%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV299-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.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 08:58:48 AM UTC 2026
% Result : Unsatisfiable 157.25s 39.47s
% Output : Refutation 161.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 358
% Syntax : Number of formulae : 1714 ( 615 unt; 0 typ; 25 def)
% Number of atoms : 3875 (1912 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 17758 (2245 ~;1564 |; 0 &;13949 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 96 ( 96 >; 0 *; 0 +; 0 <<)
% Number of symbols : 157 ( 154 usr; 26 con; 0-6 aty)
% Number of variables : 4018 ( 0 ^;3968 !; 25 ?;4018 :)
% ( 0 !>; 0 ?*; 0 @-; 25 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_A_decl,type,
v_A: $i ).
thf(c_Event_Obad_decl,type,
c_Event_Obad: $i ).
thf(tc_Message_Oagent_decl,type,
tc_Message_Oagent: $i ).
thf(v_evs3_decl,type,
v_evs3: $i ).
thf(c_OtwayRees_Ootway_decl,type,
c_OtwayRees_Ootway: $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(tc_Event_Oevent_decl,type,
tc_Event_Oevent: $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_Oused_decl,type,
c_Event_Oused: $i > $i ).
thf(tc_Message_Omsg_decl,type,
tc_Message_Omsg: $i ).
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_Omsg_OMPair_decl,type,
c_Message_Omsg_OMPair: $i > $i > $i ).
thf(c_Message_Omsg_ONonce_decl,type,
c_Message_Omsg_ONonce: $i > $i ).
thf(v_NB_decl,type,
v_NB: $i ).
thf(c_Message_Omsg_OAgent_decl,type,
c_Message_Omsg_OAgent: $i > $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(c_List_Oset_decl,type,
c_List_Oset: $i > $i > $i ).
thf(v_Aaa_decl,type,
v_Aaa: $i ).
thf(c_Message_Oagent_OServer_decl,type,
c_Message_Oagent_OServer: $i ).
thf(v_NA_decl,type,
v_NA: $i ).
thf(v_Aa_decl,type,
v_Aa: $i ).
thf(c_Message_Oparts_decl,type,
c_Message_Oparts: $i > $i ).
thf(c_Event_Oknows_decl,type,
c_Event_Oknows: $i > $i > $i ).
thf(c_Message_Oagent_OSpy_decl,type,
c_Message_Oagent_OSpy: $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_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_Event_Oevent_OGets_decl,type,
c_Event_Oevent_OGets: $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_Event_Oevent_ONotes_decl,type,
c_Event_Oevent_ONotes: $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_SetInterval_OgreaterThanLessThan_decl,type,
c_SetInterval_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(c_Message_Oagent_OFriend_decl,type,
c_Message_Oagent_OFriend: $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_Osynth_decl,type,
c_Message_Osynth: $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_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Message_Oanalz_decl,type,
c_Message_Oanalz: $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_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(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 > $i > $i > $i ).
thf(sk5_decl,type,
sk5: $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(sk9_decl,type,
sk9: $i > $i > $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i > $i ).
thf(sk21_decl,type,
sk21: $i > $i > $i ).
thf(sk22_decl,type,
sk22: $i > $i ).
thf(sk25_decl,type,
sk25: $i > $i > $i ).
thf(sk26_decl,type,
sk26: $i > $i ).
thf(sk28_decl,type,
sk28: $i > $i > $i ).
thf(sk29_decl,type,
sk29: $i > $i ).
thf(sk30_decl,type,
sk30: $i > $i ).
thf(sk31_decl,type,
sk31: $i > $i > $i ).
thf(sk33_decl,type,
sk33: $i > $i > $i ).
thf(sk35_decl,type,
sk35: $i > $i > $i ).
thf(sk36_decl,type,
sk36: $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 > $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(sk5_def,definition,
( sk5
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Event_Oevent_OGets ) @ ( 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(sk9_def,definition,
( sk9
= ( @+[A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Event_Oevent_ONotes ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OHash @ A )
= B ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[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_Event_Oevent_OGets ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Public_OpublicKey ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Event_Oevent_ONotes ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Oagent_OFriend @ A )
= B ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( @+[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_ONonce @ A )
= B ) ) ) ).
thf(sk28_def,definition,
( sk28
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_Omsg_OCrypt ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk29_def,definition,
( sk29
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OKey @ A )
= B ) ) ) ).
thf(sk30_def,definition,
( sk30
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Public_OshrK @ A )
= B ) ) ) ).
thf(sk31_def,definition,
( sk31
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_Omsg_OCrypt ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk33_def,definition,
( sk33
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_Omsg_OMPair ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk35_def,definition,
( sk35
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_Omsg_OMPair ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk36_def,definition,
( sk36
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OAgent @ A )
= B ) ) ) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',cls_Event_OSays__imp__analz__Spy__dest_0) ).
thf(809,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)],[182]) ).
thf(7,negated_conjecture,
! [A: $i] :
~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( A @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(338,plain,
! [A: $i] :
~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( A @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(347,plain,
! [A: $i] :
~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( A @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[338]) ).
thf(145,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(712,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(53,axiom,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).
thf(466,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(467,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[466]) ).
thf(17816,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)],[712,467]) ).
thf(17817,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)],[17816]) ).
thf(17880,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)],[17817]) ).
thf(17903,plain,
( ( tc_nat @ tc_set @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
!= c_Finite__Set_OFinites ),
inference(simp,[status(thm)],[17880]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Public_OMPair__used_1) ).
thf(941,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(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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
thf(425,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(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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
thf(417,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(418,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)],[417]) ).
thf(12054,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ ( E @ c_insert ) ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[425,418]) ).
thf(12055,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ ( E @ c_insert ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[12054]) ).
thf(12056,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastAtMost ) ) @ ( A @ c_insert ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[12055:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( tc_nat @ ( G @ ( F @ c_SetInterval_OatLeastAtMost ) ) )),bind(D,$thf( tc_nat )),bind(E,$thf( E ))]]) ).
thf(12172,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastAtMost ) ) @ ( A @ c_insert ) ) @ c_in ) ) ),
inference(simp,[status(thm)],[12056]) ).
thf(25434,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastAtMost ) ) @ ( A @ c_insert ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12172,467]) ).
thf(25435,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastAtMost ) ) @ ( A @ c_insert ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[25434]) ).
thf(25544,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastAtMost ) ) @ ( A @ c_insert ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[25435]) ).
thf(25580,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastAtMost ) ) @ ( A @ c_insert ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[25544]) ).
thf(312,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/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__partsD__dest_0) ).
thf(1110,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)],[312]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Public_Oanalz__spies__pubK_0) ).
thf(967,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(327,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
thf(1145,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(1146,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[1145]) ).
thf(20557,plain,
! [E: $i,D: $i,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 ) ) )
!= ( E @ ( c_emptyset @ ( D @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[967,1146]) ).
thf(20558,plain,
! [E: $i,D: $i,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 ) ) )
!= ( E @ ( c_emptyset @ ( D @ c_in ) ) ) ),
inference(simp,[status(thm)],[20557]) ).
thf(20640,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg != E )
| ( ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz )
!= c_emptyset )
| ( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey )
!= D ) ),
inference(simp,[status(thm)],[20558]) ).
thf(20668,plain,
! [A: $i] :
( ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz )
!= c_emptyset ),
inference(simp,[status(thm)],[20640]) ).
thf(199,axiom,
! [A: $i] : ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__in__initState_0) ).
thf(846,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)],[199]) ).
thf(225,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/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__in__initState_0) ).
thf(909,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)],[225]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(628,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)],[115]) ).
thf(246,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_emptyset
!= ( B @ ( A @ c_List_Oset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).
thf(962,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(54,axiom,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
thf(468,plain,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(4816,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)],[846,1146]) ).
thf(4817,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)],[4816]) ).
thf(4868,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)],[4817]) ).
thf(4877,plain,
! [A: $i] :
( ( A @ c_Event_OinitState )
!= c_emptyset ),
inference(simp,[status(thm)],[4868]) ).
thf(133,axiom,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
thf(685,plain,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(193,axiom,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__emptyE_0) ).
thf(834,plain,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(835,plain,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[834]) ).
thf(1277,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)],[685,835]) ).
thf(1278,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)],[1277]) ).
thf(1289,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)],[1278]) ).
thf(1295,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Finite__Set_OFinites ) ),
inference(simp,[status(thm)],[1289]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).
thf(481,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)],[59]) ).
thf(11,axiom,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ c_List_Orev ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv__iff2_0) ).
thf(352,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(10,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(351,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(26,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).
thf(391,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(392,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[391]) ).
thf(393,plain,
! [A: $i] :
( ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) )
| ( A = c_0 ) ),
inference(lifteq,[status(thm)],[392]) ).
thf(144,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff1_0) ).
thf(710,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)],[144]) ).
thf(711,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)],[710]) ).
thf(157,axiom,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff2_0) ).
thf(745,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(746,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
= c_0 ),
inference(lifteq,[status(thm)],[745]) ).
thf(1477,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(rewrite,[status(thm)],[711,746]) ).
thf(6324,plain,
! [A: $i] :
( ( A != tc_nat )
| ~ ( c_0 @ ( c_0 @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,1477]) ).
thf(6325,plain,
( ~ ( c_0 @ ( c_0 @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( tc_nat @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6324:[bind(A,$thf( tc_nat ))]]) ).
thf(24503,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( tc_nat @ c_lessequals ) ) ) )
| ~ ( c_0 @ ( c_0 @ ( c_0 @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[351,6325]) ).
thf(24504,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( tc_nat @ c_lessequals ) ) ) )
| ~ ( c_0 @ ( c_0 @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[24503]) ).
thf(24599,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( tc_nat != c_0 )
| ~ ( c_0 @ ( c_0 @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[24504]) ).
thf(24627,plain,
( ( tc_nat != c_0 )
| ~ ( c_0 @ ( c_0 @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[24599]) ).
thf(132,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
thf(683,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)],[132]) ).
thf(291,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).
thf(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)],[291]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(949,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(27777,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( D @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[949,835]) ).
thf(27778,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( D @ c_in ) ) ) ),
inference(simp,[status(thm)],[27777]) ).
thf(27804,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C != tc_Message_Omsg )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( c_emptyset @ c_Message_Oparts ) )
| ( A != D ) ),
inference(simp,[status(thm)],[27778]) ).
thf(27828,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( A @ ( B @ c_insert ) ) )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[27804]) ).
thf(294,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/sandbox/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)],[294]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(478,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)],[58]) ).
thf(479,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[478]) ).
thf(480,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[479]) ).
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/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff2_0) ).
thf(428,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(429,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)],[428]) ).
thf(430,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)],[429]) ).
thf(254,axiom,
! [A: $i] :
( c_emptyset
= ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).
thf(978,plain,
! [A: $i] :
( c_emptyset
= ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(979,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[978]) ).
thf(5,negated_conjecture,
tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_A @ c_Message_Omsg_OAgent @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_A @ c_Message_Omsg_OAgent @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_Aaa @ c_Event_Oevent_OSays ) ) @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(334,plain,
tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_A @ c_Message_Omsg_OAgent @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_A @ c_Message_Omsg_OAgent @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_Aaa @ c_Event_Oevent_OSays ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1404,plain,
! [B: $i,A: $i] :
( ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_A @ c_Message_Omsg_OAgent @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_A @ c_Message_Omsg_OAgent @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_Aaa @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[334,1146]) ).
thf(1405,plain,
! [B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_A @ c_Message_Omsg_OAgent @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_A @ c_Message_Omsg_OAgent @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_Aaa @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1404]) ).
thf(1420,plain,
! [B: $i,A: $i] :
( ( tc_Event_Oevent != B )
| ( ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) )
!= c_emptyset )
| ( ( v_A @ c_Message_Omsg_OAgent @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_A @ c_Message_Omsg_OAgent @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_Aaa @ c_Event_Oevent_OSays ) ) )
!= A ) ),
inference(simp,[status(thm)],[1405]) ).
thf(1430,plain,
( ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) )
!= c_emptyset ),
inference(simp,[status(thm)],[1420]) ).
thf(1470,plain,
! [A: $i] :
( ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
!= ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) ) )
| ( c_emptyset != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[979,1430]) ).
thf(1471,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
!= ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) ) ),
inference(simp,[status(thm)],[1470]) ).
thf(1472,plain,
! [A: $i] :
( ( A != tc_Event_Oevent )
| ( c_List_Olist_ONil != v_evs3 ) ),
inference(simp,[status(thm)],[1471]) ).
thf(1473,plain,
c_List_Olist_ONil != v_evs3,
inference(simp,[status(thm)],[1472]) ).
thf(15669,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil != c_List_Olist_ONil )
| ( A != v_evs3 )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[430,1473]) ).
thf(15670,plain,
! [B: $i,A: $i] :
( ( A != v_evs3 )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[15669:[]]) ).
thf(16059,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[15670]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff2_0) ).
thf(379,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)],[21]) ).
thf(380,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)],[379]) ).
thf(16405,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs3 @ 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)],[16059,380]) ).
thf(16406,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs3 @ 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)],[16405]) ).
thf(16407,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[16406:[bind(A,$thf( F )),bind(B,$thf( c_0 )),bind(C,$thf( F @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) ))]]) ).
thf(16491,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ),
inference(simp,[status(thm)],[16407]) ).
thf(17042,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_evs3 @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16491,1146]) ).
thf(17043,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_evs3 @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[17042]) ).
thf(17151,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_evs3 @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) )
!= B ) ),
inference(simp,[status(thm)],[17043]) ).
thf(17225,plain,
c_emptyset != c_Wellfounded__Relations_Oless__than,
inference(simp,[status(thm)],[17151]) ).
thf(30325,plain,
! [C: $i,B: $i,A: $i] :
( ( A != c_emptyset )
| ( B != c_Wellfounded__Relations_Oless__than )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[480,17225]) ).
thf(30326,plain,
! [B: $i,A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[30325:[bind(A,$thf( c_emptyset ))]]) ).
thf(35063,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ),
inference(simp,[status(thm)],[30326]) ).
thf(40684,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( B @ ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[685,35063]) ).
thf(40685,plain,
! [B: $i,A: $i] :
( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( B @ ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) ),
inference(simp,[status(thm)],[40684]) ).
thf(40801,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set )
!= B )
| ( ( B @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
!= c_Finite__Set_OFinites )
| ( c_emptyset != c_emptyset ) ),
inference(simp,[status(thm)],[40685]) ).
thf(40884,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
!= c_Finite__Set_OFinites ),
inference(simp,[status(thm)],[40801]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_ONonce ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3__iff1_0) ).
thf(776,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)],[170]) ).
thf(777,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_ONonce ) ) ),
inference(cnf,[status(esa)],[776]) ).
thf(778,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_ONonce ) ) ),
inference(lifteq,[status(thm)],[777]) ).
thf(779,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_ONonce @ A )
= B ),
inference(detectInverse,[status(thm)],[778]) ).
thf(780,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_ONonce @ sk26 )
= A ),
inference(cnf,[status(esa)],[779]) ).
thf(1486,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_ONonce @ sk26 )
= A ),
inference(lifteq,[status(thm)],[780]) ).
thf(51,axiom,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
thf(460,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)],[51]) ).
thf(1400,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)],[460,1146]) ).
thf(1401,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)],[1400]) ).
thf(1417,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)],[1401]) ).
thf(1427,plain,
c_Finite__Set_OFinites != c_emptyset,
inference(simp,[status(thm)],[1417]) ).
thf(6398,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,1427]) ).
thf(6399,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6398:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(10349,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)],[351,6399]) ).
thf(10350,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)],[10349]) ).
thf(10379,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[10350]) ).
thf(10387,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[10379]) ).
thf(32,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).
thf(408,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)],[32]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONumber )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__3__iff1_0) ).
thf(523,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)],[75]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).
thf(582,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',cls_Public_Ospies__pubK_0) ).
thf(829,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)],[190]) ).
thf(12905,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)],[829,835]) ).
thf(12906,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)],[12905]) ).
thf(12931,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)],[12906]) ).
thf(12949,plain,
! [A: $i] :
( ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[12931]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONonce ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_ANonce_AN_A_61_61_62_AR_0) ).
thf(1158,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)],[333]) ).
thf(260,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_ONumber_0) ).
thf(994,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(25,axiom,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).
thf(388,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(389,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(cnf,[status(esa)],[388]) ).
thf(390,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( A = c_0 ) ),
inference(lifteq,[status(thm)],[389]) ).
thf(2015,plain,
! [A: $i] :
( ( A != c_List_Olist_ONil )
| ( c_0 != v_evs3 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1473]) ).
thf(2016,plain,
( ( c_0 != v_evs3 )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[2015:[bind(A,$thf( c_List_Olist_ONil ))]]) ).
thf(4348,plain,
( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_evs3 ) ),
inference(paramod_ordered,[status(thm)],[2016,1477]) ).
thf(4349,plain,
( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
| ( c_0 != v_evs3 ) ),
inference(simp,[status(thm)],[4348]) ).
thf(4378,plain,
( ( tc_nat != tc_nat )
| ( c_List_Olist_ONil != c_0 )
| ( c_0 != c_0 )
| ( c_0 != v_evs3 ) ),
inference(simp,[status(thm)],[4349]) ).
thf(4391,plain,
( ( c_List_Olist_ONil != c_0 )
| ( c_0 != v_evs3 ) ),
inference(simp,[status(thm)],[4378]) ).
