%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV289-1 : 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 : n004.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 08:58:45 AM UTC 2026
% Result : Unsatisfiable 95.99s 21.04s
% Output : Refutation 100.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 351
% Syntax : Number of formulae : 1393 ( 491 unt; 0 typ; 16 def)
% Number of atoms : 3082 (1484 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 14585 (1786 ~;1269 |; 0 &;11530 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 149 ( 146 usr; 26 con; 0-6 aty)
% Number of variables : 3315 ( 0 ^;3283 !; 16 ?;3315 :)
% ( 0 !>; 0 ?*; 0 @-; 16 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_Event_Oevent_OSays_decl,type,
c_Event_Oevent_OSays: $i > $i > $i > $i ).
thf(v_B_decl,type,
v_B: $i ).
thf(c_Message_Oagent_OServer_decl,type,
c_Message_Oagent_OServer: $i ).
thf(c_Message_Omsg_OMPair_decl,type,
c_Message_Omsg_OMPair: $i > $i > $i ).
thf(v_NA_decl,type,
v_NA: $i ).
thf(c_Message_Omsg_OAgent_decl,type,
c_Message_Omsg_OAgent: $i > $i ).
thf(v_A_decl,type,
v_A: $i ).
thf(v_X_H_decl,type,
v_X_H: $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_NB_decl,type,
v_NB: $i ).
thf(c_List_Oset_decl,type,
c_List_Oset: $i > $i > $i ).
thf(v_evs_decl,type,
v_evs: $i ).
thf(tc_Event_Oevent_decl,type,
tc_Event_Oevent: $i ).
thf(c_Event_Oevent_OGets_decl,type,
c_Event_Oevent_OGets: $i > $i > $i ).
thf(v_X_decl,type,
v_X: $i ).
thf(c_Message_Omsg_OKey_decl,type,
c_Message_Omsg_OKey: $i > $i ).
thf(v_K_decl,type,
v_K: $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_Event_Obad_decl,type,
c_Event_Obad: $i ).
thf(tc_Message_Oagent_decl,type,
tc_Message_Oagent: $i ).
thf(c_OtwayRees_Ootway_decl,type,
c_OtwayRees_Ootway: $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $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(tc_Message_Omsg_decl,type,
tc_Message_Omsg: $i ).
thf(c_Wellfounded__Recursion_Oacyclic_decl,type,
c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).
thf(c_Relation_Oconverse_decl,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_0_decl,type,
c_0: $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i ).
thf(c_List_Orev_decl,type,
c_List_Orev: $i > $i > $i ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(c_Wellfounded__Relations_Oless__than_decl,type,
c_Wellfounded__Relations_Oless__than: $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(c_Datatype__Universe_OIn1_decl,type,
c_Datatype__Universe_OIn1: $i > $i > $i > $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_Datatype__Universe_OIn0_decl,type,
c_Datatype__Universe_OIn0: $i > $i > $i > $i ).
thf(c_Datatype__Universe_Odprod_decl,type,
c_Datatype__Universe_Odprod: $i > $i > $i > $i > $i ).
thf(tc_Datatype__Universe_Onode_decl,type,
tc_Datatype__Universe_Onode: $i > $i > $i ).
thf(c_Datatype__Universe_OScons_decl,type,
c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__1_decl,type,
c_Main_OdprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__2_decl,type,
c_Main_OdprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__3_decl,type,
c_Main_OdprodE__3: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__4_decl,type,
c_Main_OdprodE__4: $i > $i > $i > $i > $i > $i ).
thf(c_Message_Omsg_ONonce_decl,type,
c_Message_Omsg_ONonce: $i > $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_append_decl,type,
c_append: $i > $i > $i > $i ).
thf(c_Finite__Set_OFinites_decl,type,
c_Finite__Set_OFinites: $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(c_SetInterval_OgreaterThanAtMost_decl,type,
c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(c_SetInterval_OatLeastAtMost_decl,type,
c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_Nat_Osize_decl,type,
c_Nat_Osize: $i > $i > $i ).
thf(c_Wellfounded__Recursion_Owf_decl,type,
c_Wellfounded__Recursion_Owf: $i > $i > $o ).
thf(c_Wellfounded__Relations_Olex__prod_decl,type,
c_Wellfounded__Relations_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(c_SetInterval_OatLeastLessThan_decl,type,
c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_Message_Omsg_ONumber_decl,type,
c_Message_Omsg_ONumber: $i > $i ).
thf(c_Pow_decl,type,
c_Pow: $i > $i > $i ).
thf(c_Relation_Orel__comp_decl,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_Public_OpublicKey_decl,type,
c_Public_OpublicKey: $i > $i > $i ).
thf(c_SetInterval_OatMost_decl,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(c_Message_OHPair_decl,type,
c_Message_OHPair: $i > $i > $i ).
thf(c_UNIV_decl,type,
c_UNIV: $i ).
thf(c_Message_OinvKey_decl,type,
c_Message_OinvKey: $i > $i ).
thf(c_Message_OsymKeys_decl,type,
c_Message_OsymKeys: $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(c_List_Oremdups_decl,type,
c_List_Oremdups: $i > $i > $i ).
thf(c_Message_Omsg_OHash_decl,type,
c_Message_Omsg_OHash: $i > $i ).
thf(c_Datatype__Universe_Odsum_decl,type,
c_Datatype__Universe_Odsum: $i > $i > $i > $i > $i ).
thf(c_Relation_OId_decl,type,
c_Relation_OId: $i ).
thf(c_Relation_OImage_decl,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Sum__Type_OInr_decl,type,
c_Sum__Type_OInr: $i > $i > $i > $i ).
thf(c_Sum__Type_OInl_decl,type,
c_Sum__Type_OInl: $i > $i > $i > $i ).
thf(c_inter_decl,type,
c_inter: $i > $i > $i > $i ).
thf(c_List_Odistinct_decl,type,
c_List_Odistinct: $i > $i > $o ).
thf(c_Transitive__Closure_Otrancl_decl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_decl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_SetInterval_OlessThan_decl,type,
c_SetInterval_OlessThan: $i > $i > $i ).
thf(c_Main_OImageE__1_decl,type,
c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Sum__Type_OPlus_decl,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(tc_sum_decl,type,
tc_sum: $i > $i > $i ).
thf(c_Main_OPlusE__1_decl,type,
c_Main_OPlusE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OPlusE__2_decl,type,
c_Main_OPlusE__2: $i > $i > $i > $i > $i ).
thf(c_Relation_Odiag_decl,type,
c_Relation_Odiag: $i > $i > $i ).
thf(c_Datatype__Universe_Ouprod_decl,type,
c_Datatype__Universe_Ouprod: $i > $i > $i > $i > $i ).
thf(c_Message_Oagent_OFriend_decl,type,
c_Message_Oagent_OFriend: $i > $i ).
thf(c_SetInterval_OgreaterThanLessThan_decl,type,
c_SetInterval_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(c_Datatype_Ooption_OSome_decl,type,
c_Datatype_Ooption_OSome: $i > $i > $i ).
thf(c_Union_decl,type,
c_Union: $i > $i > $i ).
thf(c_Main_OUnionE__1_decl,type,
c_Main_OUnionE__1: $i > $i > $i > $i ).
thf(c_Message_Oparts_decl,type,
c_Message_Oparts: $i > $i ).
thf(c_Relation_ORange_decl,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Main_ORangeE__1_decl,type,
c_Main_ORangeE__1: $i > $i > $i > $i > $i ).
thf(c_List_Olists_decl,type,
c_List_Olists: $i > $i > $i ).
thf(c_Message_Osynth_decl,type,
c_Message_Osynth: $i > $i ).
thf(c_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Main_OconverseE__1_decl,type,
c_Main_OconverseE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OconverseE__2_decl,type,
c_Main_OconverseE__2: $i > $i > $i > $i > $i ).
thf(c_List_Olistrel_decl,type,
c_List_Olistrel: $i > $i > $i ).
thf(c_Main_Olistrel__Cons1__1_decl,type,
c_Main_Olistrel__Cons1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Event_Oused_decl,type,
c_Event_Oused: $i > $i ).
thf(c_Event_OinitState_decl,type,
c_Event_OinitState: $i > $i ).
thf(c_Main_Oin__listsI__1_decl,type,
c_Main_Oin__listsI__1: $i > $i > $i > $i ).
thf(v_sko__u__1_decl,type,
v_sko__u__1: $i > $i > $i > $i > $i > $i ).
thf(c_Inter_decl,type,
c_Inter: $i > $i > $i ).
thf(c_Main_OInterI__1_decl,type,
c_Main_OInterI__1: $i > $i > $i > $i ).
thf(c_Main_OuprodE__1_decl,type,
c_Main_OuprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OuprodE__2_decl,type,
c_Main_OuprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Datatype_Oo2s_decl,type,
c_Datatype_Oo2s: $i > $i > $i ).
thf(c_Main_Olistrel__Cons2__1_decl,type,
c_Main_Olistrel__Cons2__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Olistrel__Cons2__2_decl,type,
c_Main_Olistrel__Cons2__2: $i > $i > $i > $i > $i > $i ).
thf(c_Infinite__Set_Oatmost__one_decl,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_Main_Orel__compE__1_decl,type,
c_Main_Orel__compE__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_Orel__compE__3_decl,type,
c_Main_Orel__compE__3: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_Ofinite__Union__1_decl,type,
c_Main_Ofinite__Union__1: $i > $i > $i ).
thf(v_sko__usf_decl,type,
v_sko__usf: $i > $i > $i > $i ).
thf(c_Main_OdiagE__1_decl,type,
c_Main_OdiagE__1: $i > $i > $i > $i ).
thf(c_Main_Orel__compE__2_decl,type,
c_Main_Orel__compE__2: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_OIdE__1_decl,type,
c_Main_OIdE__1: $i > $i > $i ).
thf(c_Main_Olistrel__Cons1__2_decl,type,
c_Main_Olistrel__Cons1__2: $i > $i > $i > $i > $i > $i ).
thf(c_List_Olex_decl,type,
c_List_Olex: $i > $i > $i ).
thf(c_Relation_ODomain_decl,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_List_Olenlex_decl,type,
c_List_Olenlex: $i > $i > $i ).
thf(c_Main_ODomainE__1_decl,type,
c_Main_ODomainE__1: $i > $i > $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i > $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i > $i ).
thf(sk19_decl,type,
sk19: $i > $i ).
thf(sk22_decl,type,
sk22: $i > $i > $i ).
thf(sk26_decl,type,
sk26: $i > $i ).
thf(sk28_decl,type,
sk28: $i > $i ).
thf(sk34_decl,type,
sk34: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_List_Orev ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_ONonce @ A )
= B ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i > $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( C @ A ) ) ) )
= B ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_ONumber @ A )
= B ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Public_OpublicKey ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_OHPair ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OHash @ A )
= B ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_OHPair ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Public_OpublicKey ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Oagent_OFriend @ A )
= B ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Datatype_Ooption_OSome ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OKey @ A )
= B ) ) ) ).
thf(sk28_def,definition,
( sk28
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Public_OshrK @ A )
= B ) ) ) ).
thf(sk34_def,definition,
( sk34
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OAgent @ A )
= B ) ) ) ).
thf(334,axiom,
! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK_AX_A_58_AsymKeys_0) ).
thf(1159,plain,
! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(4,negated_conjecture,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(342,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(343,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[342]) ).
thf(1318,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1159,343]) ).
thf(1319,plain,
! [A: $i] :
( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1318]) ).
thf(1322,plain,
! [A: $i] :
( ( tc_nat != tc_Message_Oagent )
| ( c_Message_OsymKeys != c_Event_Obad )
| ( ( A @ c_Public_OshrK )
!= v_A ) ),
inference(simp,[status(thm)],[1319]) ).
thf(185,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(809,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)],[185]) ).
thf(139,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(690,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(143,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__iff1_0) ).
thf(701,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)],[143]) ).
thf(702,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[701]) ).
thf(17676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( c_Message_OsymKeys @ ( D @ ( C @ c_Public_OpublicKey ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[690,702]) ).
thf(17677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( c_Message_OsymKeys @ ( D @ ( C @ c_Public_OpublicKey ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[17676]) ).
thf(17740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != tc_nat )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_Message_OsymKeys )
| ( A
!= ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
inference(simp,[status(thm)],[17677]) ).
thf(17759,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( c_emptyset @ ( B @ ( A @ c_Public_OpublicKey ) @ c_insert ) ) )
!= c_Message_OsymKeys ),
inference(simp,[status(thm)],[17740]) ).
thf(273,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
thf(1024,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(50,axiom,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
thf(457,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(188,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(814,plain,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(815,plain,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[814]) ).
thf(1359,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[457,815]) ).
thf(1360,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[1359]) ).
thf(1365,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Finite__Set_OFinites )
| ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= B ) ),
inference(simp,[status(thm)],[1360]) ).
thf(1369,plain,
( ( ( tc_nat @ tc_set )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Finite__Set_OFinites ) ),
inference(simp,[status(thm)],[1365]) ).
thf(310,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
thf(1105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).
thf(346,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(347,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(cnf,[status(esa)],[346]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
thf(846,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(276,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( E @ c_Message_Omsg_OKey @ ( F @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_in ) ) )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( D @ c_in ) ) )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( E @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( E @ c_Message_Omsg_OKey @ ( F @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( E @ c_Message_Omsg_OKey @ ( C @ c_Message_Omsg_OMPair ) @ ( D @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OtwayRees_OSpy__not__see__encrypted__key__dest_0) ).
thf(1031,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( E @ c_Message_Omsg_OKey @ ( F @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_in ) ) )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( D @ c_in ) ) )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( E @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( E @ c_Message_Omsg_OKey @ ( F @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( E @ c_Message_Omsg_OKey @ ( C @ c_Message_Omsg_OMPair ) @ ( D @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(220,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__iff1_0) ).
thf(893,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)],[220]) ).
thf(74,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__iff1_0) ).
thf(518,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)],[74]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).
thf(468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(43,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
thf(437,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(52,axiom,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).
thf(463,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(464,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[463]) ).
thf(8395,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[437,464]) ).
thf(8396,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[8395]) ).
thf(8402,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[8396]) ).
thf(8415,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[8402]) ).
thf(59,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__iff2_0) ).
thf(480,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(481,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
inference(lifteq,[status(thm)],[480]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).
thf(408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
thf(523,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(102,axiom,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
thf(589,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
thf(419,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(420,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[419]) ).
thf(11557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
| ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( D @ c_insert ) ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[589,420]) ).
thf(11558,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
| ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( D @ c_insert ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[11557]) ).
thf(11559,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OlessThan ) @ ( A @ c_insert ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[11558:[bind(A,$thf( E )),bind(B,$thf( tc_nat @ ( E @ c_SetInterval_OlessThan ) )),bind(C,$thf( tc_nat )),bind(D,$thf( D ))]]) ).
thf(11635,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OlessThan ) @ ( A @ c_insert ) ) @ c_in ) ) ),
inference(simp,[status(thm)],[11559]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(683,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(293,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).
thf(1068,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(262,axiom,
! [A: $i] :
( c_Message_Oagent_OSpy
!= ( A @ c_Message_Oagent_OFriend ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__6__iff1_0) ).
thf(994,plain,
! [A: $i] :
( c_Message_Oagent_OSpy
!= ( A @ c_Message_Oagent_OFriend ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(296,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(1073,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)],[296]) ).
thf(24,axiom,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).
thf(385,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(386,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(cnf,[status(esa)],[385]) ).
thf(387,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( A = c_0 ) ),
inference(lifteq,[status(thm)],[386]) ).
