(353,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__6_0) ).
thf(1329,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
thf(488,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(195,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ c_List_Onth ) ) )
= ( D @ ( A @ ( C @ c_List_Onth ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__take_0) ).
thf(933,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ c_List_Onth ) ) )
= ( D @ ( A @ ( C @ c_List_Onth ) ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(122,axiom,
! [A: $i] :
( ( A @ c_Event_OinitState @ c_Message_Oparts @ c_Message_OkeysFor )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OkeysFor__parts__initState_0) ).
thf(753,plain,
! [A: $i] :
( ( A @ c_Event_OinitState @ c_Message_Oparts @ c_Message_OkeysFor )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).
thf(537,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__1_0) ).
thf(669,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(476,plain,
~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_nb @ c_Message_Omsg_OMPair ) @ ( v_na @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[472]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
thf(642,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_Nat_Osize ) )
= ( D @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__list__update_0) ).
thf(637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_Nat_Osize ) )
= ( D @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(398,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__synthD__dest_0) ).
thf(1446,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(235,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_1) ).
thf(1039,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_0) ).
thf(706,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2_0) ).
thf(1028,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(253,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Number_0) ).
thf(1082,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(302,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OMPair__used_0) ).
thf(1207,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(352,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_1) ).
thf(1324,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(220,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq_1) ).
thf(997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(340,axiom,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) ) )
| ( tc_nat @ ( B @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Key_0) ).
thf(1297,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) ) )
| ( tc_nat @ ( B @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(446,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth__eq_0) ).
thf(1552,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(240,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
thf(1050,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_union ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).
thf(984,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_union ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(110,axiom,
( ( c_emptyset @ c_Message_Oanalz )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__empty_0) ).
thf(720,plain,
( ( c_emptyset @ c_Message_Oanalz )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(721,plain,
( ( c_emptyset @ c_Message_Oanalz )
= c_emptyset ),
inference(lifteq,[status(thm)],[720]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
thf(1002,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(433,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__5_0) ).
thf(1525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Odrop ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop_Odrop__Nil_0) ).
thf(622,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Odrop ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_List_Oupt ) @ c_List_Ohd ) )
= A )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__upt_0) ).
thf(837,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_List_Oupt ) @ c_List_Ohd ) )
= A )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(435,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olenlex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
thf(1530,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olenlex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(439,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OAgent__synth_0) ).
thf(1539,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Notes_1) ).
thf(1382,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_0 @ c_List_Oreplicate ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__0_0) ).
thf(569,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_0 @ c_List_Oreplicate ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(391,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__3_0) ).
thf(1429,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(21,axiom,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_2) ).
thf(502,plain,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(503,plain,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
inference(lifteq,[status(thm)],[502]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ ( A @ c_List_Oupt ) @ ( B @ c_List_Otake ) ) )
= ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( A @ c_List_Oupt ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__upt_0) ).
thf(605,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( C @ ( A @ c_List_Oupt ) @ ( B @ c_List_Otake ) ) )
= ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( A @ c_List_Oupt ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(393,axiom,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
thf(1434,plain,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(349,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_2) ).
thf(1318,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( A @ ( B @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2_0) ).
thf(805,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( A @ ( B @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(1688,plain,
( ( ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Ba @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[469,479]) ).
thf(1689,plain,
( ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Ba @ c_in ) ) ) ),
inference(simp,[status(thm)],[1688]) ).
thf(1695,plain,
( ( tc_Message_Omsg != tc_Message_Oagent )
| ( ( v_evs3 @ c_Event_Oused )
!= c_Event_Obad )
| ( ( v_K @ c_Message_Omsg_OKey )
!= v_Ba ) ),
inference(simp,[status(thm)],[1689]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_List_Otake ) ) )
= c_List_Olist_ONil )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__Cons__number__of_0) ).
thf(541,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_List_Otake ) ) )
= c_List_Olist_ONil )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(451,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Number_0) ).
thf(1563,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
= ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( tc_Message_Omsg @ ( c_emptyset @ ( B @ c_insert ) ) @ c_Message_Oparts @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oused__Notes_0) ).
thf(1054,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
= ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( tc_Message_Omsg @ ( c_emptyset @ ( B @ c_insert ) ) @ c_Message_Oparts @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(287,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) )
!= ( E @ tc_List_Olist @ ( D @ c_Nat_Osize ) ) )
| ( ( E @ ( C @ ( A @ ( E @ ( C @ ( D @ ( B @ c_List_Ozip ) ) ) @ c_Map_Omap__of ) ) ) )
!= c_Datatype_Ooption_ONone )
| ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_0) ).
thf(1170,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) )
!= ( E @ tc_List_Olist @ ( D @ c_Nat_Osize ) ) )
| ( ( E @ ( C @ ( A @ ( E @ ( C @ ( D @ ( B @ c_List_Ozip ) ) ) @ c_Map_Omap__of ) ) ) )
!= c_Datatype_Ooption_ONone )
| ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(336,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
thf(1286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(294,axiom,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__analz_0) ).
thf(1187,plain,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(429,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__4_0) ).
thf(1515,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_0 @ c_List_Odrop ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
thf(530,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_0 @ c_List_Odrop ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_0) ).
thf(662,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(299,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).
thf(1202,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ohd ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd_Osimps_0) ).
thf(792,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ohd ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ c_List_Oconcat ) )
!= c_List_Olist_ONil )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_0) ).
thf(1466,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ c_List_Oconcat ) )
!= c_List_Olist_ONil )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(249,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey )
!= ( D @ ( C @ c_Public_OpublicKey ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OprivateKey_Ab1_AA1_A_61_ApublicKey_Ac1_AA_H1_A_61_61_AFalse_0) ).
thf(1071,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey )
!= ( D @ ( C @ c_Public_OpublicKey ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(230,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
= ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osingleton__rev__conv_1) ).
thf(1026,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
= ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__1_0) ).
thf(1167,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
thf(953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(293,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OKey__synth__eq_0) ).
thf(1185,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(131,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orotate1 ) @ c_Nat_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate1_0) ).
thf(773,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orotate1 ) @ c_Nat_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(140,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( D @ ( C @ ( F @ c_append ) ) @ ( B @ ( A @ ( E @ c_append ) ) @ c_List_Ozip ) ) ) )
= ( D @ ( B @ tc_prod ) @ ( D @ ( B @ ( C @ ( A @ c_List_Ozip ) ) ) @ ( D @ ( B @ ( F @ ( E @ c_List_Ozip ) ) ) @ c_append ) ) ) )
| ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize ) )
!= ( D @ tc_List_Olist @ ( F @ c_Nat_Osize ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__append_0) ).
thf(794,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( D @ ( C @ ( F @ c_append ) ) @ ( B @ ( A @ ( E @ c_append ) ) @ c_List_Ozip ) ) ) )
= ( D @ ( B @ tc_prod ) @ ( D @ ( B @ ( C @ ( A @ c_List_Ozip ) ) ) @ ( D @ ( B @ ( F @ ( E @ c_List_Ozip ) ) ) @ c_append ) ) ) )
| ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize ) )
!= ( D @ tc_List_Olist @ ( F @ c_Nat_Osize ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_0) ).
thf(618,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(308,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__in__used_0) ).
thf(1219,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(415,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Gets_0) ).
thf(1483,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(331,axiom,
( ( tc_Message_Oagent @ ( c_Message_Oagent_OSpy @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__3_0) ).
thf(1272,plain,
( ( tc_Message_Oagent @ ( c_Message_Oagent_OSpy @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(1273,plain,
( ( tc_Message_Oagent @ ( c_Message_Oagent_OSpy @ c_Nat_Osize ) )
= c_0 ),
inference(lifteq,[status(thm)],[1272]) ).
thf(444,axiom,
! [A: $i] :
( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff_0) ).