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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
thf(419,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(12059,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ ( E @ c_insert ) ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[419,418]) ).
thf(12060,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ ( E @ c_insert ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[12059]) ).
thf(12061,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OgreaterThanAtMost ) ) @ ( A @ c_insert ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[12060:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( tc_nat @ ( G @ ( F @ c_SetInterval_OgreaterThanAtMost ) ) )),bind(D,$thf( tc_nat )),bind(E,$thf( E ))]]) ).
thf(12173,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OgreaterThanAtMost ) ) @ ( A @ c_insert ) ) @ c_in ) ) ),
inference(simp,[status(thm)],[12061]) ).
thf(26270,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OgreaterThanAtMost ) ) @ ( A @ c_insert ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12173,467]) ).
thf(26271,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OgreaterThanAtMost ) ) @ ( A @ c_insert ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[26270]) ).
thf(26384,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OgreaterThanAtMost ) ) @ ( A @ c_insert ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[26271]) ).
thf(26400,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OgreaterThanAtMost ) ) @ ( A @ c_insert ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[26384]) ).
thf(305,axiom,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(1097,plain,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff1_0) ).
thf(357,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)],[13]) ).
thf(358,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)],[357]) ).
thf(1478,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)],[358,1477]) ).
thf(1479,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1478]) ).
thf(1480,plain,
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[1479:[bind(A,$thf( c_0 )),bind(B,$thf( c_0 ))]]) ).
thf(1503,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)],[1097,1480]) ).
thf(1504,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)],[1503]) ).
thf(1517,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)],[1504]) ).
thf(1518,plain,
c_UNIV != c_Wellfounded__Relations_Oless__than,
inference(simp,[status(thm)],[1517]) ).
thf(5885,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,1518]) ).
thf(5886,plain,
( ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5885:[bind(A,$thf( c_UNIV ))]]) ).
thf(7196,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,5886]) ).
thf(7197,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[7196]) ).
thf(7198,plain,
( ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7197:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).
thf(211,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/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth_0) ).
thf(873,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)],[211]) ).
thf(326,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/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).
thf(1142,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)],[326]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
thf(878,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)],[213]) ).
thf(44,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
thf(440,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)],[44]) ).
thf(104,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).
thf(597,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)],[104]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
!= ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).
thf(756,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)],[162]) ).
thf(757,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)],[756]) ).
thf(758,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)],[757]) ).
thf(759,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Datatype_Ooption_OSome ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[758]) ).
thf(760,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Datatype_Ooption_OSome ) @ ( B @ sk25 ) )
= A ),
inference(cnf,[status(esa)],[759]) ).
thf(19964,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Datatype_Ooption_OSome ) @ ( B @ sk25 ) )
= A ),
inference(lifteq,[status(thm)],[760]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).
thf(715,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)],[147]) ).
thf(184,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/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OHash_0) ).
thf(814,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)],[184]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).
thf(698,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)],[139]) ).
thf(8,negated_conjecture,
! [A: $i] :
( ( v_B != v_A )
| ( v_NB != v_NA )
| ( v_A != v_Aa )
| ( A
!= ( v_NB @ c_Message_Omsg_ONonce ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).
thf(340,plain,
! [A: $i] :
( ( v_B != v_A )
| ( v_NB != v_NA )
| ( v_A != v_Aa )
| ( A
!= ( v_NB @ c_Message_Omsg_ONonce ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).
thf(670,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)],[127]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).
thf(471,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)],[56]) ).
thf(472,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(cnf,[status(esa)],[471]) ).
thf(33111,plain,
! [C: $i,B: $i,A: $i] :
( ( A != c_List_Olist_ONil )
| ( B != v_evs3 )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[480,1473]) ).
thf(33112,plain,
! [B: $i,A: $i] :
( ( A != v_evs3 )
| ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_List_Olist_ONil @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[33111:[bind(A,$thf( c_List_Olist_ONil ))]]) ).
thf(34082,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( v_evs3 @ c_insert ) ) @ ( c_List_Olist_ONil @ c_in ) ) ),
inference(simp,[status(thm)],[33112]) ).
thf(1611,plain,
! [A: $i] :
( ( A
!= ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) ) )
| ( c_emptyset != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1430]) ).
thf(1612,plain,
( ( c_emptyset != c_0 )
| ( tc_nat @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1611:[bind(A,$thf( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) ))]]) ).
thf(31,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(406,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(407,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[406]) ).
thf(5701,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_emptyset != c_0 ) ),
inference(paramod_ordered,[status(thm)],[1612,407]) ).
thf(5702,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[5701]) ).
thf(5747,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) )
!= A )
| ( c_0 != A )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[5702]) ).
thf(5762,plain,
( ( ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) )
!= c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[5747]) ).
thf(6239,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) )
!= c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,5762]) ).
thf(6240,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) )
!= c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[6239]) ).
thf(6241,plain,
( ( ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) )
!= c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6240:[bind(A,$thf( c_emptyset ))]]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).
thf(747,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(227,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
thf(913,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)],[227]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Public_ONonce__notin__initState__iff1_0) ).
thf(1001,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(215,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).
thf(885,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)],[215]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_0) ).
thf(1003,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(1004,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(cnf,[status(esa)],[1003]) ).
thf(1005,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(lifteq,[status(thm)],[1004]) ).
thf(1006,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_Omsg_OMPair ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[1005]) ).
thf(1007,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) @ ( B @ sk35 ) )
= A ),
inference(cnf,[status(esa)],[1006]) ).
thf(20488,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) @ ( B @ sk35 ) )
= A ),
inference(lifteq,[status(thm)],[1007]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).
thf(451,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)],[48]) ).
thf(452,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(cnf,[status(esa)],[451]) ).
thf(20929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ c_Pow ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[440,452]) ).
thf(20930,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ c_Pow ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[20929]) ).
thf(20931,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_Pow ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[20930:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( tc_nat @ ( F @ ( E @ c_SetInterval_OatLeastLessThan ) ) )),bind(D,$thf( tc_nat ))]]) ).
thf(21203,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_Pow ) @ c_in ) ) ),
inference(simp,[status(thm)],[20931]) ).
thf(6,negated_conjecture,
~ ( tc_Message_Omsg @ ( v_evs3 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(336,plain,
~ ( tc_Message_Omsg @ ( v_evs3 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(348,plain,
~ ( tc_Message_Omsg @ ( v_evs3 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[336]) ).
thf(1347,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_evs3 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1097,348]) ).
thf(1348,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_evs3 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1347]) ).
thf(1357,plain,
! [B: $i,A: $i] :
( ( B != tc_Message_Omsg )
| ( ( v_evs3 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts )
!= c_UNIV )
| ( A
!= ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) ) ) ),
inference(simp,[status(thm)],[1348]) ).
thf(1366,plain,
( ( v_evs3 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts )
!= c_UNIV ),
inference(simp,[status(thm)],[1357]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(404,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)],[30]) ).
thf(235,axiom,
tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OSpy_A_58_Abad_0) ).
thf(938,plain,
tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(1398,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)],[938,1146]) ).
thf(1399,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)],[1398]) ).
thf(1424,plain,
! [B: $i,A: $i] :
( ( tc_Message_Oagent != B )
| ( c_emptyset != c_Event_Obad )
| ( c_Message_Oagent_OSpy != A ) ),
inference(simp,[status(thm)],[1399]) ).
thf(1425,plain,
c_emptyset != c_Event_Obad,
inference(simp,[status(thm)],[1424]) ).
thf(30427,plain,
! [C: $i,B: $i,A: $i] :
( ( A != c_emptyset )
| ( B != c_Event_Obad )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[480,1425]) ).
thf(30428,plain,
! [B: $i,A: $i] :
( ( A != c_Event_Obad )
| ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[30427:[bind(A,$thf( c_emptyset ))]]) ).
thf(35113,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( c_Event_Obad @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ),
inference(simp,[status(thm)],[30428]) ).
thf(41907,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( c_Event_Obad @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[938,35113]) ).
thf(41908,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( c_Event_Obad @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
inference(simp,[status(thm)],[41907]) ).
thf(42043,plain,
! [A: $i] :
( ( A != tc_Message_Oagent )
| ( ( A @ ( c_emptyset @ ( c_Event_Obad @ c_insert ) ) )
!= c_Event_Obad )
| ( c_emptyset != c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[41908]) ).
thf(42117,plain,
( ( ( tc_Message_Oagent @ ( c_emptyset @ ( c_Event_Obad @ c_insert ) ) )
!= c_Event_Obad )
| ( c_emptyset != c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[42043]) ).
thf(2,negated_conjecture,
tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(337,plain,
tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1414,plain,
! [B: $i,A: $i] :
( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[337,1146]) ).
thf(1415,plain,
! [B: $i,A: $i] :
( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1414]) ).
thf(1419,plain,
! [B: $i,A: $i] :
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= B )
| ( c_emptyset != c_OtwayRees_Ootway )
| ( v_evs3 != A ) ),
inference(simp,[status(thm)],[1415]) ).
thf(1429,plain,
c_emptyset != c_OtwayRees_Ootway,
inference(simp,[status(thm)],[1419]) ).
thf(1772,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != c_OtwayRees_Ootway )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1429]) ).
thf(1773,plain,
( ( c_0 != c_OtwayRees_Ootway )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1772:[bind(A,$thf( c_emptyset ))]]) ).
thf(2197,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)],[390,1773]) ).
thf(2198,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)],[2197:[]]) ).
thf(2203,plain,
( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[2198]) ).
thf(4947,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,2203]) ).
thf(4948,plain,
( ( c_0 @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[4947:[bind(A,$thf( tc_nat ))]]) ).
thf(92,axiom,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
thf(570,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)],[92]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).
thf(372,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)],[19]) ).
thf(353,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
= c_List_Olist_ONil ),
inference(lifteq,[status(thm)],[352]) ).
thf(1667,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( c_List_Olist_ONil @ c_List_Orev ) ) )
| ( c_List_Olist_ONil = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,353]) ).
thf(1668,plain,
! [A: $i] :
( ( c_List_Olist_ONil = c_0 )
| ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_List_Orev ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1667:[bind(A,$thf( D @ ( c_List_Olist_ONil @ c_List_Orev ) )),bind(B,$thf( D ))]]) ).
thf(2119,plain,
! [A: $i] :
( ( c_List_Olist_ONil = c_0 )
| ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_List_Orev ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1668]) ).
thf(20785,plain,
( ( c_List_Olist_ONil = c_0 )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) ) ),
inference(rewrite,[status(thm)],[2119,353]) ).
thf(20865,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_List_Olist_ONil = c_0 )
| ( c_0 @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,20785]) ).
thf(20866,plain,
( ( c_List_Olist_ONil = c_0 )
| ( c_0 @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[20865:[bind(A,$thf( tc_nat ))]]) ).
thf(195,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/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair__iff2_0) ).
thf(838,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)],[195]) ).
thf(342,plain,
! [A: $i] :
( ( v_B != v_A )
| ( v_NB != v_NA )
| ( v_A != v_Aa )
| ( A
!= ( v_NB @ c_Message_Omsg_ONonce ) ) ),
inference(cnf,[status(esa)],[340]) ).
thf(343,plain,
! [A: $i] :
( ( v_B != v_A )
| ( v_NA != v_NB )
| ( v_Aa != v_A )
| ( A
!= ( v_NB @ c_Message_Omsg_ONonce ) ) ),
inference(lifteq,[status(thm)],[342]) ).
thf(344,plain,
( ( v_B != v_A )
| ( v_NA != v_NB )
| ( v_Aa != v_A ) ),
inference(simp,[status(thm)],[343]) ).
thf(284,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
thf(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)],[284]) ).
thf(149,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__pubK__iff1_0) ).
thf(723,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)],[149]) ).
thf(724,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[723]) ).
thf(24,axiom,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).
thf(386,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(387,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[386]) ).
thf(2183,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 != c_OtwayRees_Ootway ) ),
inference(paramod_ordered,[status(thm)],[1773,387]) ).
thf(2184,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ( c_0 != c_OtwayRees_Ootway ) ),
inference(simp,[status(thm)],[2183]) ).
thf(2199,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_emptyset != c_0 )
| ( c_0 != A )
| ( c_0 != c_OtwayRees_Ootway ) ),
inference(simp,[status(thm)],[2184]) ).
thf(2204,plain,
( ( c_emptyset != c_0 )
| ( c_0 != c_OtwayRees_Ootway ) ),
inference(simp,[status(thm)],[2199]) ).
thf(6032,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)],[393,2204]) ).
thf(6033,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != c_OtwayRees_Ootway )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[6032]) ).
thf(6034,plain,
( ( c_0 != c_OtwayRees_Ootway )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6033:[bind(A,$thf( c_emptyset ))]]) ).
thf(7606,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)],[419,467]) ).
thf(7607,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)],[7606]) ).
thf(7674,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)],[7607]) ).
thf(7696,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[7674]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair__iff1_0) ).
thf(917,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(141,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).
thf(702,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)],[141]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OHash ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_AHash_AZ_A_61_61_62_AR_0) ).
thf(751,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)],[160]) ).
thf(137,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
thf(696,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)],[137]) ).
thf(8582,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)],[696,467]) ).
thf(8583,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)],[8582]) ).
thf(8646,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)],[8583]) ).
thf(8654,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[8646]) ).
thf(332,axiom,
! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK_AX_A_58_AsymKeys_0) ).
thf(1157,plain,
! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(180,axiom,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OServer_A_58_Abad_A_61_61_62_AR_0) ).
thf(805,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(806,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[805]) ).
thf(1306,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)],[1157,806]) ).
thf(1307,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)],[1306]) ).
thf(1313,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)],[1307]) ).
thf(81,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).
thf(542,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)],[81]) ).
thf(1446,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)],[358,387]) ).
thf(1447,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)],[1446]) ).
thf(1448,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[1447:[bind(A,$thf( A )),bind(B,$thf( c_0 )),bind(C,$thf( A ))]]) ).
thf(17838,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)],[712,1448]) ).
thf(17839,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)],[17838]) ).
thf(17872,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)],[17839]) ).
thf(17894,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)],[17872]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpriK__neq__shrK__iff1_0) ).
thf(1147,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)],[328]) ).
thf(1002,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)],[1001]) ).
thf(5077,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)],[1097,1002]) ).
thf(5078,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)],[5077]) ).
thf(5111,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)],[5078]) ).
thf(5127,plain,
! [A: $i] :
( ( A @ c_Event_OinitState @ c_Message_Oparts )
!= c_UNIV ),
inference(simp,[status(thm)],[5111]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
thf(870,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)],[210]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OMPair_0) ).
thf(770,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)],[167]) ).
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/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff__iff1_0) ).
thf(414,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(415,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)],[414]) ).