thf(254,axiom,
! [A: $i] :
( c_emptyset
= ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).
thf(974,plain,
! [A: $i] :
( c_emptyset
= ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(975,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[974]) ).
thf(1,negated_conjecture,
tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_X_H @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_B @ c_Event_Oevent_OSays ) ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(337,plain,
tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_X_H @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_B @ c_Event_Oevent_OSays ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(330,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
thf(1150,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(1151,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[1150]) ).
thf(1425,plain,
! [B: $i,A: $i] :
( ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_X_H @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_B @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[337,1151]) ).
thf(1426,plain,
! [B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_X_H @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_B @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1425]) ).
thf(1428,plain,
! [B: $i,A: $i] :
( ( tc_Event_Oevent != B )
| ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
!= c_emptyset )
| ( ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_X_H @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_B @ c_Event_Oevent_OSays ) ) )
!= A ) ),
inference(simp,[status(thm)],[1426]) ).
thf(1437,plain,
( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
!= c_emptyset ),
inference(simp,[status(thm)],[1428]) ).
thf(1472,plain,
! [A: $i] :
( ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
!= ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ) )
| ( c_emptyset != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[975,1437]) ).
thf(1473,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
!= ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ) ),
inference(simp,[status(thm)],[1472]) ).
thf(1474,plain,
! [A: $i] :
( ( A != tc_Event_Oevent )
| ( c_List_Olist_ONil != v_evs ) ),
inference(simp,[status(thm)],[1473]) ).
thf(1475,plain,
c_List_Olist_ONil != v_evs,
inference(simp,[status(thm)],[1474]) ).
thf(3510,plain,
! [A: $i] :
( ( A != c_List_Olist_ONil )
| ( c_0 != v_evs )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,1475]) ).
thf(3511,plain,
( ( c_0 != v_evs )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[3510:[bind(A,$thf( c_List_Olist_ONil ))]]) ).
thf(23,axiom,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).
thf(383,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(384,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[383]) ).
thf(4104,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_evs ) ),
inference(paramod_ordered,[status(thm)],[3511,384]) ).
thf(4105,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ( c_0 != v_evs ) ),
inference(simp,[status(thm)],[4104]) ).
thf(4140,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_List_Olist_ONil != c_0 )
| ( c_0 != A )
| ( c_0 != v_evs ) ),
inference(simp,[status(thm)],[4105]) ).
thf(4145,plain,
( ( c_List_Olist_ONil != c_0 )
| ( c_0 != v_evs ) ),
inference(simp,[status(thm)],[4140]) ).
thf(4170,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_List_Olist_ONil != c_0 )
| ( A != v_evs )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,4145]) ).
thf(4171,plain,
! [A: $i] :
( ( c_List_Olist_ONil != c_0 )
| ( A != v_evs )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[4170:[]]) ).
thf(4175,plain,
( ( c_List_Olist_ONil != c_0 )
| ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[4171]) ).
thf(17,axiom,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).
thf(367,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(368,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[367]) ).
thf(4696,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_List_Olist_ONil != c_0 ) ),
inference(paramod_ordered,[status(thm)],[4175,368]) ).
thf(4697,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ( c_List_Olist_ONil != c_0 ) ),
inference(simp,[status(thm)],[4696]) ).
thf(4700,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( c_emptyset != v_evs )
| ( c_0 != A )
| ( c_List_Olist_ONil != c_0 ) ),
inference(simp,[status(thm)],[4697]) ).
thf(4711,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( c_emptyset != v_evs )
| ( c_List_Olist_ONil != c_0 ) ),
inference(simp,[status(thm)],[4700]) ).
thf(112,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__iff1_0) ).
thf(614,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)],[112]) ).
thf(280,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__iff1_1) ).
thf(1041,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)],[280]) ).
thf(25,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__iff1_0) ).
thf(388,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(389,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[388]) ).
thf(390,plain,
! [A: $i] :
( ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) )
| ( A = c_0 ) ),
inference(lifteq,[status(thm)],[389]) ).
thf(5970,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_List_Olist_ONil != c_0 )
| ( A != v_evs )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,4145]) ).
thf(5971,plain,
! [A: $i] :
( ( c_List_Olist_ONil != c_0 )
| ( A != v_evs )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5970:[]]) ).
thf(6295,plain,
( ( c_List_Olist_ONil != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( v_evs @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5971]) ).
thf(215,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
thf(878,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(44,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__iff1_0) ).
thf(438,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)],[44]) ).
thf(439,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONumber )
!= ( B @ c_Message_Omsg_ONumber ) ) ),
inference(cnf,[status(esa)],[438]) ).
thf(440,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONumber )
!= ( B @ c_Message_Omsg_ONumber ) ) ),
inference(lifteq,[status(thm)],[439]) ).
thf(40,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__iff2_0) ).
thf(430,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)],[40]) ).
thf(431,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(cnf,[status(esa)],[430]) ).
thf(432,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[431]) ).
thf(14295,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil != c_List_Olist_ONil )
| ( A != v_evs )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[432,1475]) ).
thf(14296,plain,
! [B: $i,A: $i] :
( ( A != v_evs )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[14295:[]]) ).
thf(16020,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[14296]) ).
thf(20,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__iff2_0) ).
thf(376,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)],[20]) ).
thf(377,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(cnf,[status(esa)],[376]) ).
thf(16075,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( B @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16020,377]) ).
thf(16076,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( B @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[16075]) ).
thf(16077,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[16076:[bind(A,$thf( F )),bind(B,$thf( c_0 )),bind(C,$thf( F @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) ))]]) ).
thf(16136,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ),
inference(simp,[status(thm)],[16077]) ).
thf(16737,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16136,1151]) ).
thf(16738,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[16737]) ).
thf(16889,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ tc_prod ) )
!= C )
| ( c_emptyset != c_Wellfounded__Relations_Oless__than )
| ( ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) )
!= B ) ),
inference(simp,[status(thm)],[16738]) ).
thf(16956,plain,
c_emptyset != c_Wellfounded__Relations_Oless__than,
inference(simp,[status(thm)],[16889]) ).
thf(16967,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Wellfounded__Relations_Oless__than != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,16956]) ).
thf(16968,plain,
( ( c_Wellfounded__Relations_Oless__than != c_0 )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[16967:[bind(A,$thf( c_emptyset ))]]) ).
thf(17409,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( c_0 != c_0 )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,16968]) ).
thf(17410,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[17409]) ).
thf(17411,plain,
( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[17410:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).
thf(9,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(348,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(308,axiom,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(1102,plain,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(1331,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1102,464]) ).
thf(1332,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1331]) ).
thf(1343,plain,
! [B: $i,A: $i] :
( ( B
!= ( tc_nat @ tc_set ) )
| ( c_UNIV != c_Finite__Set_OFinites )
| ( A != c_UNIV ) ),
inference(simp,[status(thm)],[1332]) ).
thf(1350,plain,
c_UNIV != c_Finite__Set_OFinites,
inference(simp,[status(thm)],[1343]) ).
thf(5648,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1350]) ).
thf(5649,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5648:[bind(A,$thf( c_UNIV ))]]) ).
thf(6919,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
| ( c_Finite__Set_OFinites != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,5649]) ).
thf(6920,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
| ( c_Finite__Set_OFinites != c_0 ) ),
inference(simp,[status(thm)],[6919]) ).
thf(6963,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_UNIV != c_0 )
| ( c_Finite__Set_OFinites != c_0 ) ),
inference(simp,[status(thm)],[6920]) ).
thf(6971,plain,
( ( c_UNIV != c_0 )
| ( c_Finite__Set_OFinites != c_0 ) ),
inference(simp,[status(thm)],[6963]) ).
thf(7,negated_conjecture,
tc_Message_Omsg @ ( v_evs @ ( 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(340,plain,
tc_Message_Omsg @ ( v_evs @ ( 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)],[7]) ).
thf(1262,plain,
! [A: $i] :
( ( ( tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[340,815]) ).
thf(1263,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1262]) ).
thf(1270,plain,
! [A: $i] :
( ( tc_Message_Omsg != tc_Message_Omsg )
| ( ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz )
!= ( c_emptyset @ c_Message_Oparts ) )
| ( ( v_K @ c_Message_Omsg_OKey )
!= A ) ),
inference(simp,[status(thm)],[1263]) ).
thf(1275,plain,
( ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[1270]) ).
thf(241,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_OinsertCI_1) ).
thf(945,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(161,axiom,
! [A: $i] :
( c_Message_Oagent_OServer
!= ( A @ c_Message_Oagent_OFriend ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__1__iff1_0) ).
thf(747,plain,
! [A: $i] :
( c_Message_Oagent_OServer
!= ( A @ c_Message_Oagent_OFriend ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(229,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__iff1_0) ).
thf(913,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)],[229]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).
thf(670,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(235,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_0) ).
thf(934,plain,
tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(1415,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[934,1151]) ).
thf(1416,plain,
! [B: $i,A: $i] :
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1415]) ).
thf(1433,plain,
! [B: $i,A: $i] :
( ( tc_Message_Oagent != B )
| ( c_emptyset != c_Event_Obad )
| ( c_Message_Oagent_OSpy != A ) ),
inference(simp,[status(thm)],[1416]) ).
thf(1442,plain,
c_emptyset != c_Event_Obad,
inference(simp,[status(thm)],[1433]) ).
thf(6045,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1442]) ).
thf(6046,plain,
( ( c_0 != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6045:[bind(A,$thf( c_emptyset ))]]) ).
thf(222,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
thf(898,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(92,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__iff2_0) ).
thf(565,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(12,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__iff1_0) ).
thf(354,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)],[12]) ).
thf(355,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(cnf,[status(esa)],[354]) ).
thf(138,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__iff1_0) ).
thf(688,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)],[138]) ).
thf(689,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[688]) ).
thf(151,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__iff2_0) ).
thf(723,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(724,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
= c_0 ),
inference(lifteq,[status(thm)],[723]) ).
thf(1480,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(rewrite,[status(thm)],[689,724]) ).
thf(1481,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
| ~ $true
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,1480]) ).
thf(1482,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1481]) ).
thf(1483,plain,
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[1482:[bind(A,$thf( c_0 )),bind(B,$thf( c_0 ))]]) ).
thf(3276,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1102,1483]) ).
thf(3277,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[3276]) ).
thf(3287,plain,
! [B: $i,A: $i] :
( ( B
!= ( tc_nat @ ( tc_nat @ tc_prod ) ) )
| ( c_UNIV != c_Wellfounded__Relations_Oless__than )
| ( A
!= ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[3277]) ).
thf(3296,plain,
c_UNIV != c_Wellfounded__Relations_Oless__than,
inference(simp,[status(thm)],[3287]) ).
thf(6191,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,3296]) ).
thf(6192,plain,
( ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6191:[bind(A,$thf( c_UNIV ))]]) ).
thf(9971,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
| ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,6192]) ).
thf(9972,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[9971]) ).
thf(10015,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_UNIV != c_0 )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[9972]) ).
thf(10026,plain,
( ( c_UNIV != c_0 )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[10015]) ).
thf(11338,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( c_UNIV != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,10026]) ).
thf(11339,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[11338]) ).
thf(11340,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[11339:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).
thf(435,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(436,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[435]) ).
thf(1223,plain,
( ( ( tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[340,343]) ).
thf(1224,plain,
( ( tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1223]) ).
thf(1228,plain,
( ( tc_Message_Omsg != tc_Message_Oagent )
| ( ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz )
!= c_Event_Obad )
| ( ( v_K @ c_Message_Omsg_OKey )
!= v_A ) ),
inference(simp,[status(thm)],[1224]) ).
thf(202,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_Osynth_OAgent_0) ).
thf(845,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)],[202]) ).
thf(4201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[845,1151]) ).
thf(4202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[4201]) ).
thf(4240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg != D )
| ( ( B @ c_Message_Osynth )
!= c_emptyset )
| ( ( A @ c_Message_Omsg_OAgent )
!= C ) ),
inference(simp,[status(thm)],[4202]) ).
thf(4249,plain,
! [A: $i] :
( ( A @ c_Message_Osynth )
!= c_emptyset ),
inference(simp,[status(thm)],[4240]) ).
thf(305,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
thf(1095,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(30,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(403,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(404,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[403]) ).
thf(175,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(782,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)],[175]) ).
thf(1409,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1159,1151]) ).
thf(1410,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[1409]) ).
thf(1432,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != C )
| ( c_Message_OsymKeys != c_emptyset )
| ( ( A @ c_Public_OshrK )
!= B ) ),
inference(simp,[status(thm)],[1410]) ).
thf(1441,plain,
c_Message_OsymKeys != c_emptyset,
inference(simp,[status(thm)],[1432]) ).
thf(97,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
thf(575,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(576,plain,
c_UNIV != c_emptyset,
inference(polarity_switch,[status(thm)],[575]) ).
thf(577,plain,
c_UNIV != c_emptyset,
inference(lifteq,[status(thm)],[576]) ).
thf(5791,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,577]) ).
thf(5792,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5791:[bind(A,$thf( c_UNIV ))]]) ).
thf(7191,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
| ( c_emptyset != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,5792]) ).
thf(7192,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[7191]) ).
thf(7235,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_UNIV != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[7192]) ).
thf(7240,plain,
( ( c_UNIV != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[7235]) ).
thf(17680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[690,1151]) ).
thf(17681,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[17680]) ).
thf(17737,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != D )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_emptyset )
| ( A != C ) ),
inference(simp,[status(thm)],[17681]) ).
thf(17756,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(simp,[status(thm)],[17737]) ).
thf(49,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__iff1_0) ).
thf(452,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)],[49]) ).
thf(453,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Public_OpublicKey ) )
!= ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
inference(cnf,[status(esa)],[452]) ).
thf(454,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Public_OpublicKey ) )
!= ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
inference(lifteq,[status(thm)],[453]) ).
thf(455,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Public_OpublicKey ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[454]) ).
thf(456,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) @ ( B @ sk7 ) )
= A ),
inference(cnf,[status(esa)],[455]) ).
thf(13732,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) @ ( B @ sk7 ) )
= A ),
inference(lifteq,[status(thm)],[456]) ).
thf(1421,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[457,1151]) ).
thf(1422,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[1421]) ).
thf(1427,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= C )
| ( c_Finite__Set_OFinites != c_emptyset )
| ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= B ) ),
inference(simp,[status(thm)],[1422]) ).
thf(1436,plain,
c_Finite__Set_OFinites != c_emptyset,
inference(simp,[status(thm)],[1427]) ).
thf(6083,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1436]) ).
thf(6084,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6083:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(9002,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) )
| ( c_emptyset != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,6084]) ).
thf(9003,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[9002]) ).
thf(9045,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[9003]) ).
thf(9053,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[9045]) ).
thf(9408,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,9053]) ).
thf(9409,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[9408]) ).
thf(9410,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[9409:[bind(A,$thf( c_emptyset ))]]) ).
thf(129,axiom,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
thf(669,plain,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(174,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_62_AR_0) ).
thf(780,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(781,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[780]) ).
thf(1284,plain,
! [A: $i] :
( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[669,781]) ).
thf(1285,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
inference(simp,[status(thm)],[1284]) ).
thf(1298,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_Message_Oagent )
| ( c_Finite__Set_OFinites != c_Event_Obad )
| ( c_emptyset != c_Message_Oagent_OServer ) ),
inference(simp,[status(thm)],[1285]) ).
thf(6,negated_conjecture,
tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(338,plain,
tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1411,plain,
! [B: $i,A: $i] :
( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[338,1151]) ).
thf(1412,plain,
! [B: $i,A: $i] :
( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1411]) ).