thf(1548,plain,
! [A: $i] :
( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(119,axiom,
! [A: $i] :
( ( A @ c_Message_OinvKey @ c_Message_OinvKey )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
thf(745,plain,
! [A: $i] :
( ( A @ c_Message_OinvKey @ c_Message_OinvKey )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(464,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3_1) ).
thf(1595,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
thf(573,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(115,axiom,
! [A: $i] :
( c_emptyset
= ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2_1) ).
thf(732,plain,
! [A: $i] :
( c_emptyset
= ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(733,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[732]) ).
thf(272,axiom,
! [A: $i] :
( ( c_List_Olist_ONil @ ( A @ c_Event_Oknows ) )
= ( A @ c_Event_OinitState ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows_Oknows__Nil_0) ).
thf(1135,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ ( A @ c_Event_Oknows ) )
= ( A @ c_Event_OinitState ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(1642,plain,
( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) )
!= ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs3 @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[475,1592]) ).
thf(1643,plain,
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) )
!= ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs3 @ c_in ) ) ) ),
inference(simp,[status(thm)],[1642]) ).
thf(1648,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Oagent )
| ( c_Yahalom_Oyahalom != c_Event_Obad )
| ( c_Message_Oagent_OServer != v_evs3 ) ),
inference(simp,[status(thm)],[1643]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2_0) ).
thf(750,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(427,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
= ( C @ ( C @ ( B @ ( D @ c_List_Olist__inter ) ) @ ( A @ c_List_Olist_OCons ) ) ) )
| ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_0) ).
thf(1510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
= ( C @ ( C @ ( B @ ( D @ c_List_Olist__inter ) ) @ ( A @ c_List_Olist_OCons ) ) ) )
| ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_List_Odrop ) ) )
= ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__Cons__number__of_0) ).
thf(513,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ c_List_Odrop ) ) )
= ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_List_Olist @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oconcat ) )
= ( C @ ( C @ ( B @ c_List_Oconcat ) @ ( A @ c_append ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__2_0) ).
thf(694,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_List_Olist @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oconcat ) )
= ( C @ ( C @ ( B @ c_List_Oconcat ) @ ( A @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(376,axiom,
tc_nat @ class_Parity_Oeven__odd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_47) ).
thf(1389,plain,
tc_nat @ class_Parity_Oeven__odd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__5_0) ).
thf(843,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(1614,plain,
( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Ba @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[469,478]) ).
thf(1615,plain,
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Ba @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) ),
inference(simp,[status(thm)],[1614]) ).
thf(1618,plain,
( ( tc_Message_Oagent != tc_Message_Oagent )
| ( c_Event_Obad != c_Event_Obad )
| ( v_Ba != v_B ) ),
inference(simp,[status(thm)],[1615]) ).
thf(1620,plain,
v_Ba != v_B,
inference(simp,[status(thm)],[1618]) ).
thf(55,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
thf(579,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(204,axiom,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_insert ) ) @ c_Message_Oparts )
= ( B @ c_Message_Oparts ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__cut__eq_0) ).
thf(958,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_insert ) ) @ c_Message_Oparts )
= ( B @ c_Message_Oparts ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(431,axiom,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_insert ) ) @ c_Message_Oanalz @ c_Message_Osynth )
= ( B @ c_Message_Oanalz @ c_Message_Osynth ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OFake__analz__eq_0) ).
thf(1520,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_insert ) ) @ c_Message_Oanalz @ c_Message_Osynth )
= ( B @ c_Message_Oanalz @ c_Message_Osynth ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(312,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONonce__synth__eq_1) ).
thf(1226,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(57,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).
thf(584,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(281,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) )
= ( B @ ( A @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair_2) ).
thf(1154,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) )
= ( B @ ( A @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_union ) ) )
= ( D @ ( D @ ( C @ ( A @ c_union ) ) @ ( B @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
thf(826,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_union ) ) )
= ( D @ ( D @ ( C @ ( A @ c_union ) ) @ ( B @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(79,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(641,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1_0) ).
thf(936,plain,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(369,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_2) ).
thf(1371,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
thf(1312,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(244,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).
thf(1058,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(318,axiom,
tc_nat @ class_Nat_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_12) ).
thf(1239,plain,
tc_nat @ class_Nat_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(354,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3_0) ).
thf(1332,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(256,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONumber )
!= ( B @ c_Message_Omsg_ONumber ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2_0) ).
thf(1090,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONumber )
!= ( B @ c_Message_Omsg_ONumber ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1355,plain,
! [A: $i] :
( c_Message_Oagent_OSpy
!= ( A @ c_Message_Oagent_OFriend ) ),
inference(polarity_switch,[status(thm)],[1354]) ).
thf(1356,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OSpy ),
inference(lifteq,[status(thm)],[1355]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Key_0) ).
thf(1139,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(424,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( E @ ( D @ c_Event_Oevent_OGets ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__1_0) ).
thf(1503,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( E @ ( D @ c_Event_Oevent_OGets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( C @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( C @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OGets__imp__analz__Spy__dest_0) ).
thf(1258,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( C @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( C @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(105,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OFake__parts__insert__in__Un__dest_0) ).
thf(704,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth__analz_1) ).
thf(1464,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(199,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_OkeysFor )
= ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_Message_OkeysFor @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__Un_0) ).
thf(947,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_OkeysFor )
= ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_Message_OkeysFor @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
= ( C @ ( B @ c_List_Oremdups ) ) )
| ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_0) ).
thf(1194,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
= ( C @ ( B @ c_List_Oremdups ) ) )
| ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(303,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OBody__dest_0) ).
thf(1209,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(182,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oset ) )
= ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps__2_0) ).
thf(900,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oset ) )
= ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(334,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__pubK_0) ).
thf(1282,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(135,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).
thf(784,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(239,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(1048,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(361,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_0) ).
thf(1349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(1600,plain,
( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Aa @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[466,477]) ).
thf(1601,plain,
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Aa @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1600]) ).
thf(1602,plain,
( ( tc_Message_Oagent != tc_Message_Oagent )
| ( c_Event_Obad != c_Event_Obad )
| ( v_Aa != v_A ) ),
inference(simp,[status(thm)],[1601]) ).
thf(1603,plain,
v_Aa != v_A,
inference(simp,[status(thm)],[1602]) ).
thf(441,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_1) ).
thf(1542,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Otl ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__1_0) ).
thf(567,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Otl ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(68,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).
thf(616,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_Divides_Oop_Amod ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(343,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ ( B @ v_sko__uhi ) @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_0) ).
thf(1307,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ ( B @ v_sko__uhi ) @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( A @ ( B @ c_append ) ) @ c_List_Olast ) )
= ( C @ ( A @ c_List_Olast ) ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__appendR_0) ).
thf(764,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( A @ ( B @ c_append ) ) @ c_List_Olast ) )
= ( C @ ( A @ c_List_Olast ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(211,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
thf(979,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Orev ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv_0) ).
thf(681,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Orev ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(383,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__shrK_0) ).
thf(1408,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(461,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
= ( C @ c_Event_Oused ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oused__Gets_0) ).
thf(1589,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
= ( C @ c_Event_Oused ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(217,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_1) ).
thf(990,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).
thf(509,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(880,plain,
( ( c_emptyset @ c_Message_OkeysFor )
= c_emptyset ),
inference(lifteq,[status(thm)],[879]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( A @ c_List_Obutlast ) @ ( B @ c_List_Olist_OCons ) ) ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_1) ).
thf(599,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( A @ c_List_Obutlast ) @ ( B @ c_List_Olist_OCons ) ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(370,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Nonce_0) ).
thf(1376,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(166,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_append ) ) @ c_append ) ) )
= ( C @ ( C @ ( D @ ( B @ c_append ) ) @ ( A @ c_append ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__assoc_0) ).