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(lifteq,[status(thm)],[415]) ).
thf(314,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/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).
thf(1115,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)],[314]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).
thf(448,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)],[47]) ).
thf(1341,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)],[1097,467]) ).
thf(1342,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)],[1341]) ).
thf(1360,plain,
! [B: $i,A: $i] :
( ( B
!= ( tc_nat @ tc_set ) )
| ( c_UNIV != c_Finite__Set_OFinites )
| ( A != c_UNIV ) ),
inference(simp,[status(thm)],[1342]) ).
thf(1362,plain,
c_UNIV != c_Finite__Set_OFinites,
inference(simp,[status(thm)],[1360]) ).
thf(307,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
thf(1100,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)],[307]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).
thf(559,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2__iff1_1) ).
thf(623,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)],[114]) ).
thf(624,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
inference(cnf,[status(esa)],[623]) ).
thf(625,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
inference(lifteq,[status(thm)],[624]) ).
thf(626,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Event_Oevent_OGets ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[625]) ).
thf(627,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) @ ( A @ sk15 ) )
= B ),
inference(cnf,[status(esa)],[626]) ).
thf(17694,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) @ ( A @ sk15 ) )
= B ),
inference(lifteq,[status(thm)],[627]) ).
thf(107,axiom,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
thf(606,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)],[107]) ).
thf(3,negated_conjecture,
~ ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(339,plain,
~ ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(345,plain,
~ ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[339]) ).
thf(1351,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1097,345]) ).
thf(1352,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(simp,[status(thm)],[1351]) ).
thf(1359,plain,
! [B: $i,A: $i] :
( ( B != tc_Message_Omsg )
| ( ( v_evs3 @ c_Event_Oused )
!= c_UNIV )
| ( A
!= ( v_K @ c_Message_Omsg_OKey ) ) ),
inference(simp,[status(thm)],[1352]) ).
thf(1368,plain,
( ( v_evs3 @ c_Event_Oused )
!= c_UNIV ),
inference(simp,[status(thm)],[1359]) ).
thf(1862,plain,
! [A: $i] :
( ( A
!= ( v_evs3 @ c_Event_Oused ) )
| ( c_UNIV != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1368]) ).
thf(1863,plain,
( ( c_UNIV != c_0 )
| ( tc_nat @ ( v_evs3 @ c_Event_Oused @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1862:[bind(A,$thf( v_evs3 @ c_Event_Oused ))]]) ).
thf(5274,plain,
( ( ( tc_nat @ ( v_evs3 @ c_Event_Oused @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
| ~ $true
| ( c_UNIV != c_0 ) ),
inference(paramod_ordered,[status(thm)],[1863,1477]) ).
thf(5275,plain,
( ( ( tc_nat @ ( v_evs3 @ c_Event_Oused @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[5274]) ).
thf(5309,plain,
( ( tc_nat != tc_nat )
| ( ( v_evs3 @ c_Event_Oused )
!= c_0 )
| ( c_0 != c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[5275]) ).
thf(5323,plain,
( ( ( v_evs3 @ c_Event_Oused )
!= c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[5309]) ).
thf(214,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Public_OshrK )
!= ( B @ c_Public_OshrK ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__injective__iff1_0) ).
thf(880,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Public_OshrK )
!= ( B @ c_Public_OshrK ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(881,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Public_OshrK )
!= ( B @ c_Public_OshrK ) ) ),
inference(cnf,[status(esa)],[880]) ).
thf(882,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Public_OshrK )
!= ( B @ c_Public_OshrK ) ) ),
inference(lifteq,[status(thm)],[881]) ).
thf(883,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Public_OshrK @ A )
= B ),
inference(detectInverse,[status(thm)],[882]) ).
thf(884,plain,
! [A: $i] :
( ( A @ c_Public_OshrK @ sk30 )
= A ),
inference(cnf,[status(esa)],[883]) ).
thf(1489,plain,
! [A: $i] :
( ( A @ c_Public_OshrK @ sk30 )
= A ),
inference(lifteq,[status(thm)],[884]) ).
thf(57,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).
thf(473,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)],[57]) ).
thf(474,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(cnf,[status(esa)],[473]) ).
thf(475,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(lifteq,[status(thm)],[474]) ).
thf(28979,plain,
! [C: $i,B: $i,A: $i] :
( ( B != c_UNIV )
| ( A != c_Wellfounded__Relations_Oless__than )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[480,1518]) ).
thf(28980,plain,
! [B: $i,A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ~ ( B @ ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[28979:[bind(A,$thf( A )),bind(B,$thf( c_UNIV ))]]) ).
thf(34045,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ),
inference(simp,[status(thm)],[28980]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(789,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)],[173]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONumber )
!= ( B @ c_Message_Omsg_ONumber ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2__iff1_0) ).
thf(441,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)],[45]) ).
thf(442,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONumber )
!= ( B @ c_Message_Omsg_ONumber ) ) ),
inference(cnf,[status(esa)],[441]) ).
thf(443,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONumber )
!= ( B @ c_Message_Omsg_ONumber ) ) ),
inference(lifteq,[status(thm)],[442]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__2__iff1_0) ).
thf(1040,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)],[278]) ).
thf(33113,plain,
! [C: $i,B: $i,A: $i] :
( ( B != c_List_Olist_ONil )
| ( A != v_evs3 )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[480,1473]) ).
thf(33114,plain,
! [B: $i,A: $i] :
( ( A != v_evs3 )
| ~ ( B @ ( B @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[33113:[bind(A,$thf( A )),bind(B,$thf( c_List_Olist_ONil ))]]) ).
thf(34084,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) @ ( v_evs3 @ c_in ) ) ),
inference(simp,[status(thm)],[33114]) ).
thf(28977,plain,
! [C: $i,B: $i,A: $i] :
( ( A != c_UNIV )
| ( B != c_Wellfounded__Relations_Oless__than )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[480,1518]) ).
thf(28978,plain,
! [B: $i,A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[28977:[bind(A,$thf( c_UNIV ))]]) ).
thf(34043,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ),
inference(simp,[status(thm)],[28978]) ).
thf(36658,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( C @ ( C @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1097,34043]) ).
thf(36659,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( C @ ( C @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[36658]) ).
thf(36698,plain,
! [C: $i,B: $i,A: $i] :
( ( B != C )
| ( ( C @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
!= c_UNIV )
| ( A != c_UNIV ) ),
inference(simp,[status(thm)],[36659]) ).
thf(36777,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[36698]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
thf(821,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)],[186]) ).
thf(6035,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)],[393,2204]) ).
thf(6036,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( A != c_OtwayRees_Ootway )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6035:[]]) ).
thf(6840,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_OtwayRees_Ootway @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[6036]) ).
thf(4400,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_List_Olist_ONil != c_0 )
| ( A != v_evs3 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,4391]) ).
thf(4401,plain,
! [A: $i] :
( ( c_List_Olist_ONil != c_0 )
| ( A != v_evs3 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[4400:[]]) ).
thf(4410,plain,
( ( c_List_Olist_ONil != c_0 )
| ( tc_nat @ ( v_evs3 @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[4401]) ).
thf(18,axiom,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).
thf(370,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(371,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[370]) ).
thf(4983,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( v_evs3 @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_List_Olist_ONil != c_0 ) ),
inference(paramod_ordered,[status(thm)],[4410,371]) ).
thf(4984,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( v_evs3 @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ( c_List_Olist_ONil != c_0 ) ),
inference(simp,[status(thm)],[4983]) ).
thf(5015,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( c_emptyset != v_evs3 )
| ( c_0 != A )
| ( c_List_Olist_ONil != c_0 ) ),
inference(simp,[status(thm)],[4984]) ).
thf(5027,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( c_emptyset != v_evs3 )
| ( c_List_Olist_ONil != c_0 ) ),
inference(simp,[status(thm)],[5015]) ).
thf(29217,plain,
! [C: $i,B: $i,A: $i] :
( ( B != c_UNIV )
| ( A != c_Finite__Set_OFinites )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[480,1362]) ).
thf(29218,plain,
! [B: $i,A: $i] :
( ( A != c_Finite__Set_OFinites )
| ~ ( B @ ( B @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[29217:[bind(A,$thf( A )),bind(B,$thf( c_UNIV ))]]) ).
thf(34277,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Finite__Set_OFinites @ c_in ) ) ),
inference(simp,[status(thm)],[29218]) ).
thf(17822,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)],[712,1002]) ).
thf(17823,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)],[17822]) ).
thf(17876,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)],[17823]) ).
thf(17899,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)],[17876]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).
thf(374,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)],[20]) ).
thf(375,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)],[374]) ).
thf(376,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)],[375]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).
thf(485,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)],[61]) ).
thf(323,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).
thf(1136,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)],[323]) ).
thf(5944,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( ( v_evs3 @ c_Event_Oused )
!= c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,5323]) ).
thf(5945,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( ( v_evs3 @ c_Event_Oused )
!= c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5944]) ).
thf(5946,plain,
( ( ( v_evs3 @ c_Event_Oused )
!= c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5945:[bind(A,$thf( c_UNIV ))]]) ).
thf(102,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
thf(592,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(593,plain,
c_UNIV != c_emptyset,
inference(polarity_switch,[status(thm)],[592]) ).
thf(594,plain,
c_UNIV != c_emptyset,
inference(lifteq,[status(thm)],[593]) ).
thf(6299,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,594]) ).
thf(6300,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6299:[bind(A,$thf( c_UNIV ))]]) ).
thf(38884,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( C @ ( C @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) @ ( v_evs3 @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1097,34084]) ).
thf(38885,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( C @ ( C @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) @ ( v_evs3 @ c_in ) ) ) ),
inference(simp,[status(thm)],[38884]) ).
thf(38964,plain,
! [C: $i,B: $i,A: $i] :
( ( B != C )
| ( ( C @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) )
!= c_UNIV )
| ( A != v_evs3 ) ),
inference(simp,[status(thm)],[38885]) ).
thf(39025,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[38964]) ).
thf(17227,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,17225]) ).
thf(17228,plain,
( ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[17227:[bind(A,$thf( c_emptyset ))]]) ).
thf(17354,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)],[351,17228]) ).
thf(17355,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)],[17354]) ).
thf(17385,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)],[17355]) ).
thf(17398,plain,
( ( c_emptyset != c_0 )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[17385]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).
thf(514,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)],[72]) ).
thf(94,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).
thf(574,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(223,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
thf(905,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)],[223]) ).
thf(1353,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)],[1097,835]) ).
thf(1354,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)],[1353]) ).
thf(1361,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_UNIV )
| ( A != C ) ),
inference(simp,[status(thm)],[1354]) ).
thf(1363,plain,
( ( c_emptyset @ c_Message_Oparts )
!= c_UNIV ),
inference(simp,[status(thm)],[1361]) ).
thf(6590,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( c_0 @ c_Message_Oparts )
!= c_UNIV )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,1363]) ).
thf(6591,plain,
( ( ( c_0 @ c_Message_Oparts )
!= c_UNIV )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6590:[bind(A,$thf( c_emptyset ))]]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv__iff1_0) ).
thf(397,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)],[28]) ).
thf(5771,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) )
!= c_0 )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,5762]) ).
thf(5772,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) )
!= c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[5771]) ).
thf(5773,plain,
( ( ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) )
!= c_0 )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5772:[bind(A,$thf( c_emptyset ))]]) ).
thf(153,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).
thf(734,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)],[153]) ).
thf(208,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/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz__iff2_0) ).
thf(866,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)],[208]) ).
thf(49,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
thf(453,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)],[49]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).
thf(394,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)],[27]) ).
thf(395,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)],[394]) ).
thf(396,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)],[395]) ).
thf(262,axiom,
! [A: $i] :
( c_Message_Oagent_OSpy
!= ( A @ c_Message_Oagent_OFriend ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__6__iff1_0) ).
thf(998,plain,
! [A: $i] :
( c_Message_Oagent_OSpy
!= ( A @ c_Message_Oagent_OFriend ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).
thf(411,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)],[33]) ).
thf(1599,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,468]) ).
thf(1600,plain,
( ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1599:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).
thf(309,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/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).
thf(1104,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)],[309]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).
thf(507,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)],[69]) ).
thf(476,plain,
? [A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[475]) ).
thf(477,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ sk9 ) ) )
= A ),
inference(cnf,[status(esa)],[476]) ).
thf(27697,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ sk9 ) ) )
= A ),
inference(lifteq,[status(thm)],[477]) ).
thf(2051,plain,
! [A: $i] :
( ( A
!= ( tc_Event_Oevent @ tc_List_Olist ) )
| ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,337]) ).
thf(2052,plain,
( ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) )
| ( tc_nat @ ( tc_Event_Oevent @ tc_List_Olist @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[2051:[bind(A,$thf( tc_Event_Oevent @ tc_List_Olist ))]]) ).
thf(6950,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_Event_Oevent @ tc_List_Olist @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[2052,407]) ).
thf(6951,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_Event_Oevent @ tc_List_Olist @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) ) ),
inference(simp,[status(thm)],[6950]) ).
thf(6992,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_Event_Oevent @ tc_List_Olist )
!= A )
| ( c_0 != A )
| ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) ) ),
inference(simp,[status(thm)],[6951]) ).
thf(7004,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= c_0 )
| ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) ) ),
inference(simp,[status(thm)],[6992]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
thf(1119,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)],[316]) ).
thf(169,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
thf(774,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)],[169]) ).
thf(197,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/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__in__used_0) ).
thf(842,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)],[197]) ).
thf(4600,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)],[842,835]) ).
thf(4601,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)],[4600]) ).
thf(4630,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)],[4601]) ).
thf(4643,plain,
! [A: $i] :
( ( A @ c_Event_Oused )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[4630]) ).
thf(1918,plain,
! [B: $i,A: $i] :
( ( A != tc_nat )
| ( c_0 @ ( B @ ( c_0 @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,351]) ).
thf(1919,plain,
! [A: $i] :
( ( c_0 @ ( A @ ( c_0 @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1918:[bind(A,$thf( tc_nat ))]]) ).
thf(2154,plain,
! [A: $i] :
( ( c_0 @ ( A @ ( c_0 @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1919]) ).
thf(5932,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,1362]) ).
thf(5933,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5932:[bind(A,$thf( c_UNIV ))]]) ).
thf(7715,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)],[351,5933]) ).
thf(7716,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)],[7715]) ).
thf(7744,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_UNIV != c_0 )
| ( c_Finite__Set_OFinites != c_0 ) ),
inference(simp,[status(thm)],[7716]) ).
thf(7747,plain,
( ( c_UNIV != c_0 )
| ( c_Finite__Set_OFinites != c_0 ) ),
inference(simp,[status(thm)],[7744]) ).
thf(7758,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)],[393,7747]) ).
thf(7759,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[7758]) ).
thf(7760,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7759:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(295,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/sandbox/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)],[295]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OKey )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__4__iff1_0) ).
thf(920,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(71,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).
thf(512,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)],[71]) ).
thf(130,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
thf(678,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)],[130]) ).
thf(77,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).
thf(529,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)],[77]) ).
thf(7347,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != c_OtwayRees_Ootway )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,6034]) ).
thf(7348,plain,
! [A: $i] :
( ( A != c_OtwayRees_Ootway )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7347:[]]) ).
thf(7393,plain,
( ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( c_OtwayRees_Ootway @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[7348]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
thf(761,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)],[163]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__iff1_1) ).
thf(577,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)],[96]) ).
thf(578,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)],[577]) ).
thf(579,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)],[578]) ).
thf(580,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_OHPair ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[579]) ).
thf(581,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) @ ( A @ sk14 ) )
= B ),
inference(cnf,[status(esa)],[580]) ).
thf(17242,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) @ ( A @ sk14 ) )
= B ),
inference(lifteq,[status(thm)],[581]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__5__iff1_0) ).
thf(546,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)],[83]) ).
thf(174,axiom,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OSpy ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__5__iff1_0) ).
thf(791,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OSpy ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(792,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OSpy ),
inference(polarity_switch,[status(thm)],[791]) ).
thf(793,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OSpy ),
inference(lifteq,[status(thm)],[792]) ).
thf(22,axiom,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).
thf(381,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(12104,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ ( E @ c_insert ) ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[696,418]) ).
thf(12105,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ ( E @ c_insert ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[12104]) ).
thf(12106,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OgreaterThanLessThan ) ) @ ( A @ c_insert ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[12105:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( tc_nat @ ( G @ ( F @ c_SetInterval_OgreaterThanLessThan ) ) )),bind(D,$thf( tc_nat )),bind(E,$thf( E ))]]) ).
thf(12181,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OgreaterThanLessThan ) ) @ ( A @ c_insert ) ) @ c_in ) ) ),
inference(simp,[status(thm)],[12106]) ).
thf(26525,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OgreaterThanLessThan ) ) @ ( A @ c_insert ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12181,467]) ).
thf(26526,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OgreaterThanLessThan ) ) @ ( A @ c_insert ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[26525]) ).
thf(26647,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OgreaterThanLessThan ) ) @ ( A @ c_insert ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[26526]) ).
thf(26658,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OgreaterThanLessThan ) ) @ ( A @ c_insert ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[26647]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox/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)],[280]) ).