thf(1431,plain,
! [B: $i,A: $i] :
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= B )
| ( c_emptyset != c_OtwayRees_Ootway )
| ( v_evs != A ) ),
inference(simp,[status(thm)],[1412]) ).
thf(1440,plain,
c_emptyset != c_OtwayRees_Ootway,
inference(simp,[status(thm)],[1431]) ).
thf(3889,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != c_OtwayRees_Ootway )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,1440]) ).
thf(3890,plain,
( ( c_0 != c_OtwayRees_Ootway )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[3889:[bind(A,$thf( c_emptyset ))]]) ).
thf(4401,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != c_OtwayRees_Ootway )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,3890]) ).
thf(4402,plain,
! [A: $i] :
( ( A != c_OtwayRees_Ootway )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[4401:[]]) ).
thf(4415,plain,
( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[4402]) ).
thf(69,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).
thf(504,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(5,negated_conjecture,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(336,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(344,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[336]) ).
thf(11523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
| ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( D @ c_insert ) ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[457,420]) ).
thf(11524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
| ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( D @ c_insert ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[11523]) ).
thf(11525,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OatMost ) @ ( A @ c_insert ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[11524:[bind(A,$thf( E )),bind(B,$thf( tc_nat @ ( E @ c_SetInterval_OatMost ) )),bind(C,$thf( tc_nat )),bind(D,$thf( D ))]]) ).
thf(11628,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OatMost ) @ ( A @ c_insert ) ) @ c_in ) ) ),
inference(simp,[status(thm)],[11525]) ).
thf(243,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__iff1_1) ).
thf(949,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)],[243]) ).
thf(82,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).
thf(542,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(286,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
thf(1055,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(238,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(939,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)],[238]) ).
thf(9227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[939,1151]) ).
thf(9228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[9227]) ).
thf(9277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_List_Olist )
!= D )
| ( ( B @ ( A @ c_List_Olists ) )
!= c_emptyset )
| ( c_List_Olist_ONil != C ) ),
inference(simp,[status(thm)],[9228]) ).
thf(9300,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Olists ) )
!= c_emptyset ),
inference(simp,[status(thm)],[9277]) ).
thf(4405,plain,
( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
| ~ $true
| ( c_0 != c_OtwayRees_Ootway ) ),
inference(paramod_ordered,[status(thm)],[3890,1480]) ).
thf(4406,plain,
( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
| ( c_0 != c_OtwayRees_Ootway ) ),
inference(simp,[status(thm)],[4405]) ).
thf(4407,plain,
( ( tc_nat != tc_nat )
| ( c_emptyset != c_0 )
| ( c_0 != c_0 )
| ( c_0 != c_OtwayRees_Ootway ) ),
inference(simp,[status(thm)],[4406]) ).
thf(4416,plain,
( ( c_emptyset != c_0 )
| ( c_0 != c_OtwayRees_Ootway ) ),
inference(simp,[status(thm)],[4407]) ).
thf(4437,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_emptyset != c_0 )
| ( A != c_OtwayRees_Ootway )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,4416]) ).
thf(4438,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( A != c_OtwayRees_Ootway )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[4437:[]]) ).
thf(4439,plain,
( ( c_emptyset != c_0 )
| ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[4438]) ).
thf(1310,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1159,781]) ).
thf(1311,plain,
! [A: $i] :
( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
inference(simp,[status(thm)],[1310]) ).
thf(1323,plain,
! [A: $i] :
( ( tc_nat != tc_Message_Oagent )
| ( c_Message_OsymKeys != c_Event_Obad )
| ( ( A @ c_Public_OshrK )
!= c_Message_Oagent_OServer ) ),
inference(simp,[status(thm)],[1311]) ).
thf(199,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_OUnE_0) ).
thf(838,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)],[199]) ).
thf(14,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__iff2_0) ).
thf(357,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(224,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(902,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)],[224]) ).
thf(118,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(638,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(301,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( C @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).
thf(1087,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( C @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(329,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).
thf(1147,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).
thf(359,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(360,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
inference(cnf,[status(esa)],[359]) ).
thf(361,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
inference(lifteq,[status(thm)],[360]) ).
thf(362,plain,
? [A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[361]) ).
thf(363,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) @ ( C @ ( B @ sk1 ) ) )
= A ),
inference(cnf,[status(esa)],[362]) ).
thf(1479,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) @ ( C @ ( B @ sk1 ) ) )
= A ),
inference(lifteq,[status(thm)],[363]) ).
thf(109,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_91X_93_AY_A_61_ANonce_AN_A_61_61_62_AR_0) ).
thf(606,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)],[109]) ).
thf(315,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(1115,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)],[315]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).
thf(448,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(36,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
thf(421,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(212,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__iff1_0) ).
thf(870,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Public_OshrK )
!= ( B @ c_Public_OshrK ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(27,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__iff1_0) ).
thf(394,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)],[27]) ).
thf(395,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(cnf,[status(esa)],[394]) ).
thf(396,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(lifteq,[status(thm)],[395]) ).
thf(397,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_List_Orev ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[396]) ).
thf(398,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Orev ) @ ( B @ sk3 ) )
= A ),
inference(cnf,[status(esa)],[397]) ).
thf(7060,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Orev ) @ ( B @ sk3 ) )
= A ),
inference(lifteq,[status(thm)],[398]) ).
thf(216,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).
thf(881,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(34,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__iff1_0) ).
thf(416,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)],[34]) ).
thf(66,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__iff1_0) ).
thf(494,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)],[66]) ).
thf(495,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OHash ) ) ),
inference(cnf,[status(esa)],[494]) ).
thf(496,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OHash ) ) ),
inference(lifteq,[status(thm)],[495]) ).
thf(497,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OHash @ A )
= B ),
inference(detectInverse,[status(thm)],[496]) ).
thf(498,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OHash @ sk10 )
= A ),
inference(cnf,[status(esa)],[497]) ).
thf(1489,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OHash @ sk10 )
= A ),
inference(lifteq,[status(thm)],[498]) ).
thf(65,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__iff1_0) ).
thf(492,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)],[65]) ).
thf(45,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(148,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(717,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(16969,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,16956]) ).
thf(16970,plain,
( ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[16969:[bind(A,$thf( c_emptyset ))]]) ).
thf(17091,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) )
| ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[717,16970]) ).
thf(17092,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[17091]) ).
thf(17116,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( A != c_0 )
| ( c_emptyset != c_emptyset )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[17092]) ).
thf(17129,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[17116]) ).
thf(312,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(1109,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)],[312]) ).
thf(4136,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_evs ) ),
inference(paramod_ordered,[status(thm)],[3511,368]) ).
thf(4137,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ( c_0 != v_evs ) ),
inference(simp,[status(thm)],[4136]) ).
thf(4141,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( c_emptyset != c_List_Olist_ONil )
| ( c_0 != A )
| ( c_0 != v_evs ) ),
inference(simp,[status(thm)],[4137]) ).
thf(4147,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( c_emptyset != c_List_Olist_ONil )
| ( c_0 != v_evs ) ),
inference(simp,[status(thm)],[4141]) ).
thf(57,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(475,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)],[57]) ).
thf(233,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__iff1_1) ).
thf(924,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)],[233]) ).
thf(17062,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) )
| ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,16970]) ).
thf(17063,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[17062]) ).
thf(17115,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_emptyset != c_0 )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[17063]) ).
thf(17128,plain,
( ( c_emptyset != c_0 )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[17115]) ).
thf(17352,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( c_emptyset != c_0 )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,17128]) ).
thf(17353,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( c_emptyset != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[17352]) ).
thf(17354,plain,
( ( c_emptyset != c_0 )
| ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[17353:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).
thf(165,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__iff1_0) ).
thf(756,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)],[165]) ).
thf(5721,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_emptyset != c_0 )
| ( A != c_OtwayRees_Ootway )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,4416]) ).
thf(5722,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( A != c_OtwayRees_Ootway )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5721:[]]) ).
thf(6227,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_OtwayRees_Ootway @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5722]) ).
thf(178,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__iff1_0) ).
thf(789,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)],[178]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
!= ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).
thf(738,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
!= ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(739,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
!= ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
inference(cnf,[status(esa)],[738]) ).
thf(740,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
!= ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
inference(lifteq,[status(thm)],[739]) ).
thf(741,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Datatype_Ooption_OSome ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[740]) ).
thf(742,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Datatype_Ooption_OSome ) @ ( B @ sk22 ) )
= A ),
inference(cnf,[status(esa)],[741]) ).
thf(19485,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Datatype_Ooption_OSome ) @ ( B @ sk22 ) )
= A ),
inference(lifteq,[status(thm)],[742]) ).
thf(62,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__iff1_0) ).
thf(485,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)],[62]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(834,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(237,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(937,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)],[237]) ).
thf(1381,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ $true
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,384]) ).
thf(1382,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1381]) ).
thf(1383,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[1382:[bind(A,$thf( A )),bind(B,$thf( c_0 )),bind(C,$thf( A ))]]) ).
thf(11,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__iff1_0) ).
thf(351,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)],[11]) ).
thf(352,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( B @ ( A @ c_List_Orev ) ) ) ),
inference(cnf,[status(esa)],[351]) ).
thf(353,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Orev ) )
!= c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[352]) ).
thf(250,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(966,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)],[250]) ).
thf(225,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_91X_93_AY_A_61_AKey_AK_A_61_61_62_AR_0) ).
thf(903,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)],[225]) ).
thf(904,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OKey ) ),
inference(polarity_switch,[status(thm)],[903]) ).
thf(905,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OKey ) ),
inference(lifteq,[status(thm)],[904]) ).
thf(168,axiom,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OSpy ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__5__iff1_0) ).
thf(766,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OSpy ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(1165,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[338,344]) ).
thf(1166,plain,
( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) ),
inference(simp,[status(thm)],[1165]) ).
thf(1169,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Oagent )
| ( c_OtwayRees_Ootway != c_Event_Obad )
| ( v_evs != v_B ) ),
inference(simp,[status(thm)],[1166]) ).
thf(155,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_91X_93_AY_A_61_AHash_AZ_A_61_61_62_AR_0) ).
thf(732,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)],[155]) ).
thf(733,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OHash ) ),
inference(polarity_switch,[status(thm)],[732]) ).
thf(734,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OHash ) ),
inference(lifteq,[status(thm)],[733]) ).
thf(245,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
thf(956,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(3343,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( c_Message_OsymKeys @ ( D @ ( C @ c_Public_OpublicKey ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1102,702]) ).
thf(3344,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( c_Message_OsymKeys @ ( D @ ( C @ c_Public_OpublicKey ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[3343]) ).
thf(3358,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != tc_nat )
| ( c_Message_OsymKeys != c_UNIV )
| ( A
!= ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
inference(simp,[status(thm)],[3344]) ).
thf(3368,plain,
c_Message_OsymKeys != c_UNIV,
inference(simp,[status(thm)],[3358]) ).
thf(6020,plain,
! [A: $i] :
( ( A != c_Message_OsymKeys )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,3368]) ).
thf(6021,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Message_OsymKeys @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6020:[bind(A,$thf( c_Message_OsymKeys ))]]) ).
thf(7864,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_Message_OsymKeys @ c_lessequals ) ) ) )
| ( c_UNIV != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,6021]) ).
thf(7865,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_Message_OsymKeys @ c_lessequals ) ) ) )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[7864]) ).
thf(7908,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_Message_OsymKeys != c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[7865]) ).
thf(7913,plain,
( ( c_Message_OsymKeys != c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[7908]) ).
thf(7934,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Message_OsymKeys != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,7913]) ).
thf(7935,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Message_OsymKeys != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[7934]) ).
thf(7936,plain,
( ( c_Message_OsymKeys != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7935:[bind(A,$thf( c_UNIV ))]]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(774,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(3859,plain,
! [A: $i] :
( ( A
!= ( tc_Event_Oevent @ tc_List_Olist ) )
| ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,338]) ).
thf(3860,plain,
( ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
| ( tc_nat @ ( tc_Event_Oevent @ tc_List_Olist @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[3859:[bind(A,$thf( tc_Event_Oevent @ tc_List_Olist ))]]) ).
thf(6999,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_Event_Oevent @ tc_List_Olist @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[3860,384]) ).
thf(7000,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_Event_Oevent @ tc_List_Olist @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) ),
inference(simp,[status(thm)],[6999]) ).
thf(7044,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_Event_Oevent @ tc_List_Olist )
!= c_0 )
| ( c_0 != A )
| ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) ),
inference(simp,[status(thm)],[7000]) ).
thf(7051,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= c_0 )
| ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) ),
inference(simp,[status(thm)],[7044]) ).
thf(289,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(1061,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)],[289]) ).
thf(9867,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1061,815]) ).
thf(9868,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[9867]) ).
thf(9903,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg != tc_Message_Omsg )
| ( ( B @ ( A @ c_Event_Oknows ) )
!= ( c_emptyset @ c_Message_Oparts ) )
| ( ( A @ c_Public_OshrK @ c_Message_Omsg_OKey )
!= C ) ),
inference(simp,[status(thm)],[9868]) ).
thf(9923,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oknows ) )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[9903]) ).
thf(263,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__iff1_0) ).
thf(997,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)],[263]) ).
thf(998,plain,
! [B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[997]) ).
thf(33,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__iff1_0) ).
thf(411,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)],[33]) ).
thf(1335,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1102,815]) ).
thf(1336,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[1335]) ).
thf(1344,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_UNIV )
| ( A != C ) ),
inference(simp,[status(thm)],[1336]) ).
thf(1345,plain,
( ( c_emptyset @ c_Message_Oparts )
!= c_UNIV ),
inference(simp,[status(thm)],[1344]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
| ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).
thf(428,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
| ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1195,plain,
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
!= ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[338,464]) ).
thf(1196,plain,
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
!= ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) ),
inference(simp,[status(thm)],[1195]) ).
thf(1201,plain,
( ( ( tc_nat @ tc_set )
!= ( tc_Event_Oevent @ tc_List_Olist ) )
| ( c_Finite__Set_OFinites != c_OtwayRees_Ootway )
| ( c_UNIV != v_evs ) ),
inference(simp,[status(thm)],[1196]) ).
thf(297,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__iff1_0) ).
thf(1074,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)],[297]) ).
thf(5405,plain,
! [A: $i] :
( ( A
!= ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ) )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1437]) ).
thf(5406,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5405:[bind(A,$thf( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ))]]) ).
thf(22,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__iff1_0) ).
thf(380,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)],[22]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).
thf(678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).
thf(546,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(166,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__iff1_0) ).
thf(761,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)],[166]) ).
thf(186,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(810,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)],[186]) ).
thf(1449,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[589,464]) ).
thf(1450,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1449]) ).
thf(1463,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1450]) ).
thf(1470,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
!= c_UNIV ),
inference(simp,[status(thm)],[1463]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(364,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(365,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[364]) ).
thf(366,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[365]) ).
thf(80,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__iff1_0) ).
thf(534,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)],[80]) ).
thf(282,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__iff1_0) ).
thf(1045,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)],[282]) ).
thf(1046,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[1045]) ).
thf(1047,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[1046]) ).
thf(72,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__iff1_0) ).
thf(512,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)],[72]) ).
thf(240,axiom,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OServer ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__2__iff1_0) ).
thf(942,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OServer ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(2,negated_conjecture,
tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_X @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Event_Oevent_OGets ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(339,plain,
tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_X @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Event_Oevent_OGets ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1258,plain,
! [A: $i] :
( ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_X @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Event_Oevent_OGets ) @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[339,815]) ).