thf(863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_append ) ) @ c_append ) ) )
= ( C @ ( C @ ( D @ ( B @ c_append ) ) @ ( A @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(289,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( B @ ( B @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_List_Ohd ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__in__set_0) ).
thf(1175,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( B @ ( B @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_List_Ohd ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(179,axiom,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil
= ( B @ ( A @ c_List_Oconcat ) ) )
| ( ( B @ ( A @ c_Main_ONil__eq__concat__conv__1 ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_2) ).
thf(890,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil
= ( B @ ( A @ c_List_Oconcat ) ) )
| ( ( B @ ( A @ c_Main_ONil__eq__concat__conv__1 ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(409,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONumber__synth_0) ).
thf(1471,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(252,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Orotate1 ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_1) ).
thf(1080,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Orotate1 ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( B @ ( A @ c_List_Oupt ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_0) ).
thf(631,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( B @ ( A @ c_List_Oupt ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(34,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
thf(535,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Public_OpublicKey ) )
!= ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject_1) ).
thf(816,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Public_OpublicKey ) )
!= ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Obutlast ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__1_0) ).
thf(594,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Obutlast ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(284,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ( ( B @ ( A @ ( D @ c_append ) ) )
!= ( B @ ( C @ ( E @ c_append ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_2) ).
thf(1162,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ( ( B @ ( A @ ( D @ c_append ) ) )
!= ( B @ ( C @ ( E @ c_append ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(482,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[481]) ).
thf(483,plain,
! [A: $i] :
( ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) )
| ( A = c_0 ) ),
inference(lifteq,[status(thm)],[482]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONumber ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_ANumber_AN2_A_61_61_AFalse_0) ).
thf(848,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONumber ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_OinvKey )
!= ( B @ c_Message_OinvKey ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OinvKey__eq_0) ).
thf(895,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_OinvKey )
!= ( B @ c_Message_OinvKey ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_1) ).
thf(626,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(359,axiom,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__4_0) ).
thf(1344,plain,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_OkeysFor )
= ( tc_nat @ ( C @ c_Message_OkeysFor @ ( A @ c_Message_OinvKey @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Crypt_0) ).
thf(1460,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_OkeysFor )
= ( tc_nat @ ( C @ c_Message_OkeysFor @ ( A @ c_Message_OinvKey @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(338,axiom,
tc_nat @ class_Wellfounded__Recursion_Owellorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_8) ).
thf(1293,plain,
tc_nat @ class_Wellfounded__Recursion_Owellorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(245,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_0 @ ( A @ c_List_Olexn ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
thf(1061,plain,
! [B: $i,A: $i] :
( ( B @ ( c_0 @ ( A @ c_List_Olexn ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
thf(758,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_2) ).
thf(1339,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(279,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Olistset ) )
= ( A @ tc_List_Olist @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).
thf(1149,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Olistset ) )
= ( A @ tc_List_Olist @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(206,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_append ) ) )
= ( C @ ( C @ ( D @ ( B @ c_append ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_A_64_Oappend__Cons_0) ).
thf(964,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_append ) ) )
= ( C @ ( C @ ( D @ ( B @ c_append ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(411,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OKey__synth__eq_1) ).
thf(1474,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_0) ).
thf(883,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(65,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Amod ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).
thf(608,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Amod ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(215,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_2) ).
thf(986,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(2091,plain,
! [A: $i] :
( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Ba @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[469,2075]) ).
thf(2092,plain,
! [A: $i] :
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Ba @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[2091]) ).
thf(2097,plain,
! [A: $i] :
( ( tc_Message_Omsg != tc_Message_Oagent )
| ( c_emptyset != c_Event_Obad )
| ( v_Ba != A ) ),
inference(simp,[status(thm)],[2092]) ).
thf(2101,plain,
( ( tc_Message_Omsg != tc_Message_Oagent )
| ( c_emptyset != c_Event_Obad ) ),
inference(simp,[status(thm)],[2097]) ).
thf(1684,plain,
( ( ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Aa @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[466,479]) ).
thf(1685,plain,
( ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Aa @ c_in ) ) ) ),
inference(simp,[status(thm)],[1684]) ).
thf(1694,plain,
( ( tc_Message_Omsg != tc_Message_Oagent )
| ( ( v_evs3 @ c_Event_Oused )
!= c_Event_Obad )
| ( ( v_K @ c_Message_Omsg_OKey )
!= v_Aa ) ),
inference(simp,[status(thm)],[1685]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__MPair_0) ).
thf(658,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ c_plus ) ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Onth ) ) )
= ( C @ ( D @ ( B @ c_List_Onth ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length__plus_0) ).
thf(912,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ c_plus ) ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Onth ) ) )
= ( C @ ( D @ ( B @ c_List_Onth ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).
thf(521,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Crypt_0) ).
thf(1213,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(129,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_List_Otl ) @ ( B @ ( A @ c_List_Ohd ) @ c_List_Olist_OCons ) ) )
= A )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__Cons__tl_0) ).
thf(768,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_List_Otl ) @ ( B @ ( A @ c_List_Ohd ) @ c_List_Olist_OCons ) ) )
= A )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Number_0) ).
thf(1044,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(321,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_List_Oconcat ) )
= c_List_Olist_ONil )
| ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_Main_Oconcat__eq__Nil__conv__1 ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_1) ).
thf(1245,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_List_Oconcat ) )
= c_List_Olist_ONil )
| ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_Main_Oconcat__eq__Nil__conv__1 ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(247,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_0) ).
thf(1066,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(434,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__see__shrK_0) ).
thf(1528,plain,
! [B: $i,A: $i] :
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(168,axiom,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
thf(867,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(868,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[867]) ).
thf(265,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Oagent_OFriend )
!= ( B @ c_Message_Oagent_OFriend ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Oinject_0) ).
thf(1113,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Oagent_OFriend )
!= ( B @ c_Message_Oagent_OFriend ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
thf(563,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(366,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OMPair__used_1) ).
thf(1364,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(323,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K = F )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( L @ ( K @ ( J @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( G @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_3) ).
thf(1250,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K = F )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( L @ ( K @ ( J @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( G @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(162,axiom,
! [B: $i,A: $i] :
( ( A @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey ) @ c_Message_OinvKey )
!= ( B @ c_Public_OshrK ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpriEK__noteq__shrK_0) ).
thf(851,plain,
! [B: $i,A: $i] :
( ( A @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey ) @ c_Message_OinvKey )
!= ( B @ c_Public_OshrK ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) @ c_List_Olast ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__snoc_0) ).
thf(1102,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) @ c_List_Olast ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Osublist ) ) )
= c_List_Olist_ONil )
| ( tc_nat @ ( A @ ( c_0 @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_1) ).
thf(722,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Osublist ) ) )
= c_List_Olist_ONil )
| ( tc_nat @ ( A @ ( c_0 @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(233,axiom,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Message_Omsg_OAgent @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__1_0) ).
thf(1034,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Message_Omsg_OAgent @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Orev ) )
= ( C @ ( B @ ( A @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__replicate_0) ).
thf(589,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Orev ) )
= ( C @ ( B @ ( A @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(198,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_1) ).
thf(944,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(387,axiom,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Otrans ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).
thf(1420,plain,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Otrans ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Hash_0) ).
thf(927,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(333,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Public_OshrK )
!= ( B @ c_Public_OshrK ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__injective_0) ).
thf(1277,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Public_OshrK )
!= ( B @ c_Public_OshrK ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv_1) ).
thf(812,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(1081,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Orotate1 ) )
= c_List_Olist_ONil ),
inference(lifteq,[status(thm)],[1080]) ).
thf(27,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).
thf(516,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Public_OpublicKey ) )
!= ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject_0) ).
thf(939,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Public_OpublicKey ) )
!= ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(410,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).