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(1,negated_conjecture,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(335,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(346,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[335]) ).
thf(1161,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[337,346]) ).
thf(1162,plain,
( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1161]) ).
thf(1163,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Oagent )
| ( c_OtwayRees_Ootway != c_Event_Obad )
| ( v_evs3 != v_A ) ),
inference(simp,[status(thm)],[1162]) ).
thf(226,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OKey ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_AKey_AK_A_61_61_62_AR_0) ).
thf(910,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)],[226]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(894,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)],[219]) ).
thf(270,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
thf(1021,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)],[270]) ).
thf(1041,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[1040]) ).
thf(1042,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[1041]) ).
thf(1408,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)],[1157,1146]) ).
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 ) ) ) ),
inference(simp,[status(thm)],[1408]) ).
thf(1418,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != C )
| ( c_Message_OsymKeys != c_emptyset )
| ( ( A @ c_Public_OshrK )
!= B ) ),
inference(simp,[status(thm)],[1409]) ).
thf(1428,plain,
c_Message_OsymKeys != c_emptyset,
inference(simp,[status(thm)],[1418]) ).
thf(6263,plain,
! [A: $i] :
( ( A != c_Message_OsymKeys )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,1428]) ).
thf(6264,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Message_OsymKeys @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6263:[bind(A,$thf( c_Message_OsymKeys ))]]) ).
thf(1246,plain,
! [A: $i] :
( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[337,835]) ).
thf(1247,plain,
! [A: $i] :
( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1246]) ).
thf(1251,plain,
! [A: $i] :
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_OtwayRees_Ootway )
| ( v_evs3 != A ) ),
inference(simp,[status(thm)],[1247]) ).
thf(1255,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_OtwayRees_Ootway ) ),
inference(simp,[status(thm)],[1251]) ).
thf(88,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).
thf(561,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)],[88]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).
thf(362,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)],[16]) ).
thf(363,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)],[362]) ).
thf(364,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)],[363]) ).
thf(365,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)],[364]) ).
thf(366,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) @ ( C @ ( B @ sk1 ) ) )
= A ),
inference(cnf,[status(esa)],[365]) ).
thf(1487,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) @ ( C @ ( B @ sk1 ) ) )
= A ),
inference(lifteq,[status(thm)],[366]) ).
thf(21028,plain,
! [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 @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ c_Pow ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[685,452]) ).
thf(21029,plain,
! [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 @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ c_Pow ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[21028]) ).
thf(21030,plain,
! [A: $i] : ( A @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ ( c_emptyset @ c_Pow ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[21029:[bind(A,$thf( A )),bind(B,$thf( c_emptyset )),bind(C,$thf( A ))]]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).
thf(729,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)],[152]) ).
thf(17812,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)],[712,806]) ).
thf(17813,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)],[17812]) ).
thf(17879,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)],[17813]) ).
thf(17902,plain,
( ( tc_Message_Oagent @ ( c_emptyset @ ( c_Message_Oagent_OServer @ c_insert ) ) )
!= c_Event_Obad ),
inference(simp,[status(thm)],[17879]) ).
thf(27748,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[949,467]) ).
thf(27749,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[27748]) ).
thf(27803,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( tc_nat @ tc_set ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_Finite__Set_OFinites )
| ( A != c_UNIV ) ),
inference(simp,[status(thm)],[27749]) ).
thf(27827,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( A @ ( c_UNIV @ c_insert ) ) )
!= c_Finite__Set_OFinites ),
inference(simp,[status(thm)],[27803]) ).
thf(12023,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)],[606,418]) ).
thf(12024,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)],[12023]) ).
thf(12025,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OlessThan ) @ ( A @ c_insert ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[12024:[bind(A,$thf( E )),bind(B,$thf( tc_nat @ ( E @ c_SetInterval_OlessThan ) )),bind(C,$thf( tc_nat )),bind(D,$thf( D ))]]) ).
thf(12211,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)],[12025]) ).
thf(12437,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)],[12211,467]) ).
thf(12438,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)],[12437]) ).
thf(12531,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)],[12438]) ).
thf(12561,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OlessThan ) @ ( A @ c_insert ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[12531]) ).
thf(188,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/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).
thf(825,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)],[188]) ).
thf(205,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_ACrypt_AK_AX_H_A_61_61_62_AR_0) ).
thf(860,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)],[205]) ).
thf(861,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)],[860]) ).
thf(862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
inference(lifteq,[status(thm)],[861]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).
thf(349,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)],[9]) ).
thf(126,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).
thf(665,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)],[126]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_OHPair ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__iff1_0) ).
thf(461,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)],[52]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OAgent ) ),
file('/export/starexec/sandbox/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)],[297]) ).
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/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_Ono__nonce__OR1__OR2__dest_0) ).
thf(974,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(310,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/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
thf(1106,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)],[310]) ).
thf(200,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OKey )
!= ( B @ c_Message_Omsg_OKey ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4__iff1_0) ).
thf(847,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)],[200]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
thf(566,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)],[90]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).
thf(483,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(484,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
inference(lifteq,[status(thm)],[483]) ).
thf(20938,plain,
! [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 @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ c_Pow ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[460,452]) ).
thf(20939,plain,
! [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 @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ c_Pow ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[20938]) ).
thf(20940,plain,
! [A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_Pow ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[20939:[bind(A,$thf( D )),bind(B,$thf( tc_nat @ ( D @ c_SetInterval_OatMost ) )),bind(C,$thf( tc_nat ))]]) ).
thf(21206,plain,
! [A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_Pow ) @ c_in ) ) ),
inference(simp,[status(thm)],[20940]) ).
thf(1601,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,468]) ).
thf(1602,plain,
( ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1601:[bind(A,$thf( tc_nat ))]]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
thf(852,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)],[201]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2__iff1_0) ).
thf(435,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)],[43]) ).
thf(37981,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( C @ ( C @ ( c_emptyset @ ( v_evs3 @ c_insert ) ) @ ( c_List_Olist_ONil @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1097,34082]) ).
thf(37982,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( C @ ( C @ ( c_emptyset @ ( v_evs3 @ c_insert ) ) @ ( c_List_Olist_ONil @ c_in ) ) ) ),
inference(simp,[status(thm)],[37981]) ).
thf(38051,plain,
! [C: $i,B: $i,A: $i] :
( ( B != C )
| ( ( C @ ( c_emptyset @ ( v_evs3 @ c_insert ) ) )
!= c_UNIV )
| ( A != c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[37982]) ).
thf(38104,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( v_evs3 @ c_insert ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[38051]) ).
thf(8691,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)],[351,6264]) ).
thf(8692,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)],[8691]) ).
thf(8721,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_Message_OsymKeys != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[8692]) ).
thf(8732,plain,
( ( c_Message_OsymKeys != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[8721]) ).
thf(8734,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)],[393,8732]) ).
thf(8735,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Message_OsymKeys != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[8734]) ).
thf(8736,plain,
( ( c_Message_OsymKeys != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[8735:[bind(A,$thf( c_emptyset ))]]) ).
thf(583,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
inference(lifteq,[status(thm)],[582]) ).
thf(12007,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)],[460,418]) ).
thf(12008,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)],[12007]) ).
thf(12009,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OatMost ) @ ( A @ c_insert ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[12008:[bind(A,$thf( E )),bind(B,$thf( tc_nat @ ( E @ c_SetInterval_OatMost ) )),bind(C,$thf( tc_nat )),bind(D,$thf( D ))]]) ).
thf(12196,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)],[12009]) ).
thf(191,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/sandbox/benchmark/theBenchmark.p',cls_Public_OMPair__used_0) ).
thf(830,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)],[191]) ).
thf(1441,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)],[358,407]) ).
thf(1442,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)],[1441]) ).
thf(1443,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[1442:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(1468,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)],[1443]) ).
thf(17864,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)],[712,1468]) ).
thf(17865,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)],[17864]) ).
thf(17869,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)],[17865]) ).
thf(17891,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)],[17869]) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',cls_Public_OprivateKey_Ab_AA_A_61_ApublicKey_Ac_AA_H_A_61_61_62_AR_0) ).
thf(491,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)],[64]) ).
thf(492,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)],[491]) ).
thf(493,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)],[492]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).
thf(551,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)],[85]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).
thf(1128,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)],[320]) ).
thf(6168,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,1425]) ).
thf(6169,plain,
( ( c_0 != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6168:[bind(A,$thf( c_emptyset ))]]) ).
thf(8061,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)],[351,6169]) ).
thf(8062,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)],[8061]) ).
thf(8091,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_emptyset != c_0 )
| ( c_0 != c_Event_Obad ) ),
inference(simp,[status(thm)],[8062]) ).
thf(8104,plain,
( ( c_emptyset != c_0 )
| ( c_0 != c_Event_Obad ) ),
inference(simp,[status(thm)],[8091]) ).
thf(1283,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)],[685,806]) ).
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 ) ) ) ),
inference(simp,[status(thm)],[1283]) ).
thf(1291,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)],[1284]) ).
thf(30327,plain,
! [C: $i,B: $i,A: $i] :
( ( B != c_emptyset )
| ( A != c_Wellfounded__Relations_Oless__than )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[480,17225]) ).
thf(30328,plain,
! [B: $i,A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ~ ( B @ ( B @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[30327:[bind(A,$thf( A )),bind(B,$thf( c_emptyset ))]]) ).
thf(35064,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ),
inference(simp,[status(thm)],[30328]) ).
thf(41592,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( C @ ( C @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1097,35064]) ).
thf(41593,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( C @ ( C @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) ),
inference(simp,[status(thm)],[41592]) ).
thf(41640,plain,
! [C: $i,B: $i,A: $i] :
( ( B != C )
| ( ( C @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= c_UNIV )
| ( A != c_Wellfounded__Relations_Oless__than ) ),
inference(simp,[status(thm)],[41593]) ).
thf(41712,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[41640]) ).
thf(12002,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ ( E @ c_insert ) ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[440,418]) ).
thf(12003,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ ( E @ c_insert ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[12002]) ).
thf(12004,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ c_insert ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[12003:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( tc_nat @ ( G @ ( F @ c_SetInterval_OatLeastLessThan ) ) )),bind(D,$thf( tc_nat )),bind(E,$thf( E ))]]) ).
thf(12192,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ c_insert ) ) @ c_in ) ) ),
inference(simp,[status(thm)],[12004]) ).
thf(27176,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ c_insert ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12192,467]) ).
thf(27177,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ c_insert ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[27176]) ).
thf(27280,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ c_insert ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[27177]) ).
thf(27304,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ c_insert ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[27280]) ).
thf(267,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).
thf(1012,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)],[267]) ).
thf(5283,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != c_0 )
| ( tc_nat @ ( v_evs3 @ c_Event_Oused @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1863]) ).
thf(5284,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( tc_nat @ ( v_evs3 @ c_Event_Oused @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[5283]) ).
thf(5285,plain,
( ( tc_nat @ ( v_evs3 @ c_Event_Oused @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5284:[bind(A,$thf( c_UNIV ))]]) ).
thf(462,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)],[461]) ).
thf(463,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)],[462]) ).
thf(464,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_OHPair ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[463]) ).
thf(465,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) @ ( B @ sk8 ) )
= A ),
inference(cnf,[status(esa)],[464]) ).
thf(13981,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) @ ( B @ sk8 ) )
= A ),
inference(lifteq,[status(thm)],[465]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
thf(697,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)],[138]) ).
thf(5930,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != c_OtwayRees_Ootway )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,1773]) ).
thf(5931,plain,
! [A: $i] :
( ( A != c_OtwayRees_Ootway )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5930:[]]) ).
thf(6801,plain,
( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( c_OtwayRees_Ootway @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5931]) ).
thf(1543,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)],[390,979]) ).
thf(1544,plain,
! [A: $i] :
( ( c_emptyset = c_0 )
| ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_List_Oset ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1543:[bind(A,$thf( D @ ( c_List_Olist_ONil @ c_List_Oset ) )),bind(B,$thf( D ))]]) ).
thf(2078,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)],[1544]) ).
thf(14255,plain,
( ( c_emptyset = c_0 )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(rewrite,[status(thm)],[2078,979]) ).
thf(17231,plain,
( ( c_emptyset != c_emptyset )
| ( c_Wellfounded__Relations_Oless__than != c_0 )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[14255,17225]) ).
thf(17232,plain,
( ( c_Wellfounded__Relations_Oless__than != c_0 )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[17231:[]]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).
thf(615,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)],[111]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
thf(1121,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)],[317]) ).
thf(289,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/sandbox/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)],[289]) ).
thf(150,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).
thf(725,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)],[150]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONumber ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_ANumber_AN_A_61_61_62_AR_0) ).
thf(610,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)],[109]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).
thf(420,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(17824,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)],[712,1146]) ).
thf(17825,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)],[17824]) ).
thf(17875,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)],[17825]) ).
thf(17898,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(simp,[status(thm)],[17875]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
thf(989,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(156,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).
thf(742,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)],[156]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz__iff1_1) ).
thf(980,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(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(402,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)],[29]) ).
thf(403,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)],[402]) ).
thf(398,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(cnf,[status(esa)],[397]) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(lifteq,[status(thm)],[398]) ).
thf(400,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_List_Orev ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[399]) ).
thf(401,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Orev ) @ ( B @ sk3 ) )
= A ),
inference(cnf,[status(esa)],[400]) ).
thf(7838,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Orev ) @ ( B @ sk3 ) )
= A ),
inference(lifteq,[status(thm)],[401]) ).
thf(324,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
thf(1138,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)],[324]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( B @ ( A @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv__iff1_0) ).
thf(354,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)],[12]) ).
thf(355,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( B @ ( A @ c_List_Orev ) ) ) ),
inference(cnf,[status(esa)],[354]) ).
thf(356,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Orev ) )
!= c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[355]) ).
thf(7927,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)],[425,467]) ).
thf(7928,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)],[7927]) ).
thf(7995,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)],[7928]) ).
thf(8017,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[7995]) ).
thf(1345,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( C @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1097,347]) ).
thf(1346,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( C @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1345]) ).
thf(1358,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_Event_Oevent )
| ( ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) )
!= c_UNIV )
| ( A
!= ( v_K @ c_Message_Omsg_OKey @ ( C @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) ) ) ),
inference(simp,[status(thm)],[1346]) ).
thf(1367,plain,
( ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) )
!= c_UNIV ),
inference(simp,[status(thm)],[1358]) ).
thf(6660,plain,
! [A: $i] :
( ( A
!= ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) ) )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,1367]) ).
thf(6661,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6660:[bind(A,$thf( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) ))]]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).
thf(686,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)],[134]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__6__iff1_0) ).
thf(526,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)],[76]) ).
thf(6588,plain,
! [A: $i] :
( ( A
!= ( c_emptyset @ c_Message_Oparts ) )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,1363]) ).
thf(6589,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6588:[bind(A,$thf( c_emptyset @ c_Message_Oparts ))]]) ).
thf(16663,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)],[351,6589]) ).
thf(16664,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)],[16663]) ).
thf(16699,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)],[16664]) ).
thf(16715,plain,
( ( ( c_emptyset @ c_Message_Oparts )
!= c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[16699]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).
thf(590,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)],[101]) ).
thf(1159,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONonce ) ),
inference(polarity_switch,[status(thm)],[1158]) ).
thf(1160,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONonce ) ),
inference(lifteq,[status(thm)],[1159]) ).