thf(1259,plain,
! [A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_X @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Event_Oevent_OGets ) @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1258]) ).
thf(1269,plain,
! [A: $i] :
( ( tc_Message_Omsg != tc_Event_Oevent )
| ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
!= ( c_emptyset @ c_Message_Oparts ) )
| ( ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_X @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Event_Oevent_OGets ) )
!= A ) ),
inference(simp,[status(thm)],[1259]) ).
thf(1274,plain,
( ( tc_Message_Omsg != tc_Event_Oevent )
| ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
!= ( c_emptyset @ c_Message_Oparts ) ) ),
inference(simp,[status(thm)],[1269]) ).
thf(227,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__iff1_0) ).
thf(908,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)],[227]) ).
thf(909,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
inference(polarity_switch,[status(thm)],[908]) ).
thf(910,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
inference(lifteq,[status(thm)],[909]) ).
thf(193,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__3__iff1_0) ).
thf(823,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(824,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(polarity_switch,[status(thm)],[823]) ).
thf(825,plain,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
inference(lifteq,[status(thm)],[824]) ).
thf(53,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(465,plain,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(3866,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,465]) ).
thf(3867,plain,
( ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[3866:[bind(A,$thf( tc_nat ))]]) ).
thf(6030,plain,
! [A: $i] :
( ( A != c_List_Olist_ONil )
| ( c_0 != c_0 )
| ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,4175]) ).
thf(6031,plain,
! [A: $i] :
( ( A != c_List_Olist_ONil )
| ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[6030]) ).
thf(6032,plain,
( ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( c_List_Olist_ONil @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6031:[bind(A,$thf( c_List_Olist_ONil ))]]) ).
thf(106,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__iff1_0) ).
thf(598,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)],[106]) ).
thf(191,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).
thf(820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(429,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
| ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[428]) ).
thf(1355,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[457,464]) ).
thf(1356,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1355]) ).
thf(1366,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1356]) ).
thf(1370,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= c_UNIV ),
inference(simp,[status(thm)],[1366]) ).
thf(154,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__iff1_0) ).
thf(729,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)],[154]) ).
thf(272,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__iff1_0) ).
thf(1021,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)],[272]) ).
thf(173,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
thf(778,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(209,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
thf(862,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(10,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__iff2_0) ).
thf(349,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(37,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).
thf(422,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(423,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(cnf,[status(esa)],[422]) ).
thf(424,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(lifteq,[status(thm)],[423]) ).
thf(871,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Public_OshrK )
!= ( B @ c_Public_OshrK ) ) ),
inference(cnf,[status(esa)],[870]) ).
thf(872,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Public_OshrK )
!= ( B @ c_Public_OshrK ) ) ),
inference(lifteq,[status(thm)],[871]) ).
thf(873,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Public_OshrK @ A )
= B ),
inference(detectInverse,[status(thm)],[872]) ).
thf(874,plain,
! [A: $i] :
( ( A @ c_Public_OshrK @ sk28 )
= A ),
inference(cnf,[status(esa)],[873]) ).
thf(3069,plain,
! [A: $i] :
( ( A @ c_Public_OshrK @ sk28 )
= A ),
inference(lifteq,[status(thm)],[874]) ).
thf(31,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).
thf(405,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(406,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[405]) ).
thf(407,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) )
| ( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) )
= A ) ),
inference(lifteq,[status(thm)],[406]) ).
thf(141,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).
thf(693,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(116,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(630,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)],[116]) ).
thf(115,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__iff1_1) ).
thf(625,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)],[115]) ).
thf(3498,plain,
! [A: $i] :
( ( A
!= ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz ) )
| ( tc_Message_Omsg @ ( c_0 @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,340]) ).
thf(3499,plain,
( ( tc_Message_Omsg @ ( c_0 @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_nat @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[3498:[bind(A,$thf( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz ))]]) ).
thf(51,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__iff1_0) ).
thf(458,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)],[51]) ).
thf(459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(cnf,[status(esa)],[458]) ).
thf(460,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(lifteq,[status(thm)],[459]) ).
thf(461,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_OHPair ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[460]) ).
thf(462,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) @ ( B @ sk8 ) )
= A ),
inference(cnf,[status(esa)],[461]) ).
thf(13763,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) @ ( B @ sk8 ) )
= A ),
inference(lifteq,[status(thm)],[462]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
thf(665,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).
thf(583,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(299,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_91X_93_AY_A_61_AAgent_AA_A_61_61_62_AR_0) ).
thf(1079,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)],[299]) ).
thf(142,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__iff1_0) ).
thf(696,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)],[142]) ).
thf(697,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Oagent_OFriend )
!= ( B @ c_Message_Oagent_OFriend ) ) ),
inference(cnf,[status(esa)],[696]) ).
thf(698,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Oagent_OFriend )
!= ( B @ c_Message_Oagent_OFriend ) ) ),
inference(lifteq,[status(thm)],[697]) ).
thf(699,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Oagent_OFriend @ A )
= B ),
inference(detectInverse,[status(thm)],[698]) ).
thf(700,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend @ sk19 )
= A ),
inference(cnf,[status(esa)],[699]) ).
thf(3028,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend @ sk19 )
= A ),
inference(lifteq,[status(thm)],[700]) ).
thf(1374,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) )
| ~ $true
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,404]) ).
thf(1375,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1374]) ).
thf(1376,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[1375:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(1407,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(simp,[status(thm)],[1376]) ).
thf(86,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).
thf(551,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(201,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_91X_93_AY_A_61_ACrypt_AK_AX_H_A_61_61_62_AR_0) ).
thf(842,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)],[201]) ).
thf(269,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__iff1_0) ).
thf(1012,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)],[269]) ).
thf(230,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__iff1_0) ).
thf(916,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)],[230]) ).
thf(54,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__iff1_0) ).
thf(466,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)],[54]) ).
thf(467,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[466]) ).
thf(566,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
inference(lifteq,[status(thm)],[565]) ).
thf(61,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(484,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)],[61]) ).
thf(206,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__iff1_1) ).
thf(852,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)],[206]) ).
thf(98,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__iff2_0) ).
thf(578,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)],[98]) ).
thf(302,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(1089,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)],[302]) ).
thf(327,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
thf(1143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(270,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(1017,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)],[270]) ).
thf(291,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_0) ).
thf(1064,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)],[291]) ).
thf(152,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__iff2_0) ).
thf(725,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(266,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(1006,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)],[266]) ).
thf(104,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_91X_93_AY_A_61_ANumber_AN_A_61_61_62_AR_0) ).
thf(593,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)],[104]) ).
thf(67,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__iff1_0) ).
thf(499,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)],[67]) ).
thf(259,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__iff1_0) ).
thf(987,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)],[259]) ).
thf(988,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[987]) ).
thf(989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[988]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
thf(857,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(313,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(1111,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)],[313]) ).
thf(1221,plain,
( ( ( tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[340,344]) ).
thf(1222,plain,
( ( tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) ),
inference(simp,[status(thm)],[1221]) ).
thf(1227,plain,
( ( tc_Message_Omsg != tc_Message_Oagent )
| ( ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz )
!= c_Event_Obad )
| ( ( v_K @ c_Message_Omsg_OKey )
!= v_B ) ),
inference(simp,[status(thm)],[1222]) ).
thf(257,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__iff1_2) ).
thf(980,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)],[257]) ).
thf(325,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__iff1_0) ).
thf(1138,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)],[325]) ).
thf(13,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).
thf(356,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(217,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(884,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)],[217]) ).
thf(335,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__iff1_1) ).
thf(1160,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)],[335]) ).
thf(63,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_Ab_AA_A_61_ApublicKey_Ac_AA_H_A_61_61_62_AR_0) ).
thf(488,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)],[63]) ).
thf(88,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).
thf(554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(81,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__iff1_1) ).
thf(537,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)],[81]) ).
thf(120,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__iff1_0) ).
thf(642,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)],[120]) ).
thf(76,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).
thf(526,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(1329,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1102,781]) ).
thf(1330,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
inference(simp,[status(thm)],[1329]) ).
thf(1339,plain,
! [B: $i,A: $i] :
( ( B != tc_Message_Oagent )
| ( c_UNIV != c_Event_Obad )
| ( A != c_Message_Oagent_OServer ) ),
inference(simp,[status(thm)],[1330]) ).
thf(1346,plain,
c_UNIV != c_Event_Obad,
inference(simp,[status(thm)],[1339]) ).
thf(6098,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1346]) ).
thf(6099,plain,
( ( c_0 != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6098:[bind(A,$thf( c_UNIV ))]]) ).
thf(9420,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
| ( c_0 != c_Event_Obad )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,6099]) ).
thf(9421,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
| ( c_0 != c_Event_Obad ) ),
inference(simp,[status(thm)],[9420]) ).
thf(9466,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_UNIV != c_0 )
| ( c_0 != c_Event_Obad ) ),
inference(simp,[status(thm)],[9421]) ).
thf(9477,plain,
( ( c_UNIV != c_0 )
| ( c_0 != c_Event_Obad ) ),
inference(simp,[status(thm)],[9466]) ).
thf(103,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__iff1_0) ).
thf(590,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)],[103]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).
thf(371,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(372,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
inference(cnf,[status(esa)],[371]) ).
thf(373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
inference(lifteq,[status(thm)],[372]) ).
thf(374,plain,
? [A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[373]) ).
thf(375,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) @ ( C @ ( B @ sk2 ) ) )
= A ),
inference(cnf,[status(esa)],[374]) ).
thf(4444,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) @ ( C @ ( B @ sk2 ) ) )
= A ),
inference(lifteq,[status(thm)],[375]) ).
thf(252,axiom,
! [F: $i,E: $i,D: $i,C: $i,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 @ ( F @ c_Message_Omsg_OAgent @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Message_Omsg_OAgent @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OtwayRees_Ono__nonce__OR1__OR2__dest_0) ).
thf(970,plain,
! [F: $i,E: $i,D: $i,C: $i,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 @ ( F @ c_Message_Omsg_OAgent @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Message_Omsg_OAgent @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(332,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(1155,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)],[332]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
thf(1028,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(300,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__iff1_0) ).
thf(1082,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)],[300]) ).
thf(17682,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[690,1383]) ).
thf(17683,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[17682]) ).
thf(17742,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( tc_nat @ ( tc_nat @ tc_prod ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_Wellfounded__Relations_Oless__than )
| ( A
!= ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[17683]) ).
thf(17761,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( A @ c_Pair ) ) ) @ c_insert ) ) )
!= c_Wellfounded__Relations_Oless__than ),
inference(simp,[status(thm)],[17742]) ).
thf(7825,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[421,464]) ).
thf(7826,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[7825]) ).
thf(7829,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[7826]) ).
thf(7846,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[7829]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).
thf(391,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(392,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
inference(polarity_switch,[status(thm)],[391]) ).
thf(393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
inference(lifteq,[status(thm)],[392]) ).
thf(1292,plain,
! [A: $i] :
( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[669,343]) ).
thf(1293,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1292]) ).
thf(1297,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_Message_Oagent )
| ( c_Finite__Set_OFinites != c_Event_Obad )
| ( c_emptyset != v_A ) ),
inference(simp,[status(thm)],[1293]) ).
thf(228,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__iff1_0) ).
thf(911,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)],[228]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).
thf(569,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(8434,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) )
| ( c_0 != c_Event_Obad )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,6046]) ).
thf(8435,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) )
| ( c_0 != c_Event_Obad ) ),
inference(simp,[status(thm)],[8434]) ).
thf(8479,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_emptyset != c_0 )
| ( c_0 != c_Event_Obad ) ),
inference(simp,[status(thm)],[8435]) ).
thf(8493,plain,
( ( c_emptyset != c_0 )
| ( c_0 != c_Event_Obad ) ),
inference(simp,[status(thm)],[8479]) ).
thf(8992,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_emptyset != c_0 )
| ( A != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,8493]) ).
thf(8993,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( A != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[8992:[]]) ).
thf(8995,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Event_Obad @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[8993]) ).
thf(108,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__iff1_0) ).
thf(603,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)],[108]) ).
thf(604,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[603]) ).
thf(605,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[604]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).
thf(647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(307,axiom,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__4__iff1_0) ).
thf(1099,plain,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(258,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
thf(985,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(17358,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( c_emptyset != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,17128]) ).
thf(17359,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[17358]) ).
thf(17360,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[17359:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).
thf(73,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__iff1_1) ).
thf(515,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)],[73]) ).
thf(412,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_ONonce ) ) ),
inference(cnf,[status(esa)],[411]) ).
thf(413,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_ONonce ) ) ),
inference(lifteq,[status(thm)],[412]) ).
thf(414,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_ONonce @ A )
= B ),
inference(detectInverse,[status(thm)],[413]) ).
thf(415,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_ONonce @ sk4 )
= A ),
inference(cnf,[status(esa)],[414]) ).
thf(1478,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_ONonce @ sk4 )
= A ),
inference(lifteq,[status(thm)],[415]) ).
thf(322,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(1131,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)],[322]) ).
thf(123,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).
thf(654,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(38,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
thf(427,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(8272,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[427,464]) ).
thf(8273,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[8272]) ).
thf(8285,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[8273]) ).
thf(8294,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[8285]) ).
thf(1183,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)],[934,343]) ).
thf(1184,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)],[1183]) ).
thf(1189,plain,
( ( tc_Message_Oagent != tc_Message_Oagent )
| ( c_Event_Obad != c_Event_Obad )
| ( c_Message_Oagent_OSpy != v_A ) ),
inference(simp,[status(thm)],[1184]) ).
thf(1192,plain,
c_Message_Oagent_OSpy != v_A,
inference(simp,[status(thm)],[1189]) ).
thf(288,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__iff1_0) ).
thf(1058,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(1059,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) ) ),
inference(polarity_switch,[status(thm)],[1058]) ).
thf(1060,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) ) ),
inference(lifteq,[status(thm)],[1059]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).
thf(1050,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(3,negated_conjecture,
~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ 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_2) ).
thf(341,plain,
~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ 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(345,plain,
~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ 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)],[341]) ).
thf(17714,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ 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 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[690,345]) ).
thf(17715,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ 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(simp,[status(thm)],[17714]) ).
thf(17733,plain,
! [B: $i,A: $i] :
( ( B != tc_Event_Oevent )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ) )
| ( A
!= ( 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 ) ) ) ),
inference(simp,[status(thm)],[17715]) ).
thf(17752,plain,
( ( tc_Event_Oevent @ ( c_emptyset @ ( 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_insert ) ) )
!= ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ) ),
inference(simp,[status(thm)],[17733]) ).
thf(5569,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( c_0 @ c_Message_Oparts )
!= c_UNIV )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1345]) ).
thf(5570,plain,
( ( ( c_0 @ c_Message_Oparts )
!= c_UNIV )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5569:[bind(A,$thf( c_emptyset ))]]) ).
thf(16259,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) )
| ( ( c_0 @ c_Message_Oparts )
!= c_UNIV )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,5570]) ).
thf(16260,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) )
| ( ( c_0 @ c_Message_Oparts )
!= c_UNIV ) ),
inference(simp,[status(thm)],[16259]) ).
thf(16324,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_emptyset != c_0 )
| ( ( c_0 @ c_Message_Oparts )
!= c_UNIV ) ),
inference(simp,[status(thm)],[16260]) ).
thf(16328,plain,
( ( c_emptyset != c_0 )
| ( ( c_0 @ c_Message_Oparts )
!= c_UNIV ) ),
inference(simp,[status(thm)],[16324]) ).
thf(1327,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ 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 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1102,345]) ).
thf(1328,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ 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(simp,[status(thm)],[1327]) ).