thf(1472,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(754,plain,
! [A: $i] :
( ( A @ c_Event_OinitState @ c_Message_Oparts @ c_Message_OkeysFor )
= c_emptyset ),
inference(lifteq,[status(thm)],[753]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
thf(553,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(385,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
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(1413,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(11,negated_conjecture,
tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_nb @ ( v_na @ c_Message_Omsg_OMPair ) @ ( v_K @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_9) ).
thf(473,plain,
tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_nb @ ( v_na @ c_Message_Omsg_OMPair ) @ ( v_K @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Ohd ) )
= B )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__replicate_0) ).
thf(490,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Ohd ) )
= B )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(458,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Key_0) ).
thf(1583,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_OkeysFor )
= ( B @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
thf(648,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(486,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
!= c_List_Olist_ONil ) ),
inference(cnf,[status(esa)],[485]) ).
thf(487,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
!= c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[486]) ).
thf(227,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv_1) ).
thf(1018,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(291,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Agent_0) ).
thf(1181,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair_0) ).
thf(823,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(30,axiom,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(525,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ ( A @ c_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(99,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( D @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__length_0) ).
thf(690,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( D @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(311,axiom,
! [A: $i] : ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__in__initState_0) ).
thf(1225,plain,
! [A: $i] : ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).
thf(887,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_0) ).
thf(739,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(329,axiom,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_List_Olist_ONil @ c_Event_Oused @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_ONonce__notin__used__empty_0) ).
thf(1267,plain,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_List_Olist_ONil @ c_Event_Oused @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(314,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OAgent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AAgent_AA2_A_61_61_AFalse_0) ).
thf(1230,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OAgent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(218,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
thf(993,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
= B )
| ( ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__id_0) ).
thf(712,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
= B )
| ( ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_Divides_Oop_Amod ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).
thf(557,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) @ c_Divides_Oop_Amod ) ) )
= ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(1607,plain,
( ( ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[468,478]) ).
thf(1608,plain,
( ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) ),
inference(simp,[status(thm)],[1607]) ).
thf(1611,plain,
( ( tc_nat != tc_Message_Oagent )
| ( c_Message_OsymKeys != c_Event_Obad )
| ( v_K != v_B ) ),
inference(simp,[status(thm)],[1608]) ).
thf(282,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair_0) ).
thf(1156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(94,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OHash ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5_0) ).
thf(673,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OHash ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(392,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( B @ c_in ) ) )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__see__shrK_1) ).
thf(1432,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( B @ c_in ) ) )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(138,axiom,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(791,plain,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Onth ) ) )
= B )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__number__of_0) ).
thf(840,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( tc_nat @ ( A @ c_Numeral_Onumber__of ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Onth ) ) )
= B )
| ( ( tc_nat @ ( A @ c_Numeral_Onumber__of ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(316,axiom,
! [B: $i,A: $i] :
( ( tc_Event_Oevent @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__3_0) ).
thf(1235,plain,
! [B: $i,A: $i] :
( ( tc_Event_Oevent @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(309,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair_1) ).
thf(1220,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D = B )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update_Osimps__1_0) ).
thf(544,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(341,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OAgent ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1_0) ).
thf(1300,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OAgent ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(1630,plain,
( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) )
!= ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[468,1592]) ).
thf(1631,plain,
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) )
!= ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[1630]) ).
thf(1637,plain,
( ( tc_nat != tc_Message_Oagent )
| ( c_Message_OsymKeys != c_Event_Obad )
| ( c_Message_Oagent_OServer != v_K ) ),
inference(simp,[status(thm)],[1631]) ).
thf(201,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty_1) ).
thf(951,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ ( B @ c_union ) ) @ ( A @ c_union ) ) )
= ( C @ ( A @ ( B @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Ostrange__Un__eq_0) ).
thf(808,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ ( B @ c_union ) ) @ ( A @ c_union ) ) )
= ( C @ ( A @ ( B @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Oanalz__spies__pubK_0) ).
thf(1404,plain,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Olast ) )
= B )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__replicate_0) ).
thf(613,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Olast ) )
= B )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(335,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_0) ).
thf(1284,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(113,axiom,
! [A: $i] :
( ( tc_Message_Oagent @ ( A @ c_Message_Oagent_OFriend @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__2_0) ).
thf(727,plain,
! [A: $i] :
( ( tc_Message_Oagent @ ( A @ c_Message_Oagent_OFriend @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(459,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Nonce_0) ).
thf(1585,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(1662,plain,
( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1317,478]) ).
thf(1663,plain,
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) ),
inference(simp,[status(thm)],[1662]) ).
thf(1667,plain,
( ( tc_Message_Oagent != tc_Message_Oagent )
| ( c_Event_Obad != c_Event_Obad )
| ( c_Message_Oagent_OSpy != v_B ) ),
inference(simp,[status(thm)],[1663]) ).
thf(1670,plain,
c_Message_Oagent_OSpy != v_B,
inference(simp,[status(thm)],[1667]) ).
thf(224,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
thf(1008,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Otake ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__eq__Nil_2) ).
thf(571,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Otake ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(595,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Obutlast ) )
= c_List_Olist_ONil ),
inference(lifteq,[status(thm)],[594]) ).
thf(319,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
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(1240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Set_Ocontents ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
thf(1141,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Set_Ocontents ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(438,axiom,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OSpy ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__5_0) ).
thf(1536,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OSpy ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
thf(656,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(229,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ ( D @ c_append ) ) )
!= ( B @ ( C @ ( E @ c_append ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_3) ).
thf(1023,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ ( D @ c_append ) ) )
!= ( B @ ( C @ ( E @ c_append ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OprivateKey__into__used_0) ).
thf(1485,plain,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) @ c_List_Obutlast ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast__snoc_0) ).
thf(1052,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) @ c_List_Obutlast ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(425,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).
thf(1506,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_List_Oupt ) )
= c_List_Olist_ONil )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_2) ).
thf(497,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ c_List_Oupt ) )
= c_List_Olist_ONil )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_List_Osublist ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__empty_0) ).
thf(876,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_List_Osublist ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) @ c_List_Onth ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length_0) ).
thf(671,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) @ c_List_Onth ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
thf(581,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).
thf(495,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(268,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(1126,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(401,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_OHPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_1) ).
thf(1453,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_OHPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(130,axiom,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_2) ).
thf(771,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(388,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ c_List_Oset ) @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onotin__set__remove1_0) ).
thf(1421,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ c_List_Oset ) @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(347,axiom,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__in__initState_0) ).
thf(1316,plain,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(1644,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs3 @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[475,478]) ).
thf(1645,plain,
( ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( v_evs3 @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) ),
inference(simp,[status(thm)],[1644]) ).
thf(1649,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Oagent )
| ( c_Yahalom_Oyahalom != c_Event_Obad )
| ( v_evs3 != v_B ) ),
inference(simp,[status(thm)],[1645]) ).
thf(254,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( B @ ( A @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_0) ).
thf(1084,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( B @ ( A @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(194,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
thf(931,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).
thf(539,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(399,axiom,
! [B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_ONonce__notin__initState_0) ).
thf(1448,plain,
! [B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(295,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_0) ).
thf(1189,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(377,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Osublist ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onotin__set__sublistI_0) ).
thf(1390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Osublist ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(455,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H = B )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( L @ ( K @ ( J @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( G @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_0) ).
thf(1575,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H = B )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( L @ ( K @ ( J @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( G @ ( F @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OKey @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(1275,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OServer ),
inference(polarity_switch,[status(thm)],[1274]) ).
thf(1276,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OServer ),
inference(lifteq,[status(thm)],[1275]) ).
thf(412,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__6_0) ).
thf(1476,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(357,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( B @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__analz__shrK_0) ).