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/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
thf(943,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(9134,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)],[943,1146]) ).
thf(9135,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)],[9134]) ).
thf(9173,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)],[9135]) ).
thf(9186,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Olists ) )
!= c_emptyset ),
inference(simp,[status(thm)],[9173]) ).
thf(273,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/sandbox/benchmark/theBenchmark.p',cls_Message_OKey__synth_0) ).
thf(1028,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)],[273]) ).
thf(298,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/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).
thf(1082,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)],[298]) ).
thf(63,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/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__neq__privateKey__iff1_0) ).
thf(488,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)],[63]) ).
thf(377,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)],[376]) ).
thf(378,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) @ ( C @ ( B @ sk2 ) ) )
= A ),
inference(cnf,[status(esa)],[377]) ).
thf(5031,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) @ ( C @ ( B @ sk2 ) ) )
= A ),
inference(lifteq,[status(thm)],[378]) ).
thf(55,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__priK__iff1_0) ).
thf(469,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)],[55]) ).
thf(470,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)],[469]) ).
thf(17836,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)],[712,470]) ).
thf(17837,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)],[17836]) ).
thf(17868,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)],[17837]) ).
thf(17890,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)],[17868]) ).
thf(1275,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)],[685,346]) ).
thf(1276,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)],[1275]) ).
thf(1292,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_Message_Oagent )
| ( c_Finite__Set_OFinites != c_Event_Obad )
| ( c_emptyset != v_A ) ),
inference(simp,[status(thm)],[1276]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1__iff1_1) ).
thf(933,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(86,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).
thf(554,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)],[86]) ).
thf(752,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OHash ) ),
inference(polarity_switch,[status(thm)],[751]) ).
thf(753,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OHash ) ),
inference(lifteq,[status(thm)],[752]) ).
thf(17846,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)],[712,346]) ).
thf(17847,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)],[17846]) ).
thf(17873,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)],[17847]) ).
thf(17895,plain,
( ( tc_Message_Oagent @ ( c_emptyset @ ( v_A @ c_insert ) ) )
!= c_Event_Obad ),
inference(simp,[status(thm)],[17873]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
thf(537,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)],[79]) ).
thf(38908,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) @ ( v_evs3 @ c_in ) ) )
!= ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[337,34084]) ).
thf(38909,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) @ ( v_evs3 @ c_in ) ) )
!= ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) ) ),
inference(simp,[status(thm)],[38908]) ).
thf(38927,plain,
! [A: $i] :
( ( A
!= ( tc_Event_Oevent @ tc_List_Olist ) )
| ( ( A @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) )
!= c_OtwayRees_Ootway )
| ( v_evs3 != v_evs3 ) ),
inference(simp,[status(thm)],[38909]) ).
thf(38982,plain,
( ( tc_Event_Oevent @ tc_List_Olist @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) )
!= c_OtwayRees_Ootway ),
inference(simp,[status(thm)],[38927]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__shrK_0) ).
thf(970,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(113,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__5__iff1_0) ).
thf(620,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)],[113]) ).
thf(621,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[620]) ).
thf(622,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[621]) ).
thf(12883,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)],[829,1146]) ).
thf(12884,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)],[12883]) ).
thf(12940,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)],[12884]) ).
thf(12955,plain,
! [A: $i] :
( ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
!= c_emptyset ),
inference(simp,[status(thm)],[12940]) ).
thf(17096,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_evs3 @ 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)],[16491,835]) ).
thf(17097,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_evs3 @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[17096]) ).
thf(17155,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_evs3 @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) )
!= B ) ),
inference(simp,[status(thm)],[17097]) ).
thf(17170,plain,
( ( ( tc_nat @ ( tc_nat @ tc_prod ) )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Wellfounded__Relations_Oless__than ) ),
inference(simp,[status(thm)],[17155]) ).
thf(329,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/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).
thf(1150,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)],[329]) ).
thf(1349,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)],[1097,806]) ).
thf(1350,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)],[1349]) ).
thf(1355,plain,
! [B: $i,A: $i] :
( ( B != tc_Message_Oagent )
| ( c_UNIV != c_Event_Obad )
| ( A != c_Message_Oagent_OServer ) ),
inference(simp,[status(thm)],[1350]) ).
thf(1364,plain,
c_UNIV != c_Event_Obad,
inference(simp,[status(thm)],[1355]) ).
thf(6330,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,1364]) ).
thf(6331,plain,
( ( c_0 != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6330:[bind(A,$thf( c_UNIV ))]]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1__iff1_2) ).
thf(984,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(20596,plain,
! [D: $i,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 ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( D @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[967,835]) ).
thf(20597,plain,
! [D: $i,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 ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( D @ c_in ) ) ) ),
inference(simp,[status(thm)],[20596]) ).
thf(20636,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg != tc_Message_Omsg )
| ( ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz )
!= ( c_emptyset @ c_Message_Oparts ) )
| ( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey )
!= D ) ),
inference(simp,[status(thm)],[20597]) ).
thf(20666,plain,
! [A: $i] :
( ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[20636]) ).
thf(29215,plain,
! [C: $i,B: $i,A: $i] :
( ( A != c_UNIV )
| ( B != c_Finite__Set_OFinites )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[480,1362]) ).
thf(29216,plain,
! [B: $i,A: $i] :
( ( A != c_Finite__Set_OFinites )
| ~ ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[29215:[bind(A,$thf( c_UNIV ))]]) ).
thf(34275,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_emptyset @ ( c_Finite__Set_OFinites @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ),
inference(simp,[status(thm)],[29216]) ).
thf(39307,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( c_Finite__Set_OFinites @ c_insert ) ) @ ( c_UNIV @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[938,34275]) ).
thf(39308,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( c_Finite__Set_OFinites @ c_insert ) ) @ ( c_UNIV @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
inference(simp,[status(thm)],[39307]) ).
thf(39419,plain,
! [A: $i] :
( ( A != tc_Message_Oagent )
| ( ( A @ ( c_emptyset @ ( c_Finite__Set_OFinites @ c_insert ) ) )
!= c_Event_Obad )
| ( c_UNIV != c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[39308]) ).
thf(39539,plain,
( ( ( tc_Message_Oagent @ ( c_emptyset @ ( c_Finite__Set_OFinites @ c_insert ) ) )
!= c_Event_Obad )
| ( c_UNIV != c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[39419]) ).
thf(287,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/sandbox/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)],[287]) ).
thf(10111,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)],[1061,1146]) ).
thf(10112,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)],[10111]) ).
thf(10158,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)],[10112]) ).
thf(10180,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oknows ) )
!= c_emptyset ),
inference(simp,[status(thm)],[10158]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) ) ),
file('/export/starexec/sandbox/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)],[286]) ).
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(282,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).
thf(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)],[282]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Public_OpublicKey ) )
!= ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject__iff1_0) ).
thf(455,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)],[50]) ).
thf(456,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)],[455]) ).
thf(457,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)],[456]) ).
thf(444,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_ONumber @ A )
= B ),
inference(detectInverse,[status(thm)],[443]) ).
thf(445,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_ONumber @ sk6 )
= A ),
inference(cnf,[status(esa)],[444]) ).
thf(1434,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_ONumber @ sk6 )
= A ),
inference(lifteq,[status(thm)],[445]) ).
thf(165,axiom,
! [A: $i] :
( c_Message_Oagent_OServer
!= ( A @ c_Message_Oagent_OFriend ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__1__iff1_0) ).
thf(765,plain,
! [A: $i] :
( c_Message_Oagent_OServer
!= ( A @ c_Message_Oagent_OFriend ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(276,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
thf(1035,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)],[276]) ).
thf(293,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).
thf(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)],[293]) ).
thf(272,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
thf(1026,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)],[272]) ).
thf(21082,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ c_Pow ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[696,452]) ).
thf(21083,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ c_Pow ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[21082]) ).
thf(21084,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_Pow ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[21083:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( tc_nat @ ( F @ ( E @ c_SetInterval_OgreaterThanLessThan ) ) )),bind(D,$thf( tc_nat ))]]) ).
thf(21214,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_Pow ) @ c_in ) ) ),
inference(simp,[status(thm)],[21084]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_1) ).
thf(953,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(954,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(cnf,[status(esa)],[953]) ).
thf(955,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(lifteq,[status(thm)],[954]) ).
thf(956,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_Omsg_OMPair ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[955]) ).
thf(957,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) @ ( A @ sk33 ) )
= B ),
inference(cnf,[status(esa)],[956]) ).
thf(20451,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) @ ( A @ sk33 ) )
= B ),
inference(lifteq,[status(thm)],[957]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).
thf(633,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)],[117]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv__iff2_0) ).
thf(360,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(17480,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)],[390,17232]) ).
thf(17481,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[17480]) ).
thf(17482,plain,
( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[17481:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Public_OpublicKey ) )
!= ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject__iff1_1) ).
thf(644,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)],[120]) ).
thf(645,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)],[644]) ).
thf(646,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)],[645]) ).
thf(647,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Public_OpublicKey ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[646]) ).
thf(648,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) @ ( A @ sk17 ) )
= B ),
inference(cnf,[status(esa)],[647]) ).
thf(17731,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) @ ( A @ sk17 ) )
= B ),
inference(lifteq,[status(thm)],[648]) ).
thf(6257,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != v_evs3 )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,2016]) ).
thf(6258,plain,
! [A: $i] :
( ( A != v_evs3 )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6257:[]]) ).
thf(6716,plain,
( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( v_evs3 @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[6258]) ).
thf(123,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(657,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(175,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/sandbox/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_0) ).
thf(794,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)],[175]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).
thf(586,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)],[99]) ).
thf(18495,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)],[351,6591]) ).
thf(18496,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)],[18495]) ).
thf(18531,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)],[18496]) ).
thf(18544,plain,
( ( c_emptyset != c_0 )
| ( ( c_0 @ c_Message_Oparts )
!= c_UNIV ) ),
inference(simp,[status(thm)],[18531]) ).
thf(148,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Oagent_OFriend )
!= ( B @ c_Message_Oagent_OFriend ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Oinject__iff1_0) ).
thf(718,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)],[148]) ).
thf(217,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
thf(888,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)],[217]) ).
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/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_OGets__imp__Says__dest_0) ).
thf(926,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(4183,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)],[1097,724]) ).
thf(4184,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)],[4183]) ).
thf(4202,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)],[4184]) ).
thf(4214,plain,
c_Message_OsymKeys != c_UNIV,
inference(simp,[status(thm)],[4202]) ).
thf(6488,plain,
! [A: $i] :
( ( A != c_Message_OsymKeys )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,4214]) ).
thf(6489,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Message_OsymKeys @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6488:[bind(A,$thf( c_Message_OsymKeys ))]]) ).
thf(11813,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)],[351,6489]) ).
thf(11814,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)],[11813]) ).
thf(11843,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_Message_OsymKeys != c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[11814]) ).
thf(11847,plain,
( ( c_Message_OsymKeys != c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[11843]) ).
thf(12626,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)],[393,11847]) ).
thf(12627,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Message_OsymKeys != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[12626]) ).
thf(12628,plain,
( ( c_Message_OsymKeys != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[12627:[bind(A,$thf( c_UNIV ))]]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
thf(965,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(112,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
thf(618,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)],[112]) ).
thf(8288,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)],[657,403]) ).
thf(8289,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)],[8288]) ).
thf(8290,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( A @ ( A @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[8289:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(39379,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( C @ ( C @ ( c_emptyset @ ( c_Finite__Set_OFinites @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1097,34275]) ).
thf(39380,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( C @ ( C @ ( c_emptyset @ ( c_Finite__Set_OFinites @ c_insert ) ) @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[39379]) ).
thf(39439,plain,
! [C: $i,B: $i,A: $i] :
( ( B != C )
| ( ( C @ ( c_emptyset @ ( c_Finite__Set_OFinites @ c_insert ) ) )
!= c_UNIV )
| ( A != c_UNIV ) ),
inference(simp,[status(thm)],[39380]) ).
thf(39480,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_Finite__Set_OFinites @ c_insert ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[39439]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).
thf(856,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)],[203]) ).
thf(16408,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16059,407]) ).
thf(16409,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[16408]) ).
thf(16476,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) )
!= B )
| ( c_0 != B ) ),
inference(simp,[status(thm)],[16409]) ).
thf(16496,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[16476]) ).
thf(5718,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != c_0 )
| ( tc_nat @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1612]) ).
thf(5719,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( tc_nat @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[5718]) ).
thf(5720,plain,
( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5719:[bind(A,$thf( c_emptyset ))]]) ).
thf(17403,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)],[393,17398]) ).
thf(17404,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[17403]) ).
thf(17405,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[17404:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).
thf(198,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__3__iff1_0) ).
thf(843,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
thf(772,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)],[168]) ).
thf(5874,plain,
! [A: $i] :
( ( A != c_List_Olist_ONil )
| ( c_0 != c_0 )
| ( c_0 != v_evs3 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,4391]) ).
thf(5875,plain,
! [A: $i] :
( ( A != c_List_Olist_ONil )
| ( c_0 != v_evs3 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5874]) ).
thf(5876,plain,
( ( c_0 != v_evs3 )
| ~ ( tc_nat @ ( c_0 @ ( c_List_Olist_ONil @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5875:[bind(A,$thf( c_List_Olist_ONil ))]]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OCrypt_0) ).
thf(958,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(848,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OKey )
!= ( B @ c_Message_Omsg_OKey ) ) ),
inference(cnf,[status(esa)],[847]) ).
thf(849,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OKey )
!= ( B @ c_Message_Omsg_OKey ) ) ),
inference(lifteq,[status(thm)],[848]) ).
thf(850,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OKey @ A )
= B ),
inference(detectInverse,[status(thm)],[849]) ).
thf(851,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OKey @ sk29 )
= A ),
inference(cnf,[status(esa)],[850]) ).
thf(1488,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OKey @ sk29 )
= A ),
inference(lifteq,[status(thm)],[851]) ).
thf(412,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)],[411]) ).
thf(413,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)],[412]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).
thf(584,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)],[98]) ).
thf(331,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = D )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( E @ c_Message_Omsg_OAgent @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ 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 @ ( D @ c_Message_Omsg_OAgent @ ( B @ c_Message_Omsg_OAgent @ 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/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_Ounique__NA__dest_0) ).
thf(1154,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = D )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( E @ c_Message_Omsg_OAgent @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ 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 @ ( D @ c_Message_Omsg_OAgent @ ( B @ c_Message_Omsg_OAgent @ 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)],[331]) ).
thf(212,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
thf(875,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)],[212]) ).
thf(318,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
thf(1124,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)],[318]) ).
thf(5877,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_List_Olist_ONil != c_0 )
| ( A != v_evs3 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,4391]) ).
thf(5878,plain,
! [A: $i] :
( ( c_List_Olist_ONil != c_0 )
| ( A != v_evs3 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5877:[]]) ).
thf(6774,plain,
( ( c_List_Olist_ONil != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( v_evs3 @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5878]) ).
thf(17807,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)],[712,724]) ).
thf(17808,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)],[17807]) ).
thf(17882,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)],[17808]) ).
thf(17905,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( c_emptyset @ ( B @ ( A @ c_Public_OpublicKey ) @ c_insert ) ) )
!= c_Message_OsymKeys ),
inference(simp,[status(thm)],[17882]) ).
thf(146,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
| ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
thf(713,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)],[146]) ).
thf(7018,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != v_evs3 )
| ~ ( tc_nat @ ( c_0 @ ( c_List_Olist_ONil @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,5876]) ).
thf(7019,plain,
! [A: $i] :
( ( A != v_evs3 )
| ~ ( tc_nat @ ( c_0 @ ( c_List_Olist_ONil @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7018:[]]) ).
thf(7062,plain,
( ~ ( tc_nat @ ( c_0 @ ( c_List_Olist_ONil @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( v_evs3 @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[7019]) ).
thf(2055,plain,
! [A: $i] :
( ( A
!= ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) ) )
| ( c_UNIV != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1367]) ).
thf(2056,plain,
( ( c_UNIV != c_0 )
| ( tc_nat @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[2055:[bind(A,$thf( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) ))]]) ).
thf(10503,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != c_0 )
| ( tc_nat @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,2056]) ).
thf(10504,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( tc_nat @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[10503]) ).
thf(10505,plain,
( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[10504:[bind(A,$thf( c_UNIV ))]]) ).
thf(80,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).
thf(540,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)],[80]) ).
thf(458,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Public_OpublicKey ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[457]) ).
thf(459,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) @ ( B @ sk7 ) )
= A ),
inference(cnf,[status(esa)],[458]) ).
thf(13459,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Public_OpublicKey ) @ ( B @ sk7 ) )
= A ),
inference(lifteq,[status(thm)],[459]) ).
thf(21015,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ c_Pow ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[419,452]) ).
thf(21016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ c_Pow ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[21015]) ).
thf(21017,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_Pow ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[21016:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( tc_nat @ ( F @ ( E @ c_SetInterval_OgreaterThanAtMost ) ) )),bind(D,$thf( tc_nat ))]]) ).
thf(21186,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_Pow ) @ c_in ) ) ),
inference(simp,[status(thm)],[21017]) ).
thf(303,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
thf(1092,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)],[303]) ).
thf(6634,plain,
! [A: $i] :
( ( A != c_List_Olist_ONil )
| ( c_0 != c_0 )
| ( tc_nat @ ( v_evs3 @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,4410]) ).
thf(6635,plain,
! [A: $i] :
( ( A != c_List_Olist_ONil )
| ( tc_nat @ ( v_evs3 @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[6634]) ).
thf(6636,plain,
( ( tc_nat @ ( v_evs3 @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( c_List_Olist_ONil @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6635:[bind(A,$thf( c_List_Olist_ONil ))]]) ).
thf(302,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
thf(1090,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)],[302]) ).
thf(350,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)],[349]) ).
thf(9208,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)],[351,6300]) ).
thf(9209,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)],[9208]) ).
thf(9237,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_UNIV != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[9209]) ).