thf(1342,plain,
! [B: $i,A: $i] :
( ( B != tc_Event_Oevent )
| ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
!= c_UNIV )
| ( A
!= ( 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 ) ) ) ),
inference(simp,[status(thm)],[1328]) ).
thf(1349,plain,
( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
!= c_UNIV ),
inference(simp,[status(thm)],[1342]) ).
thf(3754,plain,
! [A: $i] :
( ( A
!= ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ) )
| ( c_UNIV != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,1349]) ).
thf(3755,plain,
( ( c_UNIV != c_0 )
| ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[3754:[bind(A,$thf( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ))]]) ).
thf(117,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__iff1_0) ).
thf(633,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)],[117]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).
thf(657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(278,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = G )
| ( 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_Message_Omsg_OAgent @ ( G @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Message_Omsg_OAgent @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OtwayRees_Ounique__NB__dest_1) ).
thf(1035,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = G )
| ( 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_Message_Omsg_OAgent @ ( G @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Message_Omsg_OAgent @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(9102,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != c_0 )
| ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,3755]) ).
thf(9103,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[9102]) ).
thf(9104,plain,
( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[9103:[bind(A,$thf( c_UNIV ))]]) ).
thf(274,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_0) ).
thf(1026,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)],[274]) ).
thf(78,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__iff2_0) ).
thf(530,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)],[78]) ).
thf(183,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).
thf(805,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(64,axiom,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(491,plain,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(3983,plain,
! [B: $i,A: $i] :
( ( A != c_emptyset )
| ( B @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,491]) ).
thf(3984,plain,
! [A: $i] :
( ( A @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[3983:[bind(A,$thf( c_emptyset ))]]) ).
thf(4081,plain,
! [A: $i] :
( ( A @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[3984]) ).
thf(17731,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[690,464]) ).
thf(17732,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[17731]) ).
thf(17748,plain,
! [B: $i,A: $i] :
( ( B
!= ( tc_nat @ tc_set ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_Finite__Set_OFinites )
| ( A != c_UNIV ) ),
inference(simp,[status(thm)],[17732]) ).
thf(17767,plain,
( ( tc_nat @ tc_set @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
!= c_Finite__Set_OFinites ),
inference(simp,[status(thm)],[17748]) ).
thf(1167,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[338,343]) ).
thf(1168,plain,
( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1167]) ).
thf(1170,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Oagent )
| ( c_OtwayRees_Ootway != c_Event_Obad )
| ( v_evs != v_A ) ),
inference(simp,[status(thm)],[1168]) ).
thf(90,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).
thf(558,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(295,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).
thf(1071,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(179,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(794,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)],[179]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
= ( C @ ( A @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).
thf(586,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
= ( C @ ( A @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(126,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
thf(662,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).
thf(718,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
| ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).
thf(1135,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
| ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(162,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
thf(750,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(5567,plain,
! [A: $i] :
( ( A
!= ( c_emptyset @ c_Message_Oparts ) )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1345]) ).
thf(5568,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5567:[bind(A,$thf( c_emptyset @ c_Message_Oparts ))]]) ).
thf(13948,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_emptyset @ c_Message_Oparts @ c_lessequals ) ) ) )
| ( c_UNIV != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,5568]) ).
thf(13949,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_emptyset @ c_Message_Oparts @ c_lessequals ) ) ) )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[13948]) ).
thf(14003,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[13949]) ).
thf(14015,plain,
( ( ( c_emptyset @ c_Message_Oparts )
!= c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[14003]) ).
thf(16231,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,14015]) ).
thf(16232,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[16231]) ).
thf(16233,plain,
( ( ( c_emptyset @ c_Message_Oparts )
!= c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[16232:[bind(A,$thf( c_UNIV ))]]) ).
thf(157,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
thf(737,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(8873,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[737,464]) ).
thf(8874,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[8873]) ).
thf(8877,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[8874]) ).
thf(8903,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[8877]) ).
thf(309,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
thf(1103,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(160,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(745,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)],[160]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).
thf(573,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(16048,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( B @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16020,384]) ).
thf(16049,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[16048]) ).
thf(16122,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) )
!= c_0 )
| ( c_0 != B ) ),
inference(simp,[status(thm)],[16049]) ).
thf(16152,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[16122]) ).
thf(444,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[443]) ).
thf(192,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(822,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)],[192]) ).
thf(4541,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[822,1151]) ).
thf(4542,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[4541]) ).
thf(4585,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg != D )
| ( ( B @ c_Event_Oused )
!= c_emptyset )
| ( ( A @ c_Public_OshrK @ c_Message_Omsg_OKey )
!= C ) ),
inference(simp,[status(thm)],[4542]) ).
thf(4599,plain,
! [A: $i] :
( ( A @ c_Event_Oused )
!= c_emptyset ),
inference(simp,[status(thm)],[4585]) ).
thf(107,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
thf(601,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(226,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
thf(906,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(1264,plain,
! [A: $i] :
( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[934,815]) ).
thf(1265,plain,
! [A: $i] :
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1264]) ).
thf(1268,plain,
! [A: $i] :
( ( tc_Message_Omsg != tc_Message_Oagent )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Event_Obad )
| ( c_Message_Oagent_OSpy != A ) ),
inference(simp,[status(thm)],[1265]) ).
thf(1273,plain,
( ( tc_Message_Omsg != tc_Message_Oagent )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Event_Obad ) ),
inference(simp,[status(thm)],[1268]) ).
thf(331,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__iff1_0) ).
thf(1152,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)],[331]) ).
thf(1153,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
inference(polarity_switch,[status(thm)],[1152]) ).
thf(1154,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
inference(lifteq,[status(thm)],[1153]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(401,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(402,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(cnf,[status(esa)],[401]) ).
thf(91,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__iff1_1) ).
thf(560,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)],[91]) ).
thf(561,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(cnf,[status(esa)],[560]) ).
thf(562,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
inference(lifteq,[status(thm)],[561]) ).
thf(563,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_OHPair ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[562]) ).
thf(564,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) @ ( A @ sk13 ) )
= B ),
inference(cnf,[status(esa)],[563]) ).
thf(16977,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) @ ( A @ sk13 ) )
= B ),
inference(lifteq,[status(thm)],[564]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
thf(743,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(246,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__iff1_0) ).
thf(958,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)],[246]) ).
thf(319,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
thf(1124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(5718,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != c_0 )
| ( c_0 != c_OtwayRees_Ootway )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,4416]) ).
thf(5719,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != c_OtwayRees_Ootway )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5718]) ).
thf(5720,plain,
( ( c_0 != c_OtwayRees_Ootway )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5719:[bind(A,$thf( c_emptyset ))]]) ).
thf(4134,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != v_evs )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,3511]) ).
thf(4135,plain,
! [A: $i] :
( ( A != v_evs )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[4134:[]]) ).
thf(4144,plain,
( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[4135]) ).
thf(213,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).
thf(875,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(194,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(826,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)],[194]) ).
thf(3724,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( c_List_Olist_ONil @ c_List_Oset ) ) )
| ( c_emptyset = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,975]) ).
thf(3725,plain,
! [A: $i] :
( ( c_emptyset = c_0 )
| ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_List_Oset ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[3724:[bind(A,$thf( D @ ( c_List_Olist_ONil @ c_List_Oset ) )),bind(B,$thf( D ))]]) ).
thf(4018,plain,
! [A: $i] :
( ( c_emptyset = c_0 )
| ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_List_Oset ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[3725]) ).
thf(17130,plain,
( ( c_emptyset = c_0 )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(rewrite,[status(thm)],[4018,975]) ).
thf(1219,plain,
( ( ( tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[340,464]) ).
thf(1220,plain,
( ( tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1219]) ).
thf(1226,plain,
( ( ( tc_nat @ tc_set )
!= tc_Message_Omsg )
| ( ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz )
!= c_Finite__Set_OFinites )
| ( ( v_K @ c_Message_Omsg_OKey )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1220]) ).
thf(441,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_ONumber @ A )
= B ),
inference(detectInverse,[status(thm)],[440]) ).
thf(442,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_ONumber @ sk6 )
= A ),
inference(cnf,[status(esa)],[441]) ).
thf(1488,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_ONumber @ sk6 )
= A ),
inference(lifteq,[status(thm)],[442]) ).
thf(119,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__iff1_0) ).
thf(639,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)],[119]) ).
thf(640,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[639]) ).
thf(641,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[640]) ).
thf(46,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__iff1_1) ).
thf(445,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)],[46]) ).
thf(6989,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( c_UNIV != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,6971]) ).
thf(6990,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[6989]) ).
thf(6991,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6990:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(303,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__iff1_1) ).
thf(1090,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)],[303]) ).
thf(231,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__iff1_0) ).
thf(919,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)],[231]) ).
thf(350,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
= c_List_Olist_ONil ),
inference(lifteq,[status(thm)],[349]) ).
thf(9961,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_UNIV != c_0 )
| ( A != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,9477]) ).
thf(9962,plain,
! [A: $i] :
( ( c_UNIV != c_0 )
| ( A != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[9961:[]]) ).
thf(9967,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Event_Obad @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[9962]) ).
thf(131,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__iff1_0) ).
thf(672,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)],[131]) ).
thf(311,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
thf(1107,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(764,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1187,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)],[934,344]) ).
thf(1188,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)],[1187]) ).
thf(1191,plain,
( ( tc_Message_Oagent != tc_Message_Oagent )
| ( c_Event_Obad != c_Event_Obad )
| ( c_Message_Oagent_OSpy != v_B ) ),
inference(simp,[status(thm)],[1188]) ).
thf(1194,plain,
c_Message_Oagent_OSpy != v_B,
inference(simp,[status(thm)],[1191]) ).
thf(223,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(900,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)],[223]) ).
thf(283,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).
thf(1048,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).
thf(567,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(318,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
thf(1122,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(176,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(784,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)],[176]) ).
thf(316,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__iff1_1) ).
thf(1117,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)],[316]) ).
thf(260,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_Osynth_ONumber_0) ).
thf(990,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)],[260]) ).
thf(71,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__iff1_0) ).
thf(509,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)],[71]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).
thf(649,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(281,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(1043,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)],[281]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( D @ ( C @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
thf(433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( D @ ( C @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(434,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( D @ ( C @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(cnf,[status(esa)],[433]) ).
thf(219,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
thf(890,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(626,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Public_OpublicKey ) )
!= ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
inference(cnf,[status(esa)],[625]) ).
thf(627,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Public_OpublicKey ) )
!= ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
inference(lifteq,[status(thm)],[626]) ).
thf(628,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Public_OpublicKey ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[627]) ).
thf(629,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) @ ( A @ sk15 ) )
= B ),
inference(cnf,[status(esa)],[628]) ).
thf(17637,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) @ ( A @ sk15 ) )
= B ),
inference(lifteq,[status(thm)],[629]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(609,plain,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(3423,plain,
! [A: $i] :
( ( A
!= ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ) )
| ( c_emptyset != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,1437]) ).
thf(3424,plain,
( ( c_emptyset != c_0 )
| ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[3423:[bind(A,$thf( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ))]]) ).
thf(5336,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_emptyset != c_0 ) ),
inference(paramod_ordered,[status(thm)],[3424,404]) ).
thf(5337,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[5336]) ).
thf(5383,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
!= A )
| ( c_0 != A )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[5337]) ).
thf(5392,plain,
( ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
!= c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[5383]) ).
thf(894,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
inference(polarity_switch,[status(thm)],[893]) ).
thf(895,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
inference(lifteq,[status(thm)],[894]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
thf(964,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(5465,plain,
! [A: $i] :
( ( A != c_Message_OsymKeys )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1441]) ).
thf(5466,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Message_OsymKeys @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5465:[bind(A,$thf( c_Message_OsymKeys ))]]) ).
thf(169,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_0) ).
thf(769,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)],[169]) ).
thf(189,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(816,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)],[189]) ).
thf(204,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__iff2_0) ).
thf(848,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)],[204]) ).
thf(16792,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16136,815]) ).
thf(16793,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[16792]) ).
thf(16897,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ tc_prod ) )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Wellfounded__Relations_Oless__than )
| ( ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) )
!= B ) ),
inference(simp,[status(thm)],[16793]) ).
thf(16905,plain,
( ( ( tc_nat @ ( tc_nat @ tc_prod ) )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Wellfounded__Relations_Oless__than ) ),
inference(simp,[status(thm)],[16897]) ).
thf(137,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__iff1_0) ).
thf(685,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)],[137]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(292,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_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OtwayRees_OSpy__see__shrK__D__dest_0) ).
thf(1066,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_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(607,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONonce ) ),
inference(polarity_switch,[status(thm)],[606]) ).
thf(608,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONonce ) ),
inference(lifteq,[status(thm)],[607]) ).
thf(314,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).
thf(1113,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(17700,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( c_Message_OsymKeys @ ( D @ ( C @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[690,467]) ).
thf(17701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( c_Message_OsymKeys @ ( D @ ( C @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ) ),
inference(simp,[status(thm)],[17700]) ).
thf(17739,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != tc_nat )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_Message_OsymKeys )
| ( A
!= ( D @ ( C @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ) ),
inference(simp,[status(thm)],[17701]) ).
thf(17758,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( c_emptyset @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_insert ) ) )
!= c_Message_OsymKeys ),
inference(simp,[status(thm)],[17739]) ).
thf(1013,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OAgent ) ) ),
inference(cnf,[status(esa)],[1012]) ).
thf(1014,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OAgent ) ) ),
inference(lifteq,[status(thm)],[1013]) ).
thf(1015,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OAgent @ A )
= B ),
inference(detectInverse,[status(thm)],[1014]) ).
thf(1016,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OAgent @ sk34 )
= A ),
inference(cnf,[status(esa)],[1015]) ).
thf(3142,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OAgent @ sk34 )
= A ),
inference(lifteq,[status(thm)],[1016]) ).
thf(1361,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[457,343]) ).
thf(1362,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1361]) ).
thf(1364,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= tc_Message_Oagent )
| ( c_Finite__Set_OFinites != c_Event_Obad )
| ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= v_A ) ),
inference(simp,[status(thm)],[1362]) ).
thf(5493,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != c_0 )
| ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,4439]) ).
thf(5494,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5493]) ).
thf(5495,plain,
( ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5494:[bind(A,$thf( c_emptyset ))]]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( C @ ( B @ ( A @ ( C @ ( B @ v_sko__usf ) ) @ c_Event_Oevent_OSays ) ) @ 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_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OtwayRees_OGets__imp__Says__dest_0) ).
thf(922,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( C @ ( B @ ( A @ ( C @ ( B @ v_sko__usf ) ) @ c_Event_Oevent_OSays ) ) @ 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_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(767,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OSpy ),
inference(polarity_switch,[status(thm)],[766]) ).
thf(768,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OSpy ),
inference(lifteq,[status(thm)],[767]) ).
thf(195,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__iff1_0) ).
thf(827,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)],[195]) ).
thf(5811,plain,
! [A: $i] :
( ( A
!= ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ) )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1349]) ).
thf(5812,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5811:[bind(A,$thf( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ))]]) ).
thf(135,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__iff1_0) ).
thf(680,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)],[135]) ).
thf(1260,plain,
! [A: $i] :
( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[338,815]) ).
thf(1261,plain,
! [A: $i] :
( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1260]) ).
thf(1272,plain,
! [A: $i] :
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_OtwayRees_Ootway )
| ( v_evs != A ) ),
inference(simp,[status(thm)],[1261]) ).
thf(1277,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_OtwayRees_Ootway ) ),
inference(simp,[status(thm)],[1272]) ).