thf(1341,plain,
! [B: $i,A: $i] :
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( B @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_Yahalom_Oyahalom @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(426,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_Message_OinvKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_3) ).
thf(1508,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_Message_OinvKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(84,axiom,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_1) ).
thf(652,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).
thf(1523,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Orotate ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_1) ).
thf(786,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Orotate ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(134,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( D @ ( A @ c_append ) ) )
!= ( B @ ( E @ ( C @ c_append ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_0) ).
thf(781,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( D @ ( A @ c_append ) ) )
!= ( B @ ( E @ ( C @ c_append ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_0) ).
thf(1253,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONumber )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__3_0) ).
thf(699,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONumber )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_1) ).
thf(961,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(374,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__priK_0) ).
thf(1385,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(219,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) @ c_List_Olast ) )
= ( B @ ( A @ c_List_Olast ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__appendL_0) ).
thf(995,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) @ c_List_Olast ) )
= ( B @ ( A @ c_List_Olast ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(449,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( B @ ( B @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_List_Olast ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__in__set_0) ).
thf(1558,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( B @ ( B @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_List_Olast ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(568,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Otl ) )
= c_List_Olist_ONil ),
inference(lifteq,[status(thm)],[567]) ).
thf(187,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ( ( B @ ( D @ ( A @ c_append ) ) )
!= ( B @ ( E @ ( C @ c_append ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_1) ).
thf(914,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ( ( B @ ( D @ ( A @ c_append ) ) )
!= ( B @ ( E @ ( C @ c_append ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(428,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_1) ).
thf(1513,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(344,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_1) ).
thf(1309,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpriK__neq__shrK_0) ).
thf(800,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oparts @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__synth_0) ).
thf(667,plain,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oparts @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(339,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(1294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth__eq_1) ).
thf(1440,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(193,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2_1) ).
thf(929,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Osublist ) ) )
= ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_0) ).
thf(1077,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Osublist ) ) )
= ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_OkeysFor )
= ( C @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__HPair_0) ).
thf(832,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_OkeysFor )
= ( C @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ( A
= ( A @ ( B @ v_sko__uhi ) @ c_Message_OinvKey ) )
| ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_1) ).
thf(684,plain,
! [B: $i,A: $i] :
( ( A
= ( A @ ( B @ v_sko__uhi ) @ c_Message_OinvKey ) )
| ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).
thf(549,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(397,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Agent_0) ).
thf(1444,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(396,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Osynth @ c_union ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oanalz @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__synth__Un_0) ).
thf(1442,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Osynth @ c_union ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oanalz @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oprod_Osize_0) ).
thf(620,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(456,axiom,
! [A: $i] :
( ( A @ c_Public_OshrK @ c_Message_OinvKey )
= ( A @ c_Public_OshrK ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OinvKey__shrK_0) ).
thf(1578,plain,
! [A: $i] :
( ( A @ c_Public_OshrK @ c_Message_OinvKey )
= ( A @ c_Public_OshrK ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey )
!= ( C @ c_Public_OshrK ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__neq__priK_0) ).
thf(1097,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey )
!= ( C @ c_Public_OshrK ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(163,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_emptyset
!= ( B @ ( A @ c_List_Oset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2_0) ).
thf(854,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_emptyset
!= ( B @ ( A @ c_List_Oset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(322,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_OHPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_0) ).
thf(1248,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_OHPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(167,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__Un_0) ).
thf(865,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(463,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).
thf(1593,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( C @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OCrypt_0) ).
thf(1380,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( C @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(346,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Oanalz @ c_union ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oanalz ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__analz__Un_0) ).
thf(1314,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Oanalz @ c_union ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oanalz ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2_0) ).
thf(1495,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(450,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).
thf(1561,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
thf(828,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ c_List_Odrop ) ) )
= c_List_Olist_ONil )
| ~ ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_1) ).
thf(532,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ c_List_Odrop ) ) )
= c_List_Olist_ONil )
| ~ ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osingleton__rev__conv_0) ).
thf(696,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( A @ ( B @ c_List_Onth ) ) @ ( A @ ( B @ c_List_Olist__update ) ) ) )
= B )
| ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__id_0) ).
thf(955,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( A @ ( B @ c_List_Onth ) ) @ ( A @ ( B @ c_List_Olist__update ) ) ) )
= B )
| ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(1345,plain,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
inference(polarity_switch,[status(thm)],[1344]) ).
thf(1346,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(lifteq,[status(thm)],[1345]) ).
thf(384,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
= ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Olist_OCons ) ) ) )
| ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_1) ).
thf(1410,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
= ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Olist_OCons ) ) ) )
| ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(128,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
thf(767,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(243,axiom,
! [A: $i] :
( ( A @ tc_Datatype_Ooption @ ( c_Datatype_Ooption_ONone @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__1_0) ).
thf(1056,plain,
! [A: $i] :
( ( A @ tc_Datatype_Ooption @ ( c_Datatype_Ooption_ONone @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_append ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_0) ).
thf(664,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_append ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_1) ).
thf(1288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( C @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OSays__imp__analz__Spy__dest_0) ).
thf(1197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( C @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(285,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).
thf(1165,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(72,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
thf(624,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(728,plain,
! [A: $i] :
( ( tc_Message_Oagent @ ( A @ c_Message_Oagent_OFriend @ c_Nat_Osize ) )
= c_0 ),
inference(lifteq,[status(thm)],[727]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( C @ ( B @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( C @ ( B @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_List_Oupt ) @ ( A @ c_List_Odrop ) ) )
= ( C @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ c_List_Oupt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__upt_0) ).
thf(575,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_List_Oupt ) @ ( A @ c_List_Odrop ) ) )
= ( C @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ c_List_Oupt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(445,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_0) ).
thf(1550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(363,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_insert ) ) @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_0) ).
thf(1357,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_insert ) ) @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(422,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_OkeysFor )
= ( C @ c_Message_OkeysFor ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__MPair_0) ).
thf(1500,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_OkeysFor )
= ( C @ c_Message_OkeysFor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
thf(871,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_OHPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_2) ).
thf(1532,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_OHPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(165,axiom,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
thf(860,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(61,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ ( E @ ( D @ ( A @ ( C @ c_List_Olist__update ) ) ) @ c_List_Onth ) ) )
= ( E @ ( B @ ( C @ c_List_Onth ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__list__update__neq_0) ).
thf(596,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ ( E @ ( D @ ( A @ ( C @ c_List_Olist__update ) ) ) @ c_List_Onth ) ) )
= ( E @ ( B @ ( C @ c_List_Onth ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(371,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_List_Onth ) ) @ c_in ) ) )
| ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__mem_0) ).
thf(1378,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_List_Onth ) ) @ c_in ) ) )
| ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(213,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orev ) @ c_Nat_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rev_0) ).
thf(982,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orev ) @ c_Nat_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(222,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_0) ).
thf(1004,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(380,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2_1) ).
thf(1399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(1616,plain,
( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Ba @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[469,477]) ).
thf(1617,plain,
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_Ba @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1616]) ).
thf(1619,plain,
( ( tc_Message_Oagent != tc_Message_Oagent )
| ( c_Event_Obad != c_Event_Obad )
| ( v_Ba != v_A ) ),
inference(simp,[status(thm)],[1617]) ).
thf(1621,plain,
v_Ba != v_A,
inference(simp,[status(thm)],[1619]) ).
thf(1604,plain,
( ( ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[468,477]) ).
thf(1605,plain,
( ( tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1604]) ).
thf(1606,plain,
( ( tc_nat != tc_Message_Oagent )
| ( c_Message_OsymKeys != c_Event_Obad )
| ( v_K != v_A ) ),
inference(simp,[status(thm)],[1605]) ).
thf(143,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_2) ).
thf(803,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_insert ) ) @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__HPair_0) ).