thf(9248,plain,
( ( c_UNIV != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[9237]) ).
thf(1545,plain,
! [B: $i,A: $i] :
( ( A != c_List_Olist_ONil )
| ( ( B @ ( c_0 @ c_List_Oset ) )
= c_emptyset )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,979]) ).
thf(1546,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ c_List_Oset ) )
= c_emptyset )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1545:[bind(A,$thf( c_List_Olist_ONil ))]]) ).
thf(2079,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ c_List_Oset ) )
= c_emptyset )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1546]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
thf(681,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)],[131]) ).
thf(315,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
thf(1117,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)],[315]) ).
thf(281,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/sandbox/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)],[281]) ).
thf(17416,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)],[390,17398]) ).
thf(17417,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( c_emptyset != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[17416]) ).
thf(17418,plain,
( ( c_emptyset != c_0 )
| ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[17417:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).
thf(206,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OAgent_0) ).
thf(863,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)],[206]) ).
thf(221,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
thf(900,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)],[221]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(649,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)],[121]) ).
thf(279,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/sandbox/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)],[279]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).
thf(433,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(434,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)],[433]) ).
thf(65,axiom,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(494,plain,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(116,axiom,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).
thf(631,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)],[116]) ).
thf(1322,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)],[460,835]) ).
thf(1323,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)],[1322]) ).
thf(1333,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)],[1323]) ).
thf(1339,plain,
( ( ( tc_nat @ tc_set )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Finite__Set_OFinites ) ),
inference(simp,[status(thm)],[1333]) ).
thf(185,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/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_0) ).
thf(816,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)],[185]) ).
thf(817,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(cnf,[status(esa)],[816]) ).
thf(818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(lifteq,[status(thm)],[817]) ).
thf(819,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_Omsg_OCrypt ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[818]) ).
thf(820,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) @ ( B @ sk28 ) )
= A ),
inference(cnf,[status(esa)],[819]) ).
thf(20001,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) @ ( B @ sk28 ) )
= A ),
inference(lifteq,[status(thm)],[820]) ).
thf(177,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(799,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)],[177]) ).
thf(1148,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
inference(polarity_switch,[status(thm)],[1147]) ).
thf(1149,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
inference(lifteq,[status(thm)],[1148]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz__iff1_0) ).
thf(915,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(27760,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[949,345]) ).
thf(27761,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(simp,[status(thm)],[27760]) ).
thf(27809,plain,
! [C: $i,B: $i,A: $i] :
( ( C != tc_Message_Omsg )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( v_evs3 @ c_Event_Oused ) )
| ( A
!= ( v_K @ c_Message_Omsg_OKey ) ) ),
inference(simp,[status(thm)],[27761]) ).
thf(27834,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( A @ ( v_K @ c_Message_Omsg_OKey @ c_insert ) ) )
!= ( v_evs3 @ c_Event_Oused ) ),
inference(simp,[status(thm)],[27809]) ).
thf(313,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/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair__iff1_1) ).
thf(1112,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)],[313]) ).
thf(183,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/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__3__iff1_0) ).
thf(811,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)],[183]) ).
thf(204,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/sandbox/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__privateKey_0) ).
thf(858,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)],[204]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(367,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)],[17]) ).
thf(5893,plain,
! [A: $i] :
( ( A
!= ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) ) )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,1430]) ).
thf(5894,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5893:[bind(A,$thf( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) ))]]) ).
thf(10130,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)],[1061,835]) ).
thf(10131,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)],[10130]) ).
thf(10154,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)],[10131]) ).
thf(10179,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oknows ) )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[10154]) ).
thf(17850,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)],[712,835]) ).
thf(17851,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)],[17850]) ).
thf(17878,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)],[17851]) ).
thf(17901,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[17878]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).
thf(700,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)],[140]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( A @ ( B @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff1_0) ).
thf(520,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)],[74]) ).
thf(7205,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)],[351,5886]) ).
thf(7206,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)],[7205]) ).
thf(7235,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)],[7206]) ).
thf(7239,plain,
( ( c_UNIV != c_0 )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[7235]) ).
thf(7248,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)],[393,7239]) ).
thf(7249,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[7248]) ).
thf(7250,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7249:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).
thf(1194,plain,
( ( ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[337,345]) ).
thf(1195,plain,
( ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) ) ),
inference(simp,[status(thm)],[1194]) ).
thf(1198,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Omsg )
| ( ( v_evs3 @ c_Event_Oused )
!= c_OtwayRees_Ootway )
| ( ( v_K @ c_Message_Omsg_OKey )
!= v_evs3 ) ),
inference(simp,[status(thm)],[1195]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OHash ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5__iff1_0) ).
thf(502,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)],[68]) ).
thf(503,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OHash ) ) ),
inference(cnf,[status(esa)],[502]) ).
thf(504,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OHash ) ) ),
inference(lifteq,[status(thm)],[503]) ).
thf(505,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OHash @ A )
= B ),
inference(detectInverse,[status(thm)],[504]) ).
thf(506,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OHash @ sk11 )
= A ),
inference(cnf,[status(esa)],[505]) ).
thf(1474,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OHash @ sk11 )
= A ),
inference(lifteq,[status(thm)],[506]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).
thf(636,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)],[118]) ).
thf(40346,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Finite__Set_OFinites @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[938,34277]) ).
thf(40347,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Finite__Set_OFinites @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
inference(simp,[status(thm)],[40346]) ).
thf(40463,plain,
! [A: $i] :
( ( A != tc_Message_Oagent )
| ( ( A @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
!= c_Event_Obad )
| ( c_Finite__Set_OFinites != c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[40347]) ).
thf(40515,plain,
( ( ( tc_Message_Oagent @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
!= c_Event_Obad )
| ( c_Finite__Set_OFinites != c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[40463]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).
thf(563,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)],[89]) ).
thf(38810,plain,
! [A: $i] :
( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
!= ( A @ ( A @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) @ ( v_evs3 @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[938,34084]) ).
thf(38811,plain,
! [A: $i] :
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) )
!= ( A @ ( A @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) @ ( v_evs3 @ c_in ) ) ) ),
inference(simp,[status(thm)],[38810]) ).
thf(38960,plain,
! [A: $i] :
( ( tc_Message_Oagent != A )
| ( ( A @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) )
!= c_Event_Obad )
| ( c_Message_Oagent_OSpy != v_evs3 ) ),
inference(simp,[status(thm)],[38811]) ).
thf(39021,plain,
( ( ( tc_Message_Oagent @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) )
!= c_Event_Obad )
| ( c_Message_Oagent_OSpy != v_evs3 ) ),
inference(simp,[status(thm)],[38960]) ).
thf(308,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
thf(1102,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)],[308]) ).
thf(911,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OKey ) ),
inference(polarity_switch,[status(thm)],[910]) ).
thf(912,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OKey ) ),
inference(lifteq,[status(thm)],[911]) ).
thf(21347,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_Pow ) @ c_in ) ) )
!= ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
| ( C @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ c_Pow ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21206,452]) ).
thf(21348,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_Pow ) @ c_in ) ) )
!= ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
| ( C @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ c_Pow ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[21347]) ).
thf(21349,plain,
! [A: $i] : ( tc_nat @ tc_set @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ tc_set @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_Pow ) @ c_Pow ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[21348:[bind(A,$thf( F )),bind(B,$thf( tc_nat @ ( tc_nat @ ( F @ c_SetInterval_OatMost ) @ c_Pow ) )),bind(C,$thf( tc_nat @ tc_set ))]]) ).
thf(21513,plain,
! [A: $i] : ( tc_nat @ tc_set @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ tc_set @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_Pow ) @ c_Pow ) @ c_in ) ) ),
inference(simp,[status(thm)],[21349]) ).
thf(166,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( D @ c_Message_Omsg_OAgent @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( D @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( D @ ( 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 @ ( D @ c_Message_Omsg_OAgent @ ( B @ c_Message_Omsg_OAgent @ 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/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_OCrypt__imp__OR1__dest_0) ).
thf(768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( D @ c_Message_Omsg_OAgent @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( D @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( D @ ( 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 @ ( D @ c_Message_Omsg_OAgent @ ( B @ c_Message_Omsg_OAgent @ 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)],[166]) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__analzD__dest_0) ).
thf(827,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)],[189]) ).
thf(290,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/sandbox/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)],[290]) ).
thf(209,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/sandbox/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).
thf(868,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)],[209]) ).
thf(2181,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)],[1773,371]) ).
thf(2182,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)],[2181]) ).
thf(2202,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)],[2182]) ).
thf(2207,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( c_0 != c_OtwayRees_Ootway ) ),
inference(simp,[status(thm)],[2202]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
thf(431,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(17814,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_evs3 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[712,348]) ).
thf(17815,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_evs3 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[17814]) ).
thf(17874,plain,
! [B: $i,A: $i] :
( ( B != tc_Message_Omsg )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( v_evs3 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts ) )
| ( A
!= ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) ) ) ),
inference(simp,[status(thm)],[17815]) ).
thf(17896,plain,
( ( tc_Message_Omsg @ ( c_emptyset @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_insert ) ) )
!= ( v_evs3 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[17874]) ).
thf(921,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OKey )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[920]) ).
thf(922,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OKey )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[921]) ).
thf(20956,plain,
! [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 @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ c_Pow ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[606,452]) ).
thf(20957,plain,
! [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 @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ c_Pow ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[20956]) ).
thf(20958,plain,
! [A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_Pow ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[20957:[bind(A,$thf( D )),bind(B,$thf( tc_nat @ ( D @ c_SetInterval_OlessThan ) )),bind(C,$thf( tc_nat ))]]) ).
thf(21215,plain,
! [A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_Pow ) @ c_in ) ) ),
inference(simp,[status(thm)],[20958]) ).
thf(21542,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_Pow ) @ c_in ) ) )
!= ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
| ( C @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ c_Pow ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21215,452]) ).
thf(21543,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_Pow ) @ c_in ) ) )
!= ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) ) )
| ( C @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ c_Pow ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[21542]) ).
thf(21544,plain,
! [A: $i] : ( tc_nat @ tc_set @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ tc_set @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_Pow ) @ c_Pow ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[21543:[bind(A,$thf( F )),bind(B,$thf( tc_nat @ ( tc_nat @ ( F @ c_SetInterval_OlessThan ) @ c_Pow ) )),bind(C,$thf( tc_nat @ tc_set ))]]) ).
thf(21689,plain,
! [A: $i] : ( tc_nat @ tc_set @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ tc_set @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_Pow ) @ c_Pow ) @ c_in ) ) ),
inference(simp,[status(thm)],[21544]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( B @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).
thf(658,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)],[124]) ).
thf(36586,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[938,34043]) ).
thf(36587,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_UNIV @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
inference(simp,[status(thm)],[36586]) ).
thf(36737,plain,
! [A: $i] :
( ( A != tc_Message_Oagent )
| ( ( A @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
!= c_Event_Obad )
| ( c_UNIV != c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[36587]) ).
thf(36741,plain,
( ( ( tc_Message_Oagent @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
!= c_Event_Obad )
| ( c_UNIV != c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[36737]) ).
thf(4344,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_evs3 ) ),
inference(paramod_ordered,[status(thm)],[2016,371]) ).
thf(4345,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_evs3 ) ),
inference(simp,[status(thm)],[4344]) ).
thf(4381,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( c_emptyset != c_List_Olist_ONil )
| ( c_0 != A )
| ( c_0 != v_evs3 ) ),
inference(simp,[status(thm)],[4345]) ).
thf(4394,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( c_emptyset != c_List_Olist_ONil )
| ( c_0 != v_evs3 ) ),
inference(simp,[status(thm)],[4381]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair__iff2_0) ).
thf(944,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(20979,plain,
! [D: $i,C: $i,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 ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ c_Pow ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12211,452]) ).
thf(20980,plain,
! [D: $i,C: $i,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 ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ c_Pow ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[20979]) ).
thf(20981,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OlessThan ) @ ( A @ c_insert ) ) @ c_Pow ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[20980:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( tc_nat @ ( tc_nat @ ( H @ c_SetInterval_OlessThan ) @ ( E @ c_insert ) ) )),bind(D,$thf( tc_nat ))]]) ).
thf(21227,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OlessThan ) @ ( A @ c_insert ) ) @ c_Pow ) @ c_in ) ) ),
inference(simp,[status(thm)],[20981]) ).
thf(21419,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_Pow ) @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21206,835]) ).
thf(21420,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_Pow ) @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[21419]) ).
thf(21471,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ tc_set )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Finite__Set_OFinites )
| ( ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_Pow ) )
!= B ) ),
inference(simp,[status(thm)],[21420]) ).
thf(21512,plain,
( ( ( tc_nat @ tc_set @ tc_set )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Finite__Set_OFinites ) ),
inference(simp,[status(thm)],[21471]) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
thf(487,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)],[62]) ).
thf(161,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).
thf(754,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)],[161]) ).
thf(552,plain,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(polarity_switch,[status(thm)],[551]) ).
thf(553,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
inference(lifteq,[status(thm)],[552]) ).
thf(194,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/sandbox/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).
thf(836,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)],[194]) ).
thf(27770,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[949,346]) ).
thf(27771,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
inference(simp,[status(thm)],[27770]) ).
thf(27813,plain,
! [C: $i,B: $i,A: $i] :
( ( C != tc_Message_Oagent )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_Event_Obad )
| ( A != v_A ) ),
inference(simp,[status(thm)],[27771]) ).
thf(27838,plain,
! [A: $i] :
( ( tc_Message_Oagent @ ( A @ ( v_A @ c_insert ) ) )
!= c_Event_Obad ),
inference(simp,[status(thm)],[27813]) ).
thf(40658,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[938,35063]) ).
thf(40659,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
inference(simp,[status(thm)],[40658]) ).
thf(40803,plain,
! [A: $i] :
( ( A != tc_Message_Oagent )
| ( ( A @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
!= c_Event_Obad )
| ( c_emptyset != c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[40659]) ).
thf(40886,plain,
( ( ( tc_Message_Oagent @ ( c_emptyset @ ( c_Wellfounded__Relations_Oless__than @ c_insert ) ) )
!= c_Event_Obad )
| ( c_emptyset != c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[40803]) ).
thf(489,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)],[488]) ).
thf(490,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)],[489]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).
thf(675,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)],[129]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).
thf(426,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(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).
thf(663,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)],[125]) ).
thf(547,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)],[546]) ).
thf(548,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)],[547]) ).