thf(486,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) )
!= ( D @ ( C @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
inference(polarity_switch,[status(thm)],[485]) ).
thf(487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) )
!= ( D @ ( C @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
inference(lifteq,[status(thm)],[486]) ).
thf(187,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(812,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)],[187]) ).
thf(113,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__iff1_0) ).
thf(617,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)],[113]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).
thf(1145,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(164,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(754,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)],[164]) ).
thf(87,axiom,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
thf(553,plain,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(7069,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
!= ( C @ ( B @ c_List_Orev ) ) )
| ( ( c_List_Olist_ONil @ ( C @ sk3 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[350,7060]) ).
thf(7070,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ ( A @ sk3 ) )
= c_List_Olist_ONil ),
inference(pattern_uni,[status(thm)],[7069:[bind(A,$thf( A )),bind(B,$thf( c_List_Olist_ONil )),bind(C,$thf( A ))]]) ).
thf(489,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey )
!= ( D @ ( C @ c_Public_OpublicKey ) ) ),
inference(polarity_switch,[status(thm)],[488]) ).
thf(490,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey )
!= ( D @ ( C @ c_Public_OpublicKey ) ) ),
inference(lifteq,[status(thm)],[489]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
thf(675,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1199,plain,
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[934,464]) ).
thf(1200,plain,
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
inference(simp,[status(thm)],[1199]) ).
thf(1203,plain,
( ( ( tc_nat @ tc_set )
!= tc_Message_Oagent )
| ( c_Finite__Set_OFinites != c_Event_Obad )
| ( c_UNIV != c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[1200]) ).
thf(1080,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OAgent ) ),
inference(polarity_switch,[status(thm)],[1079]) ).
thf(1081,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OAgent ) ),
inference(lifteq,[status(thm)],[1080]) ).
thf(748,plain,
! [A: $i] :
( c_Message_Oagent_OServer
!= ( A @ c_Message_Oagent_OFriend ) ),
inference(polarity_switch,[status(thm)],[747]) ).
thf(749,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OServer ),
inference(lifteq,[status(thm)],[748]) ).
thf(251,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
thf(968,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1177,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[338,781]) ).
thf(1178,plain,
( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
inference(simp,[status(thm)],[1177]) ).
thf(1181,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Oagent )
| ( c_OtwayRees_Ootway != c_Event_Obad )
| ( v_evs != c_Message_Oagent_OServer ) ),
inference(simp,[status(thm)],[1178]) ).
thf(198,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( B @ c_Message_Omsg_OAgent @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( A @ ( D @ ( C @ ( B @ ( E @ v_sko__u__1 ) ) ) ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( 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_Message_Omsg_OAgent @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OtwayRees_OCrypt__imp__OR2__dest_0) ).
thf(836,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( B @ c_Message_Omsg_OAgent @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( A @ ( D @ ( C @ ( B @ ( E @ v_sko__u__1 ) ) ) ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( 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_Message_Omsg_OAgent @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(17702,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[690,1407]) ).
thf(17703,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[17702]) ).
thf(17745,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( tc_nat @ ( tc_nat @ tc_prod ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_Wellfounded__Relations_Oless__than )
| ( A
!= ( tc_nat @ ( tc_nat @ ( C @ ( C @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[17703]) ).
thf(17764,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_Pair ) ) ) @ c_insert ) ) )
!= c_Wellfounded__Relations_Oless__than ),
inference(simp,[status(thm)],[17745]) ).
thf(17698,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[690,815]) ).
thf(17699,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[17698]) ).
thf(17743,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_Message_Omsg )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( c_emptyset @ c_Message_Oparts ) )
| ( A != C ) ),
inference(simp,[status(thm)],[17699]) ).
thf(17762,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[17743]) ).
thf(17684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( D @ c_Event_OinitState @ c_Message_Oparts @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[690,998]) ).
thf(17685,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( D @ c_Event_OinitState @ c_Message_Oparts @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
inference(simp,[status(thm)],[17684]) ).
thf(17749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != tc_Message_Omsg )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( D @ c_Event_OinitState @ c_Message_Oparts ) )
| ( A
!= ( C @ c_Message_Omsg_ONonce ) ) ),
inference(simp,[status(thm)],[17685]) ).
thf(17768,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) )
!= ( B @ c_Event_OinitState @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[17749]) ).
thf(99,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__iff1_0) ).
thf(580,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)],[99]) ).
thf(294,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(1070,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)],[294]) ).
thf(145,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__iff2_0) ).
thf(705,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)],[145]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
thf(887,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(244,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(954,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)],[244]) ).
thf(172,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(776,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)],[172]) ).
thf(147,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).
thf(712,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(89,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).
thf(557,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(1217,plain,
( ( ( tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[340,781]) ).
thf(1218,plain,
( ( tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
inference(simp,[status(thm)],[1217]) ).
thf(1225,plain,
( ( tc_Message_Omsg != tc_Message_Oagent )
| ( ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz )
!= c_Event_Obad )
| ( ( v_K @ c_Message_Omsg_OKey )
!= c_Message_Oagent_OServer ) ),
inference(simp,[status(thm)],[1218]) ).
thf(146,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).
thf(707,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(1290,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[669,815]) ).
thf(1291,plain,
! [B: $i,A: $i] :
( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[1290]) ).
thf(1296,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Finite__Set_OFinites )
| ( c_emptyset != B ) ),
inference(simp,[status(thm)],[1291]) ).
thf(1300,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Finite__Set_OFinites ) ),
inference(simp,[status(thm)],[1296]) ).
thf(200,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(840,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)],[200]) ).
thf(11975,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OlessThan ) @ ( A @ c_insert ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11635,464]) ).
thf(11976,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OlessThan ) @ ( A @ c_insert ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[11975]) ).
thf(11980,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OlessThan ) @ ( A @ c_insert ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[11976]) ).
thf(12001,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OlessThan ) @ ( A @ c_insert ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[11980]) ).
thf(4997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( D @ c_Event_OinitState @ c_Message_Oparts @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1102,998]) ).
thf(4998,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( D @ c_Event_OinitState @ c_Message_Oparts @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
inference(simp,[status(thm)],[4997]) ).
thf(5020,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != tc_Message_Omsg )
| ( ( D @ c_Event_OinitState @ c_Message_Oparts )
!= c_UNIV )
| ( A
!= ( C @ c_Message_Omsg_ONonce ) ) ),
inference(simp,[status(thm)],[4998]) ).
thf(5030,plain,
! [A: $i] :
( ( A @ c_Event_OinitState @ c_Message_Oparts )
!= c_UNIV ),
inference(simp,[status(thm)],[5020]) ).
thf(56,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__iff1_0) ).
thf(470,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)],[56]) ).
thf(83,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).
thf(544,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(279,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
thf(1038,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).
thf(369,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(370,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(cnf,[status(esa)],[369]) ).
thf(12495,plain,
! [E: $i,D: $i,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 ) ) )
!= ( E @ ( c_emptyset @ ( D @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[809,1151]) ).
thf(12496,plain,
! [E: $i,D: $i,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 ) ) )
!= ( E @ ( c_emptyset @ ( D @ c_in ) ) ) ),
inference(simp,[status(thm)],[12495]) ).
thf(12576,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg != E )
| ( ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
!= c_emptyset )
| ( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey )
!= D ) ),
inference(simp,[status(thm)],[12496]) ).
thf(12595,plain,
! [A: $i] :
( ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
!= c_emptyset ),
inference(simp,[status(thm)],[12576]) ).
thf(68,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__iff2_0) ).
thf(502,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(425,plain,
? [A: $i > $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( C @ A ) ) ) )
= B ),
inference(detectInverse,[status(thm)],[424]) ).
thf(426,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( B @ sk5 ) ) ) )
= A ),
inference(cnf,[status(esa)],[425]) ).
thf(12726,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( B @ sk5 ) ) ) )
= A ),
inference(lifteq,[status(thm)],[426]) ).
thf(6586,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_Message_OsymKeys @ c_lessequals ) ) ) )
| ( c_emptyset != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,5466]) ).
thf(6587,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_Message_OsymKeys @ c_lessequals ) ) ) )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[6586]) ).
thf(6628,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_Message_OsymKeys != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[6587]) ).
thf(6633,plain,
( ( c_Message_OsymKeys != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[6628]) ).
thf(144,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).
thf(703,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(326,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_OUnCI_1) ).
thf(1141,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)],[326]) ).
thf(4215,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[845,815]) ).
thf(4216,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[4215]) ).
thf(4236,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg != tc_Message_Omsg )
| ( ( B @ c_Message_Osynth )
!= ( c_emptyset @ c_Message_Oparts ) )
| ( ( A @ c_Message_Omsg_OAgent )
!= C ) ),
inference(simp,[status(thm)],[4216]) ).
thf(4246,plain,
! [A: $i] :
( ( A @ c_Message_Osynth )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[4236]) ).
thf(285,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__iff1_0) ).
thf(1052,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)],[285]) ).
thf(4891,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[826,815]) ).
thf(4892,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[4891]) ).
thf(4915,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg != tc_Message_Omsg )
| ( ( A @ c_Event_OinitState )
!= ( c_emptyset @ c_Message_Oparts ) )
| ( ( A @ c_Public_OshrK @ c_Message_Omsg_OKey )
!= B ) ),
inference(simp,[status(thm)],[4892]) ).
thf(4932,plain,
! [A: $i] :
( ( A @ c_Event_OinitState )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[4915]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).
thf(727,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(256,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(978,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)],[256]) ).
thf(267,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( F @ c_Message_Omsg_OKey @ ( E @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( F @ c_Message_Omsg_OKey @ ( C @ c_Message_Omsg_OMPair ) @ ( G @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( B @ c_Message_Omsg_OAgent @ ( G @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( H @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( F @ c_Message_Omsg_OKey @ ( E @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OtwayRees_OB__trusts__OR3__dest_0) ).
thf(1008,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( F @ c_Message_Omsg_OKey @ ( E @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( F @ c_Message_Omsg_OKey @ ( C @ c_Message_Omsg_OMPair ) @ ( G @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( B @ c_Message_Omsg_OAgent @ ( G @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( H @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( F @ c_Message_Omsg_OKey @ ( E @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(95,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__iff1_0) ).
thf(571,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)],[95]) ).
thf(594,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONumber ) ),
inference(polarity_switch,[status(thm)],[593]) ).
thf(595,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONumber ) ),
inference(lifteq,[status(thm)],[594]) ).
thf(111,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__iff2_0) ).
thf(612,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)],[111]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
thf(876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(261,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
thf(991,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(400,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(cnf,[status(esa)],[399]) ).
thf(7464,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( E @ tc_set @ ( C @ ( D @ c_lessequals ) ) ) )
| ~ $true
| ~ ( E @ tc_set @ ( D @ ( C @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[638,400]) ).
thf(7465,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( E @ tc_set @ ( C @ ( D @ c_lessequals ) ) ) )
| ~ ( E @ tc_set @ ( D @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[7464]) ).
thf(7466,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( A @ ( A @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[7465:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(48,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
thf(450,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).
thf(482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(17722,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[690,781]) ).
thf(17723,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
inference(simp,[status(thm)],[17722]) ).
thf(17741,plain,
! [B: $i,A: $i] :
( ( B != tc_Message_Oagent )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_Event_Obad )
| ( A != c_Message_Oagent_OServer ) ),
inference(simp,[status(thm)],[17723]) ).
thf(17760,plain,
( ( tc_Message_Oagent @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) )
!= c_Event_Obad ),
inference(simp,[status(thm)],[17741]) ).
thf(320,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_OinsertE_0) ).
thf(1126,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)],[320]) ).
thf(170,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__iff2_0) ).
thf(771,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)],[170]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
thf(1157,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(4403,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 != c_OtwayRees_Ootway ) ),
inference(paramod_ordered,[status(thm)],[3890,368]) ).
thf(4404,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ( c_0 != c_OtwayRees_Ootway ) ),
inference(simp,[status(thm)],[4403]) ).
thf(4409,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( c_emptyset != c_emptyset )
| ( c_0 != A )
| ( c_0 != c_OtwayRees_Ootway ) ),
inference(simp,[status(thm)],[4404]) ).
thf(4419,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( c_0 != c_OtwayRees_Ootway ) ),
inference(simp,[status(thm)],[4409]) ).
thf(255,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__iff1_1) ).
thf(976,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)],[255]) ).
thf(268,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__iff2_0) ).
thf(1010,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)],[268]) ).
thf(9124,plain,
( ( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
| ~ $true
| ( c_UNIV != c_0 ) ),
inference(paramod_ordered,[status(thm)],[3755,1480]) ).
thf(9125,plain,
( ( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[9124]) ).
thf(9131,plain,
( ( tc_nat != tc_nat )
| ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
!= c_0 )
| ( c_0 != c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[9125]) ).
thf(9141,plain,
( ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
!= c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[9131]) ).
thf(843,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
inference(polarity_switch,[status(thm)],[842]) ).
thf(844,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
inference(lifteq,[status(thm)],[843]) ).
thf(828,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OKey )
!= ( B @ c_Message_Omsg_OKey ) ) ),
inference(cnf,[status(esa)],[827]) ).
thf(829,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OKey )
!= ( B @ c_Message_Omsg_OKey ) ) ),
inference(lifteq,[status(thm)],[828]) ).
thf(830,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OKey @ A )
= B ),
inference(detectInverse,[status(thm)],[829]) ).
thf(831,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OKey @ sk26 )
= A ),
inference(cnf,[status(esa)],[830]) ).
thf(3056,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OKey @ sk26 )
= A ),
inference(lifteq,[status(thm)],[831]) ).
thf(1316,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1159,815]) ).
thf(1317,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[1316]) ).
thf(1324,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Message_OsymKeys )
| ( ( A @ c_Public_OshrK )
!= B ) ),
inference(simp,[status(thm)],[1317]) ).
thf(1326,plain,
( ( tc_nat != tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Message_OsymKeys ) ),
inference(simp,[status(thm)],[1324]) ).
thf(247,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
thf(961,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(248,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(963,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)],[248]) ).
thf(221,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
thf(896,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(290,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(1062,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)],[290]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
thf(946,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(730,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONumber )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[729]) ).
thf(731,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONumber )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[730]) ).
thf(417,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(cnf,[status(esa)],[416]) ).
thf(418,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(lifteq,[status(thm)],[417]) ).
thf(177,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__iff1_0) ).
thf(786,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)],[177]) ).
thf(21,axiom,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).
thf(378,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(128,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
thf(667,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(196,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(832,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)],[196]) ).
thf(535,plain,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(polarity_switch,[status(thm)],[534]) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
inference(lifteq,[status(thm)],[535]) ).
thf(12523,plain,
! [D: $i,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 ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( D @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[809,815]) ).
thf(12524,plain,
! [D: $i,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 ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( D @ c_in ) ) ) ),
inference(simp,[status(thm)],[12523]) ).
thf(12566,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg != tc_Message_Omsg )
| ( ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
!= ( c_emptyset @ c_Message_Oparts ) )
| ( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey )
!= D ) ),
inference(simp,[status(thm)],[12524]) ).
thf(12588,plain,
! [A: $i] :
( ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[12566]) ).
thf(234,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__iff1_1) ).
thf(929,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)],[234]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
thf(1077,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).
thf(478,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
thf(549,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(1413,plain,
! [B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[340,1151]) ).
thf(1414,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1413]) ).
thf(1435,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg != B )
| ( ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz )
!= c_emptyset )
| ( ( v_K @ c_Message_Omsg_OKey )
!= A ) ),
inference(simp,[status(thm)],[1414]) ).