thf(1320,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_insert ) ) @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(190,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( c_0 @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onth ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__0_0) ).
thf(923,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( c_0 @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onth ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Otl ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__2_0) ).
thf(639,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Otl ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(123,axiom,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
thf(755,plain,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Ospies__pubK_0) ).
thf(1204,plain,
! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(248,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_2) ).
thf(1069,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(209,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
thf(972,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(1463,plain,
( ( tc_Message_Oagent @ ( c_Message_Oagent_OServer @ c_Nat_Osize ) )
= c_0 ),
inference(lifteq,[status(thm)],[1462]) ).
thf(452,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( E @ ( D @ ( B @ ( C @ ( A @ c_List_Ozip ) ) ) @ c_Map_Omap__of ) ) ) )
= c_Datatype_Ooption_ONone )
| ( B @ ( B @ ( A @ c_List_Oset ) @ ( E @ c_in ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_1) ).
thf(1565,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( E @ ( D @ ( B @ ( C @ ( A @ c_List_Ozip ) ) ) @ c_Map_Omap__of ) ) ) )
= c_Datatype_Ooption_ONone )
| ( B @ ( B @ ( A @ c_List_Oset ) @ ( E @ c_in ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(419,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair_1) ).
thf(1490,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oset ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__replicate_0) ).
thf(775,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oset ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(560,plain,
! [A: $i] :
( ( c_0 @ ( A @ c_List_Oupt ) )
= c_List_Olist_ONil ),
inference(lifteq,[status(thm)],[559]) ).
thf(13326,plain,
$false,
inference(e,[status(thm)],[645,1322,1036,1337,1469,1369,479,893,468,555,1554,481,1237,846,628,1031,977,1211,523,1544,1591,1269,1692,1305,1437,1041,873,1205,878,655,511,1173,1486,1426,1671,1137,500,797,715,472,1233,814,1260,747,1640,1063,1354,1458,1095,709,1613,1650,1243,1127,885,1046,565,1366,1518,1265,1228,1482,504,1455,949,917,702,1462,1132,1545,902,559,1087,1147,1479,1013,881,1568,1641,1362,1100,969,1347,1415,475,756,591,1109,1151,1020,966,1183,821,2105,1450,485,834,905,480,602,687,692,734,660,988,1405,1104,507,527,1696,1215,634,1074,920,678,546,925,1199,761,810,1274,1223,1343,778,1580,1255,1123,1217,1502,561,1487,788,729,1387,910,1423,467,484,879,1555,1178,830,1159,493,551,1392,1573,1106,1360,1143,2100,650,1111,725,1138,869,610,1118,989,1592,742,578,1534,1017,980,1587,1540,1006,857,1397,471,1493,1329,488,933,753,537,669,476,642,637,1446,1039,706,1028,1082,1016,1207,1324,997,1297,654,1552,1050,984,721,1002,1525,622,837,1530,1539,1382,569,1429,503,605,1434,1318,805,1695,541,1563,1054,1170,1286,1187,1515,530,662,1202,792,1466,1071,1026,1167,953,1185,773,794,618,1219,1483,1273,1548,745,1595,573,733,1135,1648,750,1510,513,1146,694,732,1389,843,1620,579,958,1520,1226,584,1154,826,577,641,936,1371,1312,1058,1239,1332,466,1090,1356,1139,1503,1258,704,1464,947,1194,1209,900,1282,784,1048,1349,1603,1542,567,616,1307,764,979,681,1408,1589,990,509,880,599,1376,863,1175,890,477,1471,1080,631,535,816,594,1162,483,848,895,626,1344,1460,1293,1061,758,1339,1149,964,2075,1474,883,608,986,2101,1694,658,912,521,1213,768,1044,1245,1066,1528,868,1113,563,1364,1250,851,1102,722,1034,589,944,1420,927,1277,812,1081,516,939,1472,754,553,1413,473,490,1583,648,487,1145,1018,1181,823,525,690,1225,887,739,1267,1230,993,712,557,1611,1156,673,1432,791,502,840,1235,1317,470,1220,544,1300,1637,951,808,1404,613,1284,727,1585,1670,1008,571,595,1272,1240,1141,1536,656,1023,1485,1052,1506,497,876,671,581,495,1126,1453,771,1421,465,1316,1649,1084,931,539,1448,1189,1390,1575,1276,1476,1341,1508,652,1523,786,781,1253,699,961,1385,995,1558,568,914,1513,1309,800,667,1294,1440,929,1077,478,832,684,549,1444,1442,620,1578,1097,854,1248,867,865,1593,1380,1314,1495,1561,828,532,696,955,1346,474,1410,767,1056,664,1288,1197,720,1165,624,728,1129,575,1550,1357,1500,871,1532,860,596,1378,982,1004,1399,1621,1606,803,1320,469,923,639,755,1204,1069,972,1463,1565,1490,775,560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV342-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.24/0.49 % Computer : n011.cluster.edu
% 0.24/0.49 % Model : x86_64 x86_64
% 0.24/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.49 % Memory : 8046.5625MB
% 0.24/0.49 % OS : Linux 6.8.0-71-generic
% 0.24/0.49 % CPULimit : 300
% 0.24/0.49 % WCLimit : 300
% 0.24/0.49 % DateTime : Sat Sep 26 13:35:15 UTC 2026
% 0.24/0.49 % CPUTime :
% 0.24/0.49 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.43/1.37 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 4.26/2.21 % [INFO] Parsing done (835ms).
% 4.26/2.23 % [INFO] Running in sequential loop mode.
% 5.12/2.79 % [INFO] eprover registered as external prover.
% 5.29/2.80 % [INFO] Scanning for conjecture ...
% 6.71/3.27 % [INFO] Found a conjecture (or negated_conjecture) and 2945 axioms. Running axiom selection ...
% 9.49/3.92 % [INFO] Axiom selection finished. Selected 453 axioms (removed 2492 axioms).
% 10.34/4.21 % [INFO] Problem is propositional (TPTP CNF).
% 10.34/4.25 % [INFO] Type checking passed.
% 10.34/4.25 % [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 ...
% 108.14/25.33 % External prover 'e' found a proof!
% 108.14/25.33 % [INFO] Killing All external provers ...