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(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).
thf(749,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)],[159]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).
thf(939,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(1318,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)],[460,467]) ).
thf(1319,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)],[1318]) ).
thf(1334,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)],[1319]) ).
thf(1340,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= c_UNIV ),
inference(simp,[status(thm)],[1334]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
thf(968,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(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
thf(823,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)],[187]) ).
thf(136,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/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3__iff1_0) ).
thf(691,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)],[136]) ).
thf(692,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
inference(cnf,[status(esa)],[691]) ).
thf(693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
inference(lifteq,[status(thm)],[692]) ).
thf(694,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Event_Oevent_ONotes ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[693]) ).
thf(695,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) @ ( B @ sk21 ) )
= A ),
inference(cnf,[status(esa)],[694]) ).
thf(17768,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) @ ( B @ sk21 ) )
= A ),
inference(lifteq,[status(thm)],[695]) ).
thf(524,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONumber )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[523]) ).
thf(525,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONumber )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[524]) ).
thf(292,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/sandbox/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)],[292]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(705,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)],[142]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).
thf(707,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)],[143]) ).
thf(1240,plain,
! [A: $i] :
( ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_A @ c_Message_Omsg_OAgent @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_A @ c_Message_Omsg_OAgent @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_Aaa @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[334,835]) ).
thf(1241,plain,
! [A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_A @ c_Message_Omsg_OAgent @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_A @ c_Message_Omsg_OAgent @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_Aaa @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1240]) ).
thf(1248,plain,
! [A: $i] :
( ( tc_Message_Omsg != tc_Event_Oevent )
| ( ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) )
!= ( c_emptyset @ c_Message_Oparts ) )
| ( ( v_A @ c_Message_Omsg_OAgent @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_A @ c_Message_Omsg_OAgent @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_Aaa @ c_Event_Oevent_OSays ) ) )
!= A ) ),
inference(simp,[status(thm)],[1241]) ).
thf(1252,plain,
( ( tc_Message_Omsg != tc_Event_Oevent )
| ( ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) )
!= ( c_emptyset @ c_Message_Oparts ) ) ),
inference(simp,[status(thm)],[1248]) ).
thf(154,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(739,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(306,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
thf(1098,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)],[306]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__6__iff1_0) ).
thf(991,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(992,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)],[991]) ).
thf(993,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[992]) ).
thf(9251,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)],[393,9248]) ).
thf(9252,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[9251]) ).
thf(9253,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[9252:[bind(A,$thf( c_emptyset ))]]) ).
thf(12070,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)],[685,418]) ).
thf(12071,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)],[12070]) ).
thf(12072,plain,
! [B: $i,A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ ( c_emptyset @ ( B @ c_insert ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[12071:[bind(A,$thf( A )),bind(B,$thf( c_emptyset )),bind(C,$thf( A ))]]) ).
thf(12174,plain,
! [B: $i,A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ ( c_emptyset @ ( B @ c_insert ) ) @ c_in ) ) ),
inference(simp,[status(thm)],[12072]) ).
thf(4573,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)],[842,1146]) ).
thf(4574,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)],[4573]) ).
thf(4626,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)],[4574]) ).
thf(4641,plain,
! [A: $i] :
( ( A @ c_Event_Oused )
!= c_emptyset ),
inference(simp,[status(thm)],[4626]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).
thf(673,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)],[128]) ).
thf(1183,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)],[938,467]) ).
thf(1184,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)],[1183]) ).
thf(1188,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)],[1184]) ).
thf(196,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).
thf(840,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)],[196]) ).
thf(14,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).
thf(359,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(321,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
| ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).
thf(1130,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)],[321]) ).
thf(277,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).
thf(1038,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)],[277]) ).
thf(20976,plain,
! [D: $i,C: $i,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 ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ c_Pow ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12196,452]) ).
thf(20977,plain,
! [D: $i,C: $i,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 ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ c_Pow ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[20976]) ).
thf(20978,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OatMost ) @ ( A @ c_insert ) ) @ c_Pow ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[20977:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( tc_nat @ ( tc_nat @ ( H @ c_SetInterval_OatMost ) @ ( E @ c_insert ) ) )),bind(D,$thf( tc_nat ))]]) ).
thf(21225,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OatMost ) @ ( A @ c_insert ) ) @ c_Pow ) @ c_in ) ) ),
inference(simp,[status(thm)],[20978]) ).
thf(421,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)],[420]) ).
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(lifteq,[status(thm)],[421]) ).
thf(423,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)],[422]) ).
thf(424,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( B @ sk4 ) ) ) )
= A ),
inference(cnf,[status(esa)],[423]) ).
thf(13149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( B @ sk4 ) ) ) )
= A ),
inference(lifteq,[status(thm)],[424]) ).
thf(1300,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)],[1157,835]) ).
thf(1301,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)],[1300]) ).
thf(1312,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)],[1301]) ).
thf(1317,plain,
( ( tc_nat != tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Message_OsymKeys ) ),
inference(simp,[status(thm)],[1312]) ).
thf(41516,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[938,35064]) ).
thf(41517,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
inference(simp,[status(thm)],[41516]) ).
thf(41658,plain,
! [A: $i] :
( ( A != tc_Message_Oagent )
| ( ( A @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= c_Event_Obad )
| ( c_Wellfounded__Relations_Oless__than != c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[41517]) ).
thf(41735,plain,
( ( ( tc_Message_Oagent @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= c_Event_Obad )
| ( c_Wellfounded__Relations_Oless__than != c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[41658]) ).
thf(8456,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)],[440,467]) ).
thf(8457,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)],[8456]) ).
thf(8516,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)],[8457]) ).
thf(8528,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[8516]) ).
thf(300,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/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair__iff1_1) ).
thf(1085,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)],[300]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff__iff2_0) ).
thf(544,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)],[82]) ).
thf(224,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
thf(907,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)],[224]) ).
thf(5947,plain,
! [A: $i] :
( ( A
!= ( v_evs3 @ c_Event_Oused ) )
| ( c_0 != c_0 )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,5323]) ).
thf(5948,plain,
! [A: $i] :
( ( A
!= ( v_evs3 @ c_Event_Oused ) )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5947]) ).
thf(5949,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( v_evs3 @ c_Event_Oused @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5948:[bind(A,$thf( v_evs3 @ c_Event_Oused ))]]) ).
thf(271,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/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff1_0) ).
thf(1023,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)],[271]) ).
thf(110,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).
thf(613,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)],[110]) ).
thf(105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).
thf(600,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)],[105]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
thf(864,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)],[207]) ).
thf(151,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/sandbox/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff__iff2_0) ).
thf(727,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)],[151]) ).
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/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
thf(1008,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(103,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff2_0) ).
thf(595,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)],[103]) ).
thf(611,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONumber ) ),
inference(polarity_switch,[status(thm)],[610]) ).
thf(612,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONumber ) ),
inference(lifteq,[status(thm)],[611]) ).
thf(719,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Oagent_OFriend )
!= ( B @ c_Message_Oagent_OFriend ) ) ),
inference(cnf,[status(esa)],[718]) ).
thf(720,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Oagent_OFriend )
!= ( B @ c_Message_Oagent_OFriend ) ) ),
inference(lifteq,[status(thm)],[719]) ).
thf(721,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Oagent_OFriend @ A )
= B ),
inference(detectInverse,[status(thm)],[720]) ).
thf(722,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend @ sk22 )
= A ),
inference(cnf,[status(esa)],[721]) ).
thf(1485,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend @ sk22 )
= A ),
inference(lifteq,[status(thm)],[722]) ).
thf(283,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/sandbox/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)],[283]) ).
thf(304,axiom,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__4__iff1_0) ).
thf(1094,plain,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).
thf(1140,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)],[325]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(446,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)],[46]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).
thf(571,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)],[93]) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3__iff1_1) ).
thf(497,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)],[67]) ).
thf(17064,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_evs3 @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( B @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16491,1448]) ).
thf(17065,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_evs3 @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( B @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[17064]) ).
thf(17157,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ tc_prod ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) ) )
| ( c_Wellfounded__Relations_Oless__than != c_Wellfounded__Relations_Oless__than )
| ( ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) )
!= ( tc_nat @ ( tc_nat @ ( c_0 @ ( B @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[17065]) ).
thf(17172,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) @ ( c_0 @ c_Pair ) ) ) )
!= ( tc_nat @ ( tc_nat @ ( c_0 @ ( B @ c_Pair ) ) ) ) ),
inference(simp,[status(thm)],[17157]) ).
thf(24241,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) ) )
| ( ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) )
!= ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[746,17172]) ).
thf(24355,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) ) )
| ( tc_nat != tc_nat )
| ( tc_nat != tc_nat )
| ( c_0 != c_0 )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[24241]) ).
thf(24380,plain,
! [B: $i,A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) ) ),
inference(simp,[status(thm)],[24355]) ).
thf(24891,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) )
!= c_0 ),
inference(rewrite,[status(thm)],[24380,746]) ).
thf(10020,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)],[351,6331]) ).
thf(10021,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)],[10020]) ).
thf(10050,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_UNIV != c_0 )
| ( c_0 != c_Event_Obad ) ),
inference(simp,[status(thm)],[10021]) ).
thf(10054,plain,
( ( c_UNIV != c_0 )
| ( c_0 != c_Event_Obad ) ),
inference(simp,[status(thm)],[10050]) ).
thf(10311,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)],[393,10054]) ).
thf(10312,plain,
! [A: $i] :
( ( c_UNIV != c_0 )
| ( A != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[10311:[]]) ).
thf(10332,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Event_Obad @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[10312]) ).
thf(4252,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)],[863,835]) ).
thf(4253,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)],[4252]) ).
thf(4276,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)],[4253]) ).
thf(4289,plain,
! [A: $i] :
( ( A @ c_Message_Osynth )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[4276]) ).
thf(1175,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)],[938,346]) ).
thf(1176,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)],[1175]) ).
thf(1178,plain,
( ( tc_Message_Oagent != tc_Message_Oagent )
| ( c_Event_Obad != c_Event_Obad )
| ( c_Message_Oagent_OSpy != v_A ) ),
inference(simp,[status(thm)],[1176]) ).
thf(1180,plain,
c_Message_Oagent_OSpy != v_A,
inference(simp,[status(thm)],[1178]) ).
thf(482,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(cnf,[status(esa)],[481]) ).
thf(5534,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( ( v_evs3 @ c_Event_Oused )
!= c_0 )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,5323]) ).
thf(5535,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( ( v_evs3 @ c_Event_Oused )
!= c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[5534]) ).
thf(5536,plain,
( ( ( v_evs3 @ c_Event_Oused )
!= c_0 )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5535:[bind(A,$thf( c_UNIV ))]]) ).
thf(66,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/sandbox/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff__iff1_0) ).
thf(495,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)],[66]) ).
thf(2213,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)],[390,2204]) ).
thf(2214,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( A != c_OtwayRees_Ootway )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[2213:[]]) ).
thf(2215,plain,
( ( c_emptyset != c_0 )
| ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[2214]) ).
thf(218,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/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).
thf(891,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)],[218]) ).
thf(319,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/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).
thf(1126,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)],[319]) ).
thf(311,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/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).
thf(1108,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)],[311]) ).
thf(844,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(polarity_switch,[status(thm)],[843]) ).
thf(845,plain,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
inference(lifteq,[status(thm)],[844]) ).
thf(1298,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)],[1157,346]) ).
thf(1299,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)],[1298]) ).
thf(1316,plain,
! [A: $i] :
( ( tc_nat != tc_Message_Oagent )
| ( c_Message_OsymKeys != c_Event_Obad )
| ( ( A @ c_Public_OshrK )
!= v_A ) ),
inference(simp,[status(thm)],[1299]) ).
thf(449,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(cnf,[status(esa)],[448]) ).
thf(450,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(lifteq,[status(thm)],[449]) ).
thf(299,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/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__into__used_0) ).
thf(1084,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)],[299]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
thf(976,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(135,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).
thf(688,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)],[135]) ).
thf(222,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
thf(903,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)],[222]) ).
thf(1185,plain,
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
!= ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[337,467]) ).
thf(1186,plain,
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
!= ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) ) ),
inference(simp,[status(thm)],[1185]) ).
thf(1189,plain,
( ( ( tc_nat @ tc_set )
!= ( tc_Event_Oevent @ tc_List_Olist ) )
| ( c_Finite__Set_OFinites != c_OtwayRees_Ootway )
| ( c_UNIV != v_evs3 ) ),
inference(simp,[status(thm)],[1186]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth__synthD__dest_0) ).
thf(1010,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(1369,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)],[606,467]) ).
thf(1370,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)],[1369]) ).
thf(1383,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)],[1370]) ).
thf(1390,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
!= c_UNIV ),
inference(simp,[status(thm)],[1383]) ).
thf(6336,plain,
! [B: $i,A: $i] :
( ( c_0 != c_0 )
| ( ( B @ tc_set )
!= tc_nat )
| ( A != c_OtwayRees_Ootway )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,2207]) ).
thf(6337,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( A != c_OtwayRees_Ootway )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6336:[]]) ).
thf(6743,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ~ ( tc_nat @ ( c_0 @ ( c_OtwayRees_Ootway @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[6337]) ).
thf(812,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(polarity_switch,[status(thm)],[811]) ).
thf(813,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(lifteq,[status(thm)],[812]) ).
thf(73,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).
thf(517,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)],[73]) ).
thf(1800,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)],[390,494]) ).
thf(1801,plain,
! [A: $i] :
( ( A @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1800:[bind(A,$thf( c_emptyset ))]]) ).
thf(2135,plain,
! [A: $i] :
( ( A @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1801]) ).
thf(288,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
thf(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)],[288]) ).
thf(240,axiom,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OServer ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__2__iff1_0) ).
thf(946,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OServer ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(7839,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)],[353,7838]) ).
thf(7840,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ ( A @ sk3 ) )
= c_List_Olist_ONil ),
inference(pattern_uni,[status(thm)],[7839:[bind(A,$thf( A )),bind(B,$thf( c_List_Olist_ONil )),bind(C,$thf( A ))]]) ).
thf(4693,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)],[390,2207]) ).
thf(4694,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)],[4693:[]]) ).
thf(4705,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[4694]) ).
thf(171,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/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1__iff1_0) ).
thf(781,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)],[171]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_1) ).
thf(928,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(929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(cnf,[status(esa)],[928]) ).
thf(930,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(lifteq,[status(thm)],[929]) ).
thf(931,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Message_Omsg_OCrypt ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[930]) ).
thf(932,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) @ ( A @ sk31 ) )
= B ),
inference(cnf,[status(esa)],[931]) ).
thf(20414,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) @ ( A @ sk31 ) )
= B ),
inference(lifteq,[status(thm)],[932]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
thf(995,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(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).
thf(588,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)],[100]) ).
thf(1242,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)],[938,835]) ).
thf(1243,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)],[1242]) ).
thf(1249,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)],[1243]) ).
thf(1253,plain,
( ( tc_Message_Omsg != tc_Message_Oagent )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Event_Obad ) ),
inference(simp,[status(thm)],[1249]) ).
thf(27742,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[949,806]) ).
thf(27743,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ) ),
inference(simp,[status(thm)],[27742]) ).
thf(27801,plain,
! [C: $i,B: $i,A: $i] :
( ( C != tc_Message_Oagent )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_Event_Obad )
| ( A != c_Message_Oagent_OServer ) ),
inference(simp,[status(thm)],[27743]) ).
thf(27825,plain,
! [A: $i] :
( ( tc_Message_Oagent @ ( A @ ( c_Message_Oagent_OServer @ c_insert ) ) )
!= c_Event_Obad ),
inference(simp,[status(thm)],[27801]) ).
thf(122,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).
thf(652,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)],[122]) ).
thf(172,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/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair__iff1_0) ).
thf(786,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)],[172]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
thf(1030,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)],[274]) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).
thf(763,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)],[164]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Orev ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv__iff1_0) ).
thf(383,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)],[23]) ).
thf(1669,plain,
! [B: $i,A: $i] :
( ( A != c_List_Olist_ONil )
| ( ( B @ ( c_0 @ c_List_Orev ) )
= c_List_Olist_ONil )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,353]) ).
thf(1670,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ c_List_Orev ) )
= c_List_Olist_ONil )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1669:[bind(A,$thf( c_List_Olist_ONil ))]]) ).
thf(2120,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ c_List_Orev ) )
= c_List_Olist_ONil )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1670]) ).
thf(11770,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)],[393,10387]) ).
thf(11771,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[11770]) ).
thf(11772,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[11771:[bind(A,$thf( c_emptyset ))]]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).
thf(549,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)],[84]) ).
thf(91,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).
thf(568,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)],[91]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).
thf(510,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(296,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
thf(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)],[296]) ).
thf(192,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/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OBody__dest_0) ).
thf(832,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)],[192]) ).
thf(436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
inference(cnf,[status(esa)],[435]) ).
thf(437,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
inference(lifteq,[status(thm)],[436]) ).
thf(438,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Event_Oevent_OGets ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[437]) ).
thf(439,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) @ ( B @ sk5 ) )
= A ),
inference(cnf,[status(esa)],[438]) ).
thf(13428,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) @ ( B @ sk5 ) )
= A ),
inference(lifteq,[status(thm)],[439]) ).
thf(322,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/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__2__iff1_0) ).
thf(1133,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)],[322]) ).
thf(4843,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)],[846,835]) ).
thf(4844,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)],[4843]) ).
thf(4871,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)],[4844]) ).
thf(4880,plain,
! [A: $i] :
( ( A @ c_Event_OinitState )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[4871]) ).
thf(447,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)],[446]) ).
thf(17282,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)],[393,16715]) ).
thf(17283,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[17282]) ).
thf(17284,plain,
( ( ( c_emptyset @ c_Message_Oparts )
!= c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[17283:[bind(A,$thf( c_UNIV ))]]) ).
thf(405,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)],[404]) ).
thf(17352,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)],[739,17228]) ).
thf(17353,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)],[17352]) ).
thf(17384,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)],[17353]) ).
thf(17397,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[17384]) ).
thf(41981,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( C @ ( C @ ( c_emptyset @ ( c_Event_Obad @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1097,35113]) ).
thf(41982,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( C @ ( C @ ( c_emptyset @ ( c_Event_Obad @ c_insert ) ) @ ( c_emptyset @ c_in ) ) ) ),
inference(simp,[status(thm)],[41981]) ).
thf(42021,plain,
! [C: $i,B: $i,A: $i] :
( ( B != C )
| ( ( C @ ( c_emptyset @ ( c_Event_Obad @ c_insert ) ) )
!= c_UNIV )
| ( A != c_emptyset ) ),
inference(simp,[status(thm)],[41982]) ).