thf(1444,plain,
( ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz )
!= c_emptyset ),
inference(simp,[status(thm)],[1435]) ).
thf(323,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__iff1_0) ).
thf(1133,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)],[323]) ).
thf(163,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(752,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)],[163]) ).
thf(446,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(cnf,[status(esa)],[445]) ).
thf(447,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(lifteq,[status(thm)],[446]) ).
thf(306,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_OinsertCI_0) ).
thf(1097,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)],[306]) ).
thf(16180,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,16152]) ).
thf(16181,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[16180]) ).
thf(16182,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[16181:[bind(A,$thf( E @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) )),bind(B,$thf( E ))]]) ).
thf(16207,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ tc_List_Olist @ ( v_evs @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[16182]) ).
thf(190,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__iff2_0) ).
thf(818,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)],[190]) ).
thf(4559,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[822,815]) ).
thf(4560,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[4559]) ).
thf(4582,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg != tc_Message_Omsg )
| ( ( B @ c_Event_Oused )
!= ( c_emptyset @ c_Message_Oparts ) )
| ( ( A @ c_Public_OshrK @ c_Message_Omsg_OKey )
!= C ) ),
inference(simp,[status(thm)],[4560]) ).
thf(4597,plain,
! [A: $i] :
( ( A @ c_Event_Oused )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[4582]) ).
thf(156,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).
thf(735,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(264,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__iff1_0) ).
thf(999,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)],[264]) ).
thf(114,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__iff1_1) ).
thf(620,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)],[114]) ).
thf(9843,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1061,1151]) ).
thf(9844,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[9843]) ).
thf(9901,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg != D )
| ( ( B @ ( A @ c_Event_Oknows ) )
!= c_emptyset )
| ( ( A @ c_Public_OshrK @ c_Message_Omsg_OKey )
!= C ) ),
inference(simp,[status(thm)],[9844]) ).
thf(9922,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oknows ) )
!= c_emptyset ),
inference(simp,[status(thm)],[9901]) ).
thf(409,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
inference(polarity_switch,[status(thm)],[408]) ).
thf(410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
inference(lifteq,[status(thm)],[409]) ).
thf(3864,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,465]) ).
thf(3865,plain,
( ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[3864:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).
thf(211,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( 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_Message_Omsg_OAgent @ ( G @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Message_Omsg_OAgent @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OtwayRees_Ounique__NB__dest_0) ).
thf(867,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( 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_Message_Omsg_OAgent @ ( G @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( B @ c_Message_Omsg_OAgent @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(3495,plain,
! [A: $i] :
( ( A
!= ( v_K @ c_Message_Omsg_OKey ) )
| ( tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( c_0 @ c_in ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,340]) ).
thf(3496,plain,
( ( tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( c_0 @ c_in ) ) )
| ( tc_nat @ ( v_K @ c_Message_Omsg_OKey @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[3495:[bind(A,$thf( v_K @ c_Message_Omsg_OKey ))]]) ).
thf(210,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(865,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)],[210]) ).
thf(70,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__iff1_1) ).
thf(506,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)],[70]) ).
thf(184,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(807,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)],[184]) ).
thf(11520,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
| ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( D @ c_insert ) ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[669,420]) ).
thf(11521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
| ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( D @ c_insert ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[11520]) ).
thf(11522,plain,
! [B: $i,A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ ( c_emptyset @ ( B @ c_insert ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[11521:[bind(A,$thf( A )),bind(B,$thf( c_emptyset )),bind(C,$thf( A ))]]) ).
thf(11627,plain,
! [B: $i,A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ ( c_emptyset @ ( B @ c_insert ) ) @ c_in ) ) ),
inference(simp,[status(thm)],[11522]) ).
thf(287,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__into__parts__dest_0) ).
thf(1056,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)],[287]) ).
thf(150,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__iff1_0) ).
thf(720,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)],[150]) ).
thf(180,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__iff1_0) ).
thf(796,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)],[180]) ).
thf(17706,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[690,343]) ).
thf(17707,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
inference(simp,[status(thm)],[17706]) ).
thf(17738,plain,
! [B: $i,A: $i] :
( ( B != tc_Message_Oagent )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_Event_Obad )
| ( A != v_A ) ),
inference(simp,[status(thm)],[17707]) ).
thf(17757,plain,
( ( tc_Message_Oagent @ ( c_emptyset @ ( v_A @ c_insert ) ) )
!= c_Event_Obad ),
inference(simp,[status(thm)],[17738]) ).
thf(917,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OKey )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[916]) ).
thf(918,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OKey )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[917]) ).
thf(181,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
thf(801,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(4349,plain,
! [A: $i] :
( ( A != tc_nat )
| ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,3865]) ).
thf(4350,plain,
( ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[4349:[bind(A,$thf( tc_nat ))]]) ).
thf(277,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).
thf(1033,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(17678,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[690,344]) ).
thf(17679,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) ),
inference(simp,[status(thm)],[17678]) ).
thf(17746,plain,
! [B: $i,A: $i] :
( ( B != tc_Message_Oagent )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_Event_Obad )
| ( A != v_B ) ),
inference(simp,[status(thm)],[17679]) ).
thf(17765,plain,
( ( tc_Message_Oagent @ ( c_emptyset @ ( v_B @ c_insert ) ) )
!= c_Event_Obad ),
inference(simp,[status(thm)],[17746]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).
thf(532,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(304,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(1093,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)],[304]) ).
thf(321,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(208,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(860,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)],[208]) ).
thf(271,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
thf(1019,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(77,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).
thf(528,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(4873,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[826,1151]) ).
thf(4874,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[4873]) ).
thf(4921,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg != C )
| ( ( A @ c_Event_OinitState )
!= c_emptyset )
| ( ( A @ c_Public_OshrK @ c_Message_Omsg_OKey )
!= B ) ),
inference(simp,[status(thm)],[4874]) ).
thf(4936,plain,
! [A: $i] :
( ( A @ c_Event_OinitState )
!= c_emptyset ),
inference(simp,[status(thm)],[4921]) ).
thf(265,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(1004,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)],[265]) ).
thf(1288,plain,
! [A: $i] :
( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[669,344]) ).
thf(1289,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) ),
inference(simp,[status(thm)],[1288]) ).
thf(1299,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_Message_Oagent )
| ( c_Finite__Set_OFinites != c_Event_Obad )
| ( c_emptyset != v_B ) ),
inference(simp,[status(thm)],[1289]) ).
thf(3493,plain,
! [A: $i] :
( ( A
!= ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) )
| ( tc_Message_Omsg @ ( c_0 @ c_Message_Oanalz @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,340]) ).
thf(3494,plain,
( ( tc_Message_Omsg @ ( c_0 @ c_Message_Oanalz @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_nat @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[3493:[bind(A,$thf( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ))]]) ).
thf(317,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(1120,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)],[317]) ).
thf(6656,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Message_OsymKeys != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,6633]) ).
thf(6657,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Message_OsymKeys != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[6656]) ).
thf(6658,plain,
( ( c_Message_OsymKeys != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6657:[bind(A,$thf( c_emptyset ))]]) ).
thf(11774,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OatMost ) @ ( A @ c_insert ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11628,464]) ).
thf(11775,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OatMost ) @ ( A @ c_insert ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[11774]) ).
thf(11785,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OatMost ) @ ( A @ c_insert ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[11775]) ).
thf(11794,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OatMost ) @ ( A @ c_insert ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[11785]) ).
thf(105,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).
thf(596,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(5467,plain,
! [A: $i] :
( ( A != c_List_Olist_ONil )
| ( c_0 != v_evs )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1475]) ).
thf(5468,plain,
( ( c_0 != v_evs )
| ~ ( tc_nat @ ( c_0 @ ( c_List_Olist_ONil @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5467:[bind(A,$thf( c_List_Olist_ONil ))]]) ).
thf(7261,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_UNIV != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,7240]) ).
thf(7262,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[7261]) ).
thf(7263,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7262:[bind(A,$thf( c_emptyset ))]]) ).
thf(205,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(850,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)],[205]) ).
thf(5374,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != c_0 )
| ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,3424]) ).
thf(5375,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[5374]) ).
thf(5376,plain,
( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5375:[bind(A,$thf( c_emptyset ))]]) ).
thf(140,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
| ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
thf(691,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
| ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(182,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_OUnCI_0) ).
thf(803,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)],[182]) ).
thf(1314,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1159,344]) ).
thf(1315,plain,
! [A: $i] :
( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) ),
inference(simp,[status(thm)],[1314]) ).
thf(1320,plain,
! [A: $i] :
( ( tc_nat != tc_Message_Oagent )
| ( c_Message_OsymKeys != c_Event_Obad )
| ( ( A @ c_Public_OshrK )
!= v_B ) ),
inference(simp,[status(thm)],[1315]) ).
thf(125,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__iff1_1) ).
thf(659,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)],[125]) ).
thf(543,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[542]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).
thf(676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(1357,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[457,344]) ).
thf(1358,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) ) ),
inference(simp,[status(thm)],[1357]) ).
thf(1367,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= tc_Message_Oagent )
| ( c_Finite__Set_OFinites != c_Event_Obad )
| ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= v_B ) ),
inference(simp,[status(thm)],[1358]) ).
thf(239,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__iff2_0) ).
thf(940,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)],[239]) ).
thf(236,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(935,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)],[236]) ).
thf(4728,plain,
! [B: $i,A: $i] :
( ( c_0 != c_0 )
| ( ( B @ tc_set )
!= tc_nat )
| ( A != c_OtwayRees_Ootway )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[387,4419]) ).
thf(4729,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( A != c_OtwayRees_Ootway )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[4728:[]]) ).
thf(4734,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[4729]) ).
thf(253,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
thf(972,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(25475,plain,
$false,
inference(e,[status(thm)],[1322,809,17759,1024,1369,1105,347,846,1031,893,518,468,8415,481,408,523,11635,683,1068,994,1073,4711,614,1437,1041,6295,878,440,17411,6971,385,384,1275,814,945,340,747,913,670,6046,898,1475,565,11340,436,1228,4249,1095,404,782,1441,7240,17756,13732,9410,1298,4415,504,702,344,11628,949,542,1055,724,9300,4439,1323,838,934,357,902,638,1087,1147,1479,606,1115,448,5792,421,870,7060,881,416,1489,492,443,17129,1109,4147,475,924,17354,756,6227,789,376,19485,485,834,1151,937,1383,348,353,966,905,480,766,1169,734,956,7936,774,396,7051,9923,16136,998,6021,411,1345,428,1201,1074,452,5406,380,678,546,761,810,1470,366,534,1047,512,942,1274,910,825,3867,6032,598,820,429,1370,815,729,1021,778,862,349,424,3069,407,693,630,361,625,3499,13763,665,583,1159,1079,3028,1407,551,842,974,1012,916,467,566,484,852,435,1350,578,1089,1143,1017,16968,1064,725,1006,388,593,420,499,989,857,1111,1227,980,403,1138,356,884,1160,488,339,554,537,669,642,526,9477,590,4444,970,1155,1028,1082,17761,7846,393,701,1297,738,10026,911,9053,7913,569,8995,4416,605,647,997,1099,985,17360,515,1150,1478,1131,654,8294,1192,1060,1050,457,17752,371,16328,3755,343,633,657,1035,9104,1026,530,805,4081,17767,1170,558,1071,794,586,662,718,1135,750,16233,8903,430,1103,3890,745,573,16152,444,4599,601,6192,906,6084,1273,1154,975,402,732,16977,743,958,1124,413,5720,4144,875,826,577,17130,1226,1488,641,391,445,6991,466,1090,919,17128,350,9967,672,1058,1107,764,1194,900,419,1048,1349,567,737,1122,784,1117,377,990,509,649,1043,434,890,387,17637,494,609,5392,895,964,5466,769,1061,345,367,16020,816,848,16905,685,399,1066,608,394,1113,17758,3142,1364,1102,438,5495,922,768,827,780,16970,5812,680,1277,487,812,617,939,342,1145,355,754,553,7070,490,675,1203,589,1081,749,968,458,1181,823,836,17764,17762,17768,580,690,1070,705,887,954,5570,776,712,557,1225,707,1300,717,840,12001,5030,338,470,359,544,1038,370,12595,502,4145,463,12726,6633,703,1141,4246,1052,4932,727,978,1008,571,595,612,876,991,7466,336,845,465,450,482,17760,1126,771,16956,1157,4419,976,688,903,1010,14015,9141,844,368,3056,1326,961,963,896,1062,946,351,390,401,781,731,418,786,3368,378,667,383,832,346,536,1045,4175,433,12588,1440,929,1077,478,5568,549,1444,1442,1133,752,447,1097,16207,818,405,422,4597,735,999,620,3860,3511,9922,432,410,3865,867,3496,865,1480,373,603,506,807,11627,437,1056,696,720,1346,796,1436,17757,918,801,341,4350,1033,17765,400,3424,532,1093,987,464,1129,860,1019,528,908,723,822,4936,1004,1299,3494,1120,6658,6099,575,1152,427,11794,596,5468,7263,850,5376,691,369,8493,803,1320,337,354,659,543,560,639,676,491,1367,940,935,5649,364,3296,4734,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV289-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % 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
% 0.15/0.40 % Computer : n004.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 13:28:07 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 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
% 0.89/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.44/1.43 % [INFO] Parsing done (455ms).
% 2.44/1.45 % [INFO] Running in sequential loop mode.
% 3.35/1.83 % [INFO] eprover registered as external prover.
% 3.35/1.84 % [INFO] Scanning for conjecture ...
% 4.07/2.04 % [INFO] Found a conjecture (or negated_conjecture) and 1477 axioms. Running axiom selection ...
% 4.81/2.29 % [INFO] Axiom selection finished. Selected 328 axioms (removed 1149 axioms).
% 5.75/2.49 % [INFO] Problem is propositional (TPTP CNF).
% 6.19/2.51 % [INFO] Type checking passed.
% 6.19/2.51 % [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 ...
% 95.99/21.03 % External prover 'e' found a proof!
% 95.99/21.03 % [INFO] Killing All external provers ...