% 108.14/25.33 % Time passed: 24625ms (effective reasoning time: 23086ms)
% 108.14/25.34 % Axioms used in derivation (453): cls_Event_Oevent_Oinject__3_0, cls_List_Onth__upt_0, cls_Message_Oanalz__synth__Un_0, cls_Nat_Onot__less0_0, cls_List_Oself__append__conv2_0, cls_Nat_Onot__gr0_0, cls_Message_Oanalz_OInj_0, cls_Nat_Onat__add__left__cancel__less_1, cls_List_Ohd__Cons__tl_0, 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_Public_OpublicKey__into__used_0, cls_List_Olist__update__overwrite_0, cls_List_Onth__zip_0, cls_List_Otake__all_0, cls_List_Oremdups__eq__nil__iff_1, cls_Yahalom_Ounique__session__keys__dest_3, cls_List_Oappend__eq__append__conv_1, cls_Event_OkeysFor__synth_H_0, cls_List_Onth__append__length_0, cls_Message_Oparts__Un_0, cls_List_Olists_ONil_0, cls_Message_OHPair__neqs__2_0, cls_Message_Oanalz__analzD__dest_0, cls_Message_OCrypt__synth__eq_0, cls_Message_Omsg_Osize__2_0, cls_List_Olength__append_0, cls_Nat_Onat__add__right__cancel_0, cls_Event_Oused__Gets_0, cls_List_Olast__snoc_0, cls_List_Olength__remdups__eq_1, cls_Wellfounded__Recursion_Owf__insert_0, cls_List_Onotin__set__remove1_0, cls_Message_Oanalz__synth_0, cls_Message_Oparts__insert__Crypt_0, cls_List_Otake__Cons__number__of_0, cls_List_Olist__update_Osimps__1_0, cls_Message_OkeysFor__Un_0, cls_List_Orev__is__Nil__conv_0, cls_Message_Oparts__empty_0, cls_Message_OKey__synth__eq_1, cls_List_Oappend__in__lists__conv_2, cls_Message_Oanalz__conj__parts_0, cls_Message_Oanalz__idem_0, cls_Message_OHPair__synth__analz_1, cls_Public_OpubK__neq__shrK_0, cls_Message_Oagent_Oinject_0, cls_List_Olast_Osimps_0, cls_Message_Oanalz__empty_0, cls_Message_Oparts__insert__MPair_0, cls_Set_Osingleton__inject__dest_0, cls_Message_Oanalz__insert__HPair_0, cls_List_Olength__0__conv_1, cls_Public_Onot__symKeys__priK_0, cls_List_Olist_Oinject_1, cls_Event_Oused__Notes_0, cls_List_Oappend__same__eq_0, cls_Message_Oparts__insert__Nonce_0, cls_Nat_Oadd__is__0_0, cls_List_Oupt__eq__Nil__conv_2, 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_Yahalom_OSpy__see__shrK_0, cls_List_Onth__Cons__number__of_0, cls_List_Onth__list__update__neq_0, cls_Event_Oevent_Odistinct__6_0, cls_Nat_Oless__irrefl_0, cls_Message_Omsg_Oinject__1_0, cls_Event_OkeysFor__synth_H_3, cls_List_Obutlast__snoc_0, cls_List_Orotate__is__Nil__conv_0, cls_List_Olast__in__set_0, cls_Message_OMPair__synth__analz_2, cls_List_Odrop__eq__Nil_1, cls_Public_OpriK__neq__shrK_0, cls_List_Oself__append__conv_1, cls_List_Otake__eq__Nil_1, cls_Divides_Omod__add__self1_0, cls_Message_OHash__synth_0, cls_Set_Osingleton__insert__inj__eq_H_0, clsarity_nat_47, cls_List_Onth__mem_0, cls_Yahalom_Ounique__session__keys__dest_0, 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_List_Oconcat__eq__Nil__conv_2, cls_List_Onth__drop_0, 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_Event_Oevent_Osize__3_0, cls_List_Olength__replicate_0, cls_List_Olength__list__update_0, cls_List_Otl_Osimps__2_0, cls_Public_OCrypt__notin__used__empty_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_Message_Oanalz__insert__Nonce_0, cls_List_Oremdups__eq__nil__iff_0, cls_List_Oremove1_Osimps__2_1, cls_List_Orev__rev__ident_0, cls_Nat_Oadd__gr__0_2, cls_Public_ONonce__notin__initState_0, cls_List_Olist__inter_Osimps__2_1, cls_List_Oset__empty2_1, cls_Public_OshrK__injective_0, cls_Message_Oagent_Odistinct__1_0, cls_Public_OMPair__used_1, cls_Message_Oparts_OInj_0, cls_List_Olength__remdups__leq_0, cls_List_Ohd_Osimps_0, cls_List_Odrop__Cons__number__of_0, cls_Message_Oparts__synth_0, cls_List_Otake__upt_0, cls_List_ONil__eq__concat__conv_1, cls_List_Olist__inter_Osimps__2_0, cls_List_Olast__replicate_0, cls_List_Obutlast_Osimps__2_0, cls_Message_OkeysFor__empty_0, cls_Message_Omsg_Oinject__5_0, cls_Message_OCrypt__synth_1, cls_List_Olength__rotate_0, cls_List_Oset__remdups_0, cls_List_OlistsE_0, cls_Message_OHPair__neqs__6_0, cls_List_Osingleton__rev__conv_0, cls_List_Oconcat__eq__Nil__conv_1, clsarity_nat_44, cls_Divides_Omod__le__divisor_0, cls_Public_OkeysFor__parts__initState_0, cls_Public_OinvKey__K_0, cls_Message_Omsg_Osize__4_0, cls_List_Orev__is__rev__conv_0, cls_Message_Oparts__insert__Key_0, cls_Event_OServer_A_58_Abad_A_61_61_AFalse_0, cls_Message_OHPair__synth__analz_0, cls_Public_OsymKeys__invKey__iff_0, cls_Nat_Oadd__is__0_1, cls_Message_Osynth_OMPair_0, cls_Message_ONonce__synth__eq_1, cls_Event_Oevent_Odistinct__4_0, cls_Set_OUn__iff_0, cls_Message_Oparts__insert__HPair_0, cls_Set_OUn__empty_1, cls_List_Oappend1__eq__conv_1, cls_Message_Omsg_Oinject__2_0, cls_Message_Omsg_Oinject__7_1, cls_Set_Oinsert__iff_2, cls_List_Oremdups__eq__nil__right__iff_0, cls_List_Oappend__self__conv_0, cls_List_Orotate1__is__Nil__conv_0, cls_List_Orev__is__Nil__conv_1, cls_Event_Oevent_Oinject__2_0, cls_Message_Oagent_Odistinct__3_0, cls_List_Ozip__append_0, cls_Set_OsingletonD__dest_0, cls_Set_Oinsert__not__empty_0, cls_List_Otake__eq__Nil_2, cls_Event_Oknows__Spy__Says_0, cls_Message_OFake__analz__eq_0, cls_Nat_Ole__0__eq_0, cls_Event_Oevent_Odistinct__3_0, cls_Public_OprivateKey_Ab1_AA1_A_61_ApublicKey_Ac1_AA_H1_A_61_61_AFalse_0, cls_List_Oappend__self__conv_1, cls_Map_Omap__of__zip__is__None_0, cls_List_Oupt__eq__Nil__conv_1, cls_List_Osublist__nil_0, cls_Divides_Omod__add__self2_0, cls_List_Odrop__0_0, cls_List_Oappend__in__lists__conv_1, cls_List_Olist_Oinject_0, cls_Set_Oempty__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_Message_ONumber__synth_0, cls_Event_Oevent_Osize__2_0, cls_Event_Oknows__Spy__Notes_0, cls_Message_OAgent__synth_0, cls_List_Oin__listsI_1, cls_List_Oremdups_Osimps__2_0, cls_List_Olast_Osimps_1, cls_Set_OsingletonI_0, cls_Message_Oparts__partsD__dest_0, cls_Message_OHPair__eq__MPair_0, cls_List_Ohd__replicate_0, cls_Message_Oparts__insert__Hash_0, cls_Message_Omsg_Oinject__6_1, cls_List_Obutlast_Osimps__2_1, cls_Nat_Onat__add__left__cancel__le_1, cls_Divides_Omod__less__divisor_0, cls_Event_Oevent_Oinject__1_2, 