thf(42092,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_Event_Obad @ c_insert ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[42021]) ).
thf(20998,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ c_Pow ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[425,452]) ).
thf(20999,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) ) )
| ( D @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ ( C @ c_Pow ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[20998]) ).
thf(21000,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_Pow ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[20999:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( tc_nat @ ( F @ ( E @ c_SetInterval_OatLeastAtMost ) ) )),bind(D,$thf( tc_nat ))]]) ).
thf(21167,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_Pow ) @ c_in ) ) ),
inference(simp,[status(thm)],[21000]) ).
thf(432,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)],[431]) ).
thf(6437,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)],[393,2215]) ).
thf(6438,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[6437]) ).
thf(6439,plain,
( ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6438:[bind(A,$thf( c_emptyset ))]]) ).
thf(409,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)],[408]) ).
thf(410,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)],[409]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
thf(950,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(14374,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_emptyset = c_0 )
| ( c_0 @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,14255]) ).
thf(14375,plain,
( ( c_emptyset = c_0 )
| ( c_0 @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[14374:[bind(A,$thf( tc_nat ))]]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(854,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)],[202]) ).
thf(37907,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( v_evs3 @ c_insert ) ) @ ( c_List_Olist_ONil @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[938,34082]) ).
thf(37908,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( v_evs3 @ c_insert ) ) @ ( c_List_Olist_ONil @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
inference(simp,[status(thm)],[37907]) ).
thf(38044,plain,
! [A: $i] :
( ( A != tc_Message_Oagent )
| ( ( A @ ( c_emptyset @ ( v_evs3 @ c_insert ) ) )
!= c_Event_Obad )
| ( c_List_Olist_ONil != c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[37908]) ).
thf(38095,plain,
( ( ( tc_Message_Oagent @ ( c_emptyset @ ( v_evs3 @ c_insert ) ) )
!= c_Event_Obad )
| ( c_List_Olist_ONil != c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[38044]) ).
thf(373,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)],[372]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
= ( C @ ( A @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).
thf(603,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)],[106]) ).
thf(178,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/sandbox/benchmark/theBenchmark.p',cls_Message_OFake__parts__insert__in__Un__dest_0) ).
thf(801,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)],[178]) ).
thf(4231,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)],[863,1146]) ).
thf(4232,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)],[4231]) ).
thf(4271,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)],[4232]) ).
thf(4286,plain,
! [A: $i] :
( ( A @ c_Message_Osynth )
!= c_emptyset ),
inference(simp,[status(thm)],[4271]) ).
thf(285,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/sandbox/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)],[285]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( D @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).
thf(532,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)],[78]) ).
thf(176,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/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff2_0) ).
thf(796,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)],[176]) ).
thf(1308,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1157,345]) ).
thf(1309,plain,
! [A: $i] :
( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(simp,[status(thm)],[1308]) ).
thf(1314,plain,
! [A: $i] :
( ( tc_nat != tc_Message_Omsg )
| ( ( v_evs3 @ c_Event_Oused )
!= c_Message_OsymKeys )
| ( ( A @ c_Public_OshrK )
!= ( v_K @ c_Message_Omsg_OKey ) ) ),
inference(simp,[status(thm)],[1309]) ).
thf(4,negated_conjecture,
tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_B @ ( v_A @ c_Event_Oevent_OSays ) ) @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(341,plain,
tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_B @ ( v_A @ c_Event_Oevent_OSays ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(181,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/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).
thf(807,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)],[181]) ).
thf(1169,plain,
( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) )
!= ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[337,806]) ).
thf(1170,plain,
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) )
!= ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs3 @ c_in ) ) ) ),
inference(simp,[status(thm)],[1169]) ).
thf(1172,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Oagent )
| ( c_OtwayRees_Ootway != c_Event_Obad )
| ( c_Message_Oagent_OServer != v_evs3 ) ),
inference(simp,[status(thm)],[1170]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
thf(897,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)],[220]) ).
thf(766,plain,
! [A: $i] :
( c_Message_Oagent_OServer
!= ( A @ c_Message_Oagent_OFriend ) ),
inference(polarity_switch,[status(thm)],[765]) ).
thf(767,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OServer ),
inference(lifteq,[status(thm)],[766]) ).
thf(12233,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)],[12196,467]) ).
thf(12234,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)],[12233]) ).
thf(12324,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)],[12234]) ).
thf(12352,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_SetInterval_OatMost ) @ ( A @ c_insert ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[12324]) ).
thf(275,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).
thf(1033,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(1285,plain,
! [A: $i] :
( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[685,345]) ).
thf(1286,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(simp,[status(thm)],[1285]) ).
thf(1288,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_Message_Omsg )
| ( ( v_evs3 @ c_Event_Oused )
!= c_Finite__Set_OFinites )
| ( ( v_K @ c_Message_Omsg_OKey )
!= c_emptyset ) ),
inference(simp,[status(thm)],[1286]) ).
thf(1192,plain,
( ( ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[938,345]) ).
thf(1193,plain,
( ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
inference(simp,[status(thm)],[1192]) ).
thf(1197,plain,
( ( tc_Message_Omsg != tc_Message_Oagent )
| ( ( v_evs3 @ c_Event_Oused )
!= c_Event_Obad )
| ( ( v_K @ c_Message_Omsg_OKey )
!= c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[1193]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
thf(960,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(216,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
thf(886,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)],[216]) ).
thf(155,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).
thf(740,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)],[155]) ).
thf(95,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).
thf(575,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)],[95]) ).
thf(4360,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != v_evs3 )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,2016]) ).
thf(4361,plain,
! [A: $i] :
( ( A != v_evs3 )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[4360:[]]) ).
thf(4382,plain,
( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( v_evs3 @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[4361]) ).
thf(269,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/sandbox/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).
thf(1019,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)],[269]) ).
thf(527,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)],[526]) ).
thf(528,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)],[527]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0) ).
thf(982,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(37594,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( C @ ( C @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1097,34045]) ).
thf(37595,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( C @ ( C @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) ) ),
inference(simp,[status(thm)],[37594]) ).
thf(37640,plain,
! [C: $i,B: $i,A: $i] :
( ( B != C )
| ( ( C @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
!= c_UNIV )
| ( A != c_Wellfounded__Relations_Oless__than ) ),
inference(simp,[status(thm)],[37595]) ).
thf(37684,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[37640]) ).
thf(10493,plain,
( ( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs3 @ 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)],[2056,1477]) ).
thf(10494,plain,
( ( ( tc_nat @ ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[10493]) ).
thf(10534,plain,
( ( tc_nat != tc_nat )
| ( ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) )
!= c_0 )
| ( c_0 != c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[10494]) ).
thf(10554,plain,
( ( ( tc_Event_Oevent @ ( v_evs3 @ c_List_Oset ) )
!= c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[10534]) ).
thf(330,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
thf(1152,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)],[330]) ).
thf(427,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)],[426]) ).
thf(368,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)],[367]) ).
thf(369,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)],[368]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff1_0) ).
thf(607,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)],[108]) ).
thf(486,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(cnf,[status(esa)],[485]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
thf(803,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)],[179]) ).
thf(231,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Oset ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).
thf(923,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(16517,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[393,16496]) ).
thf(16518,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[16517]) ).
thf(16519,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[16518:[bind(A,$thf( E @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) )),bind(B,$thf( E ))]]) ).
thf(16549,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ tc_List_Olist @ ( v_evs3 @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[16519]) ).
thf(17832,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[712,345]) ).
thf(17833,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_evs3 @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(simp,[status(thm)],[17832]) ).
thf(17871,plain,
! [B: $i,A: $i] :
( ( B != tc_Message_Omsg )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( v_evs3 @ c_Event_Oused ) )
| ( A
!= ( v_K @ c_Message_Omsg_OKey ) ) ),
inference(simp,[status(thm)],[17833]) ).
thf(17893,plain,
( ( tc_Message_Omsg @ ( c_emptyset @ ( v_K @ c_Message_Omsg_OKey @ c_insert ) ) )
!= ( v_evs3 @ c_Event_Oused ) ),
inference(simp,[status(thm)],[17871]) ).
thf(37522,plain,
! [A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[938,34045]) ).
thf(37523,plain,
! [A: $i] :
( ( A @ ( A @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) ) ),
inference(simp,[status(thm)],[37522]) ).
thf(37624,plain,
! [A: $i] :
( ( A != tc_Message_Oagent )
| ( ( A @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
!= c_Event_Obad )
| ( c_Wellfounded__Relations_Oless__than != c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[37523]) ).
thf(37751,plain,
( ( ( tc_Message_Oagent @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
!= c_Event_Obad )
| ( c_Wellfounded__Relations_Oless__than != c_Message_Oagent_OSpy ) ),
inference(simp,[status(thm)],[37624]) ).
thf(268,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OAgent ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1__iff1_0) ).
thf(1014,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)],[268]) ).
thf(1015,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OAgent ) ) ),
inference(cnf,[status(esa)],[1014]) ).
thf(1016,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OAgent ) ) ),
inference(lifteq,[status(thm)],[1015]) ).
thf(1017,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OAgent @ A )
= B ),
inference(detectInverse,[status(thm)],[1016]) ).
thf(1018,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OAgent @ sk36 )
= A ),
inference(cnf,[status(esa)],[1017]) ).
thf(1490,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OAgent @ sk36 )
= A ),
inference(lifteq,[status(thm)],[1018]) ).
thf(4312,plain,
! [A: $i] :
( ( A != tc_nat )
| ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[390,1600]) ).
thf(4313,plain,
( ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[4312:[bind(A,$thf( tc_nat ))]]) ).
thf(560,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[559]) ).
thf(8112,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)],[393,8104]) ).
thf(8113,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( A != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[8112:[]]) ).
thf(8130,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Event_Obad @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[8113]) ).
thf(119,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).
thf(639,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)],[119]) ).
thf(301,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/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).
thf(1088,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)],[301]) ).
thf(496,plain,
! [A: $i] :
( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) ) ),
inference(cnf,[status(esa)],[495]) ).
thf(454,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(cnf,[status(esa)],[453]) ).
thf(498,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
inference(cnf,[status(esa)],[497]) ).
thf(499,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
inference(lifteq,[status(thm)],[498]) ).
thf(500,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Event_Oevent_ONotes ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[499]) ).
thf(501,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) @ ( A @ sk10 ) )
= B ),
inference(cnf,[status(esa)],[500]) ).
thf(14102,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) @ ( A @ sk10 ) )
= B ),
inference(lifteq,[status(thm)],[501]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
thf(972,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(47149,plain,
$false,
inference(e,[status(thm)],[809,347,17903,941,25580,1110,20668,846,909,628,962,468,4877,1295,481,352,24627,683,1068,12172,27828,1073,40884,1486,10387,408,523,582,12949,1158,994,4391,26400,7198,873,1142,379,878,440,597,19964,715,814,698,340,670,472,34082,6241,747,913,16491,1001,417,885,20488,21203,1366,1518,829,404,42117,4948,570,1430,372,20866,838,344,357,949,1055,724,6034,7696,917,702,751,8654,1313,542,460,17894,1147,5127,870,770,416,1115,1773,448,1362,1100,559,17694,606,5323,1489,475,34045,789,443,1040,623,34084,36777,806,353,821,6840,756,5027,34277,17899,376,485,1136,834,5946,6300,39025,17398,514,348,574,905,480,6591,397,5773,734,866,453,396,998,411,1600,1104,507,27697,7004,1119,774,4643,428,2154,7760,1863,1074,452,920,380,512,2204,678,529,7393,761,17242,546,793,381,26658,1047,1163,910,894,1021,1042,6264,1255,561,1487,407,21030,729,17902,334,27827,746,12561,825,16059,862,349,467,665,461,1079,842,974,1106,847,566,484,21206,1602,852,435,38104,8736,583,12196,830,17891,493,551,1128,8104,1291,710,41712,27304,1012,5285,13981,697,6801,17232,615,1121,1064,725,388,610,420,17898,989,12211,742,17225,980,403,7838,1425,1138,356,471,8017,339,6661,686,526,16715,590,1160,9186,1028,1082,488,5031,17890,1292,933,554,753,17895,537,1612,38982,970,622,393,12955,17170,1150,6331,984,20666,39539,8732,17228,1002,1429,2052,10180,371,1060,1050,457,1434,938,765,1035,1071,1026,21214,953,2203,20451,633,360,17482,805,17731,6716,657,794,586,18544,718,888,926,12173,12628,965,618,425,5762,8290,39480,856,745,16496,1146,430,5720,17405,5933,402,843,772,2016,5876,958,1488,413,584,1154,875,577,1124,6774,391,17905,713,335,35063,7062,10505,540,1428,34043,13459,21186,34275,1058,466,1092,6636,1090,350,9248,979,2079,681,1117,419,1048,17418,863,900,406,362,451,880,649,1043,434,494,631,1339,20001,594,799,1149,915,27834,1061,1112,811,387,345,858,367,5894,816,10179,17901,483,700,520,943,7250,6589,1198,399,1474,636,455,40515,394,563,39021,1477,1364,6325,1102,912,685,21513,768,827,1066,868,2207,431,17896,922,14255,21689,12192,658,36741,4394,21215,944,21227,374,21512,487,1145,35113,754,553,836,27838,473,40886,490,675,426,5886,663,548,1081,749,939,1340,968,823,17768,776,525,1070,705,707,1252,739,1098,993,712,1003,9253,6399,414,12174,1368,4641,673,791,1188,441,840,359,1130,1038,370,21225,502,463,13149,1317,41735,8528,338,1085,470,544,907,2056,5949,336,1023,613,600,864,1427,727,1008,595,612,991,1485,1052,386,1094,978,1140,446,571,497,24891,10332,4289,1180,482,5536,1157,495,2215,891,1126,1108,7239,845,1316,450,1084,976,688,903,1448,1189,1010,1390,6743,813,517,6489,2135,20785,1062,946,7840,390,11847,4705,781,20414,995,588,1253,27825,652,351,418,786,1030,35064,7747,763,383,2120,346,11772,549,1045,568,12181,433,4214,510,1077,478,832,13428,1133,4880,447,17284,405,422,17397,42092,21167,620,432,6439,410,967,950,1097,835,14375,854,10054,38095,373,603,801,4286,437,1056,532,696,796,1363,1314,6169,341,358,807,1172,897,767,12352,1033,1288,1197,960,1473,886,928,740,575,860,4382,1019,528,644,982,691,37684,17172,10554,1152,427,723,4410,369,607,486,803,337,354,923,16549,17893,37751,364,469,1367,1490,4313,560,8130,639,491,1088,592,1468,496,454,14102,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV299-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.14 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.27/0.50 % Computer : n007.cluster.edu
% 0.27/0.50 % Model : x86_64 x86_64
% 0.27/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.50 % Memory : 8046.5625MB
% 0.27/0.50 % OS : Linux 6.8.0-71-generic
% 0.27/0.50 % CPULimit : 300
% 0.27/0.50 % WCLimit : 300
% 0.27/0.50 % DateTime : Sat Sep 26 13:27:39 UTC 2026
% 0.27/0.50 % CPUTime :
% 0.27/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.16/1.13 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.14/1.64 % [INFO] Parsing done (503ms).
% 3.14/1.65 % [INFO] Running in sequential loop mode.
% 4.42/2.15 % [INFO] eprover registered as external prover.
% 4.42/2.15 % [INFO] Scanning for conjecture ...
% 5.14/2.39 % [INFO] Found a conjecture (or negated_conjecture) and 1474 axioms. Running axiom selection ...
% 6.54/2.63 % [INFO] Axiom selection finished. Selected 325 axioms (removed 1149 axioms).
% 7.52/2.83 % [INFO] Problem is propositional (TPTP CNF).
% 7.52/2.86 % [INFO] Type checking passed.
% 7.52/2.86 % [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 ...
% 157.25/39.46 % External prover 'e' found a proof!
% 157.25/39.46 % [INFO] Killing All external provers ...
% 157.25/39.46 % Time passed: 38804ms (effective reasoning time: 37805ms)
% 157.25/39.47 % Axioms used in derivation (325): 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_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_OtwayRees_Ounique__NA__dest_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_OtwayRees_OCrypt__imp__OR1__dest_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_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_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_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
% 157.25/39.47 % No. of inferences in proof: 1689
% 157.25/39.47 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 38804 ms resp. 37805 ms w/o parsing
% 161.48/40.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 161.48/40.14 % [INFO] Killing All external provers ...
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