% 95.99/21.03 % Time passed: 20488ms (effective reasoning time: 19571ms)
% 95.99/21.04 % Axioms used in derivation (328): cls_List_Olistrel__Cons1_0, cls_Message_Omsg_Oinject__7__iff1_0, cls_Finite__Set_Ofinite__Union_0, cls_List_Oset__empty2__iff2_0, cls_Public_Onot__symKeys__pubK__iff1_0, cls_Datatype__Universe_OuprodI_0, cls_Nat_Ole__0__eq__iff1_0, cls_Finite__Set_Ofinite__converse__iff1_0, cls_Message_Oanalz_OInj_0, cls_List_Ofinite__set_0, cls_List_Orev__is__Nil__conv__iff1_0, cls_Finite__Set_Ofinite__Un__iff1_1, cls_Datatype__Universe_OdprodE_0, cls_List_Oappend__in__lists__conv__iff2_0, cls_List_Oset__empty2__iff1_0, cls_Event_OSays__imp__analz__Spy__dest_0, cls_Public_OpublicKey__into__used_0, cls_List_ONil__notin__lex__iff1_0, cls_Relation_OImageI_0, cls_List_Olistrel__Cons2_1, cls_Public_ONonce__notin__initState__iff1_0, cls_Event_Oevent_Odistinct__3__iff1_0, cls_Message_Oanalz__analzD__dest_0, cls_Set_OsubsetI_1, cls_Sum__Type_OInr__not__Inl__iff1_0, cls_Datatype__Universe_Odsum__In0I_0, cls_List_Olength__remdups__eq__iff2_0, cls_List_Olists_ONil_0, cls_Set_OInterD_0, cls_Message_OMPair__eq__HPair__iff1_1, cls_List_ONil__is__append__conv__iff2_0, cls_Message_Osynth_OAgent_0, cls_Event_Oevent_Odistinct__1__iff1_0, cls_Sum__Type_OInr__eq__iff1_0, cls_Set_OemptyE_0, cls_Set_OUNIV__not__empty__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0, cls_Finite__Set_OFinites_OemptyI_0, cls_List_Oappend__self__conv2__iff1_0, cls_Relation_OImageE_0, cls_Event_Oevent_Oinject__3__iff1_0, cls_Message_Oagent_Odistinct__5__iff1_0, cls_Message_Oagent_Oinject__iff1_0, cls_Set_Osingleton__insert__inj__eq__iff1_1, cls_List_Orev__eq__Cons__iff__iff2_0, cls_Wellfounded__Recursion_Owf__insert__iff1_0, cls_Public_OpriK__neq__shrK__iff1_0, cls_Datatype_Ooption_Oinject__iff1_0, cls_Transitive__Closure_Otrancl_Or__into__trancl_0, cls_Message_OHPair__neqs__1__iff1_0, cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0, cls_Set_Osingleton__inject__dest_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_1, cls_Set_OUnionE_1, cls_Message_OHPair__neqs__3__iff1_0, cls_Nat_Oless__irrefl_0, cls_Event_Oevent_Oinject__1__iff1_2, cls_List_Olistrel__Nil1_0, cls_Nat_Onot__less0__iff1_0, cls_Finite__Set_OFinites_OinsertI_0, cls_Wellfounded__Relations_Owf__lex__prod_0, cls_Datatype__Universe_OIn1__eq__iff1_0, cls_Message_OMPair__synth__analz__iff1_1, cls_OtwayRees_OSpy__not__see__encrypted__key__dest_0, cls_Public_OshrK_AX_A_58_AsymKeys_0, cls_Message_OHPair__eq__iff1_0, cls_Finite__Set_Ofinite__Int_0, cls_Message_OHash__synth_0, cls_Relation_OconverseE_1, cls_Nat_Oneq0__conv__iff2_0, cls_Sum__Type_OPlusE_0, cls_List_ONil__is__append__conv__iff1_0, cls_Relation_Orel__compE_0, cls_Finite__Set_Ofinite__Pow__iff__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1, cls_Sum__Type_OInlI_0, cls_Infinite__Set_Onat__not__finite_0, cls_Message_Osynth_OHash_0, cls_Message_OMPair__eq__HPair__iff1_0, cls_Set_OpsubsetI_0, cls_Relation_Oconverse__iff__iff2_0, cls_Set_Osubset__refl_0, cls_List_Olist_Oinject__iff1_0, cls_Message_Oagent_Odistinct__6__iff1_0, cls_Message_OHash_91X_93_AY_A_61_AAgent_AA_A_61_61_62_AR_0, cls_Relation_ORangeE_0, cls_Message_Osynth_ONumber_0, cls_Set_OInterI_1, cls_Message_Omsg_Oinject__7__iff1_1, cls_List_Oset__empty__iff2_0, cls_SetInterval_Ofinite__greaterThanAtMost_0, cls_Product__Type_OPair__eq__iff1_0, cls_Set_OinsertCI_0, cls_Message_OHash_91X_93_AY_A_61_AHash_AZ_A_61_61_62_AR_0, cls_Set_OUnCI_1, cls_Set_Osingleton__insert__inj__eq_H__iff2_0, cls_Message_Oparts_OInj_0, cls_List_Oappend__in__lists__conv__iff1_0, cls_Finite__Set_Ofinite__converse__iff2_0, cls_List_Olength__remdups__leq_0, cls_Nat_Ole__0__eq__iff2_0, cls_Relation_OdiagI_0, cls_Event_Oevent_Oinject__3__iff1_1, cls_Datatype__Universe_OIn0__not__In1__iff1_0, cls_Public_OMPair__used_1, cls_Set_OPow__iff__iff2_0, cls_Message_OHPair__eq__MPair__iff1_0, cls_Datatype__Universe_OdprodE_1, cls_Set_OUNIV__I_0, cls_Message_OCrypt__synth_1, cls_Set_OsubsetI_0, cls_Sum__Type_OPlusE_3, cls_Public_OsymKeys__invKey__iff__iff1_0, cls_Finite__Set_Ofinite__Diff__insert__iff1_0, cls_List_OlistsE_0, cls_List_Olength__0__conv__iff2_0, cls_Finite__Set_Ofinite__Un__iff1_0, cls_List_Oself__append__conv__iff2_0, cls_Relation_ODomainI_0, cls_Set_Onot__psubset__empty__iff1_0, cls_Message_Osynth_OMPair_0, cls_Set_OUnE_0, cls_List_Olistrel__Cons2_0, cls_Message_OHPair__eq__MPair__iff2_0, cls_Message_Omsg_Oinject__4__iff1_0, cls_Set_OinsertE_0, cls_Message_Oagent_Odistinct__2__iff1_0, cls_List_Owf__lex_0, cls_List_Orev__is__Nil__conv__iff2_0, cls_Set_OUn__empty__iff1_1, cls_Public_OpublicKey__inject__iff1_1, cls_Relation_Orel__compE_2, cls_Relation_OImageE_1, cls_Relation_OdiagE_0, cls_Set_OsingletonD__dest_0, cls_SetInterval_Ofinite__atLeastAtMost_0, cls_Message_Omsg_Oinject__3__iff1_0, cls_SetInterval_Ofinite__atLeastLessThan_0, cls_Set_OUn__empty__iff1_0, cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, cls_Message_OHPair__neqs__4__iff1_0, cls_Wellfounded__Recursion_Owf__insert__iff2_0, cls_Set_Oempty__subsetI_0, cls_Finite__Set_Ofinite__Int_1, cls_List_Oappend__is__Nil__conv__iff2_0, cls_Relation_OIdI_0, cls_SetInterval_Ofinite__lessThan_0, cls_List_Olength__greater__0__conv__iff1_0, cls_List_Oappend1__eq__conv__iff1_1, cls_Set_OsubsetD_0, cls_Product__Type_OPair__eq__iff1_1, cls_Event_Oevent_Oinject__2__iff1_0, cls_List_Osame__append__eq__iff1_0, cls_Set_OsingletonI_0, cls_Message_Oparts__partsD__dest_0, cls_Wellfounded__Relations_Oless__than__iff__iff1_0, cls_Set_Osubset__antisym_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0, cls_List_Oself__append__conv__iff1_0, cls_List_Oin__listsI_1, cls_List_Orev__eq__Cons__iff__iff1_0, cls_Message_Oagent_Odistinct__1__iff1_0, cls_Public_OprivateKey_Ab_AA_A_61_ApublicKey_Ac_AA_H_A_61_61_62_AR_0, cls_Datatype_Oelem__o2s__iff1_0, cls_Message_OMPair__eq__HPair__iff2_0, cls_Message_Oparts_OBody__dest_0, cls_Datatype__Universe_OuprodE_2, cls_Relation_Oconverse__iff__iff1_0, cls_Relation_OconverseE_0, cls_List_Olength__greater__0__conv__iff2_0, cls_Datatype__Universe_OIn1__not__In0__iff1_0, cls_Datatype__Universe_OScons__Scons__eq__iff1_0, cls_Datatype_Oelem__o2s__iff2_0, cls_List_Olist_Oinject__iff1_1, cls_Public_OshrK__in__used_0, cls_Message_Omsg_Oinject__5__iff1_0, cls_Datatype__Universe_OuprodE_0, cls_Public_OMPair__used_0, cls_Set_ODiffE_0, cls_Public_OshrK__in__initState_0, cls_Message_OHash_91X_93_AY_A_61_ACrypt_AK_AX_H_A_61_61_62_AR_0, cls_Sum__Type_OInl__not__Inr__iff1_0, cls_Infinite__Set_Oatmost__one__unique_0, cls_Message_OHPair__neqs__6__iff1_0, cls_Message_Oin__parts__UnE_0, cls_OtwayRees_OGets__imp__Says__dest_0, cls_Relation_ORangeI_0, cls_List_Oset__empty__iff1_0, cls_Message_Omsg_Oinject__1__iff1_0, cls_Message_OMPair__analz_1, cls_Datatype__Universe_OdprodE_2, cls_Public_OpublicKey__inject__iff1_0, cls_List_Oself__append__conv2__iff2_0, cls_Set_OIntE_1, cls_Message_OCrypt__synth_0, cls_List_Odistinct__remdups_0, cls_Finite__Set_Ofinite__Union_1, cls_Message_Omsg_Oinject__2__iff1_0, cls_Event_Oevent_Oinject__1__iff1_0, cls_Relation_Opair__in__Id__conv__iff1_0, cls_Set_OIntI_0, cls_Message_OHash_91X_93_AY_A_61_AKey_AK_A_61_61_62_AR_0, cls_Sum__Type_OPlusE_2, cls_Set_Osingleton__insert__inj__eq__iff2_0, cls_Wellfounded__Relations_Oless__than__iff__iff2_0, cls_Message_Omsg_Oinject__6__iff1_0, cls_Public_Oanalz__spies__pubK_0, cls_Wellfounded__Relations_Owf__less__than_0, cls_List_Olist_Odistinct__2__iff1_0, cls_Transitive__Closure_Or__into__rtrancl_0, cls_Finite__Set_Ofinite__Diff__insert__iff2_0, cls_Public_Onot__symKeys__priK__iff1_0, cls_Event_Oevent_Odistinct__5__iff1_0, cls_Message_OMPair__parts_1, cls_Wellfounded__Recursion_Owf__empty_0, cls_Message_OMPair__synth__analz__iff1_0, cls_Message_Osynth_OCrypt_0, cls_Datatype__Universe_OdprodI_0, cls_Message_Oagent_Odistinct__4__iff1_0, cls_SetInterval_Ofinite__greaterThanLessThan_0, cls_Message_Osynth__synthD__dest_0, cls_List_Olistrel__Cons1_2, cls_List_OlistsE_1, cls_List_Oappend__self__conv2__iff2_0, cls_Public_OSpy__spies__bad__shrK_0, cls_List_Oappend__self__conv__iff2_0, cls_Set_OUn__empty__iff2_0, cls_List_Oappend__same__eq__iff1_0, cls_OtwayRees_OCrypt__imp__OR2__dest_0, cls_OtwayRees_OB__trusts__OR3__dest_0, cls_Set_ODiffI_0, cls_Public_OpublicKey__neq__privateKey__iff1_0, cls_Sum__Type_OInrI_0, cls_Datatype__Universe_Odsum__In1I_0, cls_Message_ONonce__synth_0, cls_List_Orev__is__rev__conv__iff1_0, cls_Datatype__Universe_OuprodE_1, cls_Set_OpsubsetE_0, cls_Set_OUnionI_0, cls_List_Olistrel__Nil2_0, cls_Message_OHPair__neqs__5__iff1_0, cls_Relation_Orel__compI_0, cls_Finite__Set_Ofinite__Pow__iff__iff2_0, cls_List_Oappend__is__Nil__conv__iff1_0, cls_Public_OSpy__spies__bad__privateKey_0, cls_Datatype__Universe_OScons__Scons__eq__iff1_1, cls_OtwayRees_Ounique__NB__dest_1, cls_Datatype__Universe_OIn0__eq__iff1_0, cls_Event_Oevent_Oinject__2__iff1_1, cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0, cls_Message_OMPair__synth__analz__iff2_0, cls_Relation_OdiagE_1, cls_Message_Oanalz__into__parts__dest_0, cls_Relation_OImage__singleton__iff__iff1_0, cls_List_ONil2__notin__lex__iff1_0, cls_List_Oself__append__conv2__iff1_0, cls_Nat_Oneq0__conv__iff1_0, cls_Message_OMPair__synth_1, cls_Message_OHPair__eq__MPair__iff1_1, cls_List_Olist_Odistinct__1__iff1_0, cls_Public_Ospies__pubK_0, cls_Message_OHash_91X_93_AY_A_61_ANonce_AN_A_61_61_62_AR_0, cls_List_Olistrel__Cons1_1, cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0, cls_Set_OInterI_0, cls_List_Olistrel__Cons2_2, cls_Message_Osynth_OInj_0, cls_List_ONil__is__rev__conv__iff2_0, cls_Relation_ODomainE_0, cls_List_Oin__listsI_0, cls_Message_OMPair__analz_0, cls_Public_OprivateKey__into__used_0, cls_Sum__Type_OPlusE_1, cls_Event_Oevent_Odistinct__4__iff1_0, cls_Wellfounded__Recursion_Owf__insert__iff1_1, cls_Set_OUnionE_0, cls_Event_Oevent_Odistinct__6__iff1_0, cls_Message_Omsg_Oinject__6__iff1_1, cls_Message_Oagent_Odistinct__3__iff1_0, cls_Message_OFake__parts__insert__in__Un__dest_0, cls_Message_OHPair__neqs__2__iff1_0, cls_Public_OpriK__in__initState_0, cls_Message_OHPair__eq__iff1_1, cls_List_Oappend1__eq__conv__iff1_0, cls_Message_OKey__synth_0, cls_Message_Oanalz_ODecrypt__dest_0, cls_Public_OpublicKey__in__initState_0, cls_Message_OHash_91X_93_AY_A_61_ANumber_AN_A_61_61_62_AR_0, cls_OtwayRees_Ono__nonce__OR1__OR2__dest_0, cls_List_Oin__listsD__dest_0, cls_Set_OPow__iff__iff1_0, cls_Nat_Ole0_0, cls_Event_OSpy_A_58_Abad_0, cls_Set_Osingleton__insert__inj__eq__iff1_0, cls_Sum__Type_OInl__eq__iff1_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_0, cls_List_ONil__is__rev__conv__iff1_0, cls_Event_Oevent_Oinject__1__iff1_1, cls_Message_OMPair__parts_0, cls_Relation_OImage__singleton__iff__iff2_0, cls_OtwayRees_OSpy__see__shrK__D__dest_0, cls_List_Olength__0__conv__iff1_0, cls_List_Owf__lenlex_0, cls_Relation_OIdE_0, cls_Message_Oparts__emptyE_0, cls_Set_OpsubsetE_1, cls_Public_OshrK__injective__iff1_0, cls_SetInterval_Ofinite__atMost_0, cls_Set_OIntE_0, cls_OtwayRees_Ounique__NB__dest_0, cls_Relation_Orel__compE_1, cls_List_Oappend__is__Nil__conv__iff1_1, cls_Event_Oevent_Odistinct__2__iff1_0, cls_Finite__Set_Ofinite__Un__iff2_0, cls_Public_OsymKeys__invKey__iff__iff2_0, cls_List_Olength__remdups__eq__iff1_0, cls_Message_OMPair__synth_0, cls_List_Oappend__in__lists__conv__iff1_1, cls_Set_OinsertCI_1, cls_Set_ODiffE_1, cls_List_ONil__is__append__conv__iff1_1, cls_Transitive__Closure_Otrancl__into__rtrancl_0, cls_List_Oappend__self__conv__iff1_0, cls_Public_OpubK__neq__shrK__iff1_0, cls_Event_OServer_A_58_Abad_A_61_61_62_AR_0, cls_Public_OshrK__in__knows_0, cls_Set_OUnCI_0, cls_List_Olists_OCons_0
% 95.99/21.04 % No. of inferences in proof: 1377
% 95.99/21.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 20488 ms resp. 19571 ms w/o parsing
% 100.52/21.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 100.52/21.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------