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_Message_Oparts_OBody__dest_0, cls_Event_Oknows_Oknows__Nil_0, cls_List_Oappend__self__conv2_1, cls_Yahalom_OSpy__analz__shrK_1, cls_List_Otl__append2_0, cls_List_Olist__inter_Osimps__1_0, cls_List_Onth__append__length__plus_0, cls_List_Orev__singleton__conv_1, cls_Set_Oall__not__in__conv_0, cls_List_Orotate1__is__Nil__conv_1, cls_Set_Oinsert__iff_1, cls_Yahalom_OSpy__analz__shrK_0, cls_Public_OshrK__in__used_0, cls_Message_OHash__synth__analz_1, cls_Public_OMPair__used_0, cls_List_Obutlast_Osimps__1_0, cls_Public_OshrK__in__initState_0, cls_Public_OpublicKey__inject_0, cls_List_Oset__empty_0, cls_Message_OHash_91X2_93_AY2_A_61_AKey_AK2_A_61_61_AFalse_0, cls_Event_OkeysFor__synth_H_2, cls_List_Orev__replicate_0, cls_List_Olength__0__conv_0, cls_List_Oconcat_Osimps__1_0, cls_Wellfounded__Relations_Otrans__less__than_0, cls_Message_OHash_91X2_93_AY2_A_61_AAgent_AA2_A_61_61_AFalse_0, cls_Message_OMPair__analz_1, cls_Public_Onot__symKeys__pubK_0, cls_Infinite__Set_Oatmost__one__unique_0, cls_List_ONil__is__rev__conv_1, cls_Message_Oin__parts__UnE_0, cls_List_Oappend1__eq__conv_0, cls_List_Oupt__eq__Nil__conv_0, cls_Message_OMPair__eq__HPair_0, cls_List_Oconcat__append_0, cls_List_Oop_A_64_Oappend__Cons_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_Nat_Oadd__gr__0_0, cls_Datatype_Ooption_Osize__1_0, cls_List_Olist__update__beyond_0, cls_List_Oself__append__conv_0, cls_Set_OUn__insert__left_0, cls_List_Oappend__is__Nil__conv_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_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_List_Oappend__self__conv2_0, cls_Wellfounded__Recursion_Owf__empty_0, cls_Wellfounded__Relations_Owf__less__than_0, cls_Message_OHPair__neqs__3_0, cls_List_Orev__append_0, cls_Message_Osynth_OCrypt_0, cls_Event_Oevent_Odistinct__2_0, cls_Message_OMPair__parts_1, cls_List_ONil__is__append__conv_2, cls_Public_OinvKey__shrK_0, cls_Message_ONonce__synth__eq_0, cls_Message_Osynth__synthD__dest_0, cls_Message_Omsg_Osize__1_0, clsarity_nat_12, cls_Message_OkeysFor__insert__Hash_0, cls_Public_OSpy__spies__bad__shrK_0, cls_List_Onot__Cons__self_0, cls_Set_OUn__iff_1, cls_Message_OkeysFor__insert__Number_0, cls_List_Orev__eq__Cons__iff_0, cls_Event_Oevent_Oinject__2_1, cls_Nat_Oadd__0__right_0, cls_Message_Oagent_Odistinct__4_0, cls_List_Osublist__singleton_1, cls_List_ONil__is__append__conv_0, cls_Message_Omsg_Osize__3_0, cls_List_OlistsE_1, cls_List_Olast__appendL_0, cls_Message_Oagent_Odistinct__6_0, cls_Event_Oevent_Oinject__1_1, cls_List_Onth__Cons__0_0, cls_List_Olist_Odistinct__1_0, cls_Set_Oempty__not__insert_0, cls_List_Ohd__append2_0, cls_Nat_Onot__gr0_1, cls_Message_OHPair__neqs__1_0, cls_Nat_Onot__add__less2_0, cls_Message_Oagent_Osize__2_0, cls_Message_Oanalz__insert__MPair_0, cls_List_Ohd__upt_0, cls_Yahalom_Ounique__session__keys__dest_1, cls_Wellfounded__Relations_Oless__than__iff_1, cls_List_Oset__append_0, cls_Public_OSpy__spies__bad__privateKey_0, cls_List_Onotin__set__sublistI_0, cls_Event_Oused__Says_0, cls_List_Onth__replicate_0, cls_List_Oappend__assoc_0, cls_Message_Oagent_Odistinct__2_0, cls_Message_Oanalz__insert__Number_0, cls_List_ONil__eq__concat__conv_2, cls_Message_OinvKey__eq_0, cls_List_Olength__rev_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_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_List_Olist__update__id_0, cls_Message_OMPair__synth_1, cls_Divides_Omod__less_0, 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_Odrop_Odrop__Nil_0, cls_Event_Oevent_Odistinct__5_0, cls_List_Oset__rotate_0, cls_List_Oset__rev_0, cls_Message_OHash_91X2_93_AY2_A_61_ANonce_AN2_A_61_61_AFalse_0, cls_Divides_Omod__self_0, cls_Public_Ospies__pubK_0, cls_Message_Osynth_OInj_0, cls_List_Oset__empty_1, cls_List_Otl_Osimps__1_0, cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0, cls_Set_Ocontents__eq_0, cls_List_Ozip__Nil_0, cls_Message_OkeysFor__insert__MPair_0, cls_List_Osingleton__rev__conv_1, cls_Divides_ODIVISION__BY__ZERO__MOD_0, cls_List_Onth__list__update__eq_0, cls_List_Odrop__eq__Nil_0, cls_List_Oin__listsI_0, cls_Message_OMPair__analz_0, cls_Public_OprivateKey__into__used_0, cls_List_Oappend__in__lists__conv_0, cls_Message_OMPair__eq__HPair_1, cls_List_Oremove1_Osimps__1_0, cls_Message_Oanalz__analz__Un_0, cls_Public_OpublicKey__inject_1, cls_Event_OkeysFor__synth_H_1, cls_Nat_Onat__add__left__cancel_0, cls_Message_Ostrange__Un__eq_0, cls_Map_Omap__of__zip__is__None_1, clsarity_nat_8, cls_Message_OkeysFor__insert__Key_0, cls_Event_OSpy_A_58_Abad_A_61_61_ATrue_0, 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_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_Otake__eq__Nil_0, cls_Divides_Onat__mod__mod__trivial_0, 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_Event_Oevent_Osize__1_0, cls_Message_Omsg_Oinject__7_0, cls_List_Oremdups__eq__nil__right__iff_1, cls_Message_OMPair__parts_0, cls_Message_Omsg_Oinject__3_0, cls_Message_Oparts__analz_0, cls_Set_Oinsert__iff_0, cls_Nat_Oadd__gr__0_1, cls_Nat_Ole0_0, cls_List_Ozip__Cons__Cons_0, cls_List_Oset_Osimps__2_0, cls_Set_OUn__empty_0, cls_Set_Oinsert__absorb2_0, cls_Nat_Oop_A_L_Oadd__0_0, cls_Set_OUn__empty_2, cls_Event_Oevent_Oinject__1_0, cls_Message_Oparts__emptyE_0, cls_Set_OUn__iff_2, cls_List_Olist__update__length_0, cls_Nat_Ole__0__eq_1, cls_Message_Oagent_Osize__1_0, cls_List_Owf__lenlex_0, cls_Yahalom_OSpy__see__shrK_1, cls_Public_ONonce__notin__used__empty_0, cls_Yahalom_Onew__keys__not__used_0, cls_List_Oremove1_Osimps__2_0, cls_Message_OMPair__eq__HPair_2, cls_Message_OMPair__synth__analz_0, cls_List_Oappend__take__drop__id_0, cls_List_Olength__rotate1_0, cls_List_ONil__eq__concat__conv_0, cls_List_Odrop__upt_0, cls_List_Oset__rotate1_0, cls_Public_OsymKeys__invKey__iff_1, cls_Divides_Omod__0_0, cls_Message_Oparts__idem_0, cls_Wellfounded__Relations_Oless__than__iff_0, cls_Yahalom_Ounique__session__keys__dest_2, cls_Message_OMPair__synth_0, cls_Message_OHPair__neqs__4_0, cls_List_Orotate__id_0, cls_List_Oappend__is__Nil__conv_2, cls_List_Osublist__singleton_0, cls_Message_OHPair__eq_1, cls_Event_Oknows__Spy__Gets_0, cls_List_Odrop__drop_0, cls_Public_OshrK__in__knows_0, cls_List_Onth__take_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_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0, cls_List_Oremdups_Osimps__2_1, cls_List_Orotate__is__Nil__conv_1, cls_List_Olast__drop_0
% 108.14/25.34 % No. of inferences in proof: 1040
% 108.14/25.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 24625 ms resp. 23086 ms w/o parsing
% 106.48/25.58 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 106.48/25.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------