%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV293-1 : 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 : n013.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 08:58:47 AM UTC 2026
% Result : Unsatisfiable 257.80s 68.98s
% Output : Refutation 260.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 331
% Syntax : Number of formulae : 1057 ( 362 unt; 0 typ; 9 def)
% Number of atoms : 2225 (1014 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 11165 (1239 ~; 923 |; 0 &;9003 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 136 ( 133 usr; 22 con; 0-6 aty)
% Number of variables : 2670 ( 0 ^;2652 !; 9 ?;2670 :)
% ( 0 !>; 0 ?*; 0 @-; 9 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_Event_Oevent_OGets_decl,type,
c_Event_Oevent_OGets: $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(v_NA_decl,type,
v_NA: $i ).
thf(c_Message_Omsg_OAgent_decl,type,
c_Message_Omsg_OAgent: $i > $i ).
thf(v_A_decl,type,
v_A: $i ).
thf(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_evs_decl,type,
v_evs: $i ).
thf(tc_Event_Oevent_decl,type,
tc_Event_Oevent: $i ).
thf(c_Event_Obad_decl,type,
c_Event_Obad: $i ).
thf(tc_Message_Oagent_decl,type,
tc_Message_Oagent: $i ).
thf(c_OtwayRees_Ootway_decl,type,
c_OtwayRees_Ootway: $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(c_Event_Oevent_OSays_decl,type,
c_Event_Oevent_OSays: $i > $i > $i > $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_Message_OHPair_decl,type,
c_Message_OHPair: $i > $i > $i ).
thf(c_Message_Omsg_ONumber_decl,type,
c_Message_Omsg_ONumber: $i > $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(c_Datatype__Universe_OIn1_decl,type,
c_Datatype__Universe_OIn1: $i > $i > $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_Message_Omsg_ONonce_decl,type,
c_Message_Omsg_ONonce: $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_Message_Osynth_decl,type,
c_Message_Osynth: $i > $i ).
thf(tc_Message_Omsg_decl,type,
tc_Message_Omsg: $i ).
thf(c_Message_Omsg_OHash_decl,type,
c_Message_Omsg_OHash: $i > $i ).
thf(c_Message_Oparts_decl,type,
c_Message_Oparts: $i > $i ).
thf(c_Message_Oanalz_decl,type,
c_Message_Oanalz: $i > $i ).
thf(c_SetInterval_OatLeastLessThan_decl,type,
c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_Message_Omsg_OKey_decl,type,
c_Message_Omsg_OKey: $i > $i ).
thf(c_Public_OpublicKey_decl,type,
c_Public_OpublicKey: $i > $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_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_SetInterval_OatMost_decl,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(c_Message_Oagent_OServer_decl,type,
c_Message_Oagent_OServer: $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_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_Event_OinitState_decl,type,
c_Event_OinitState: $i > $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_Event_Oused_decl,type,
c_Event_Oused: $i > $i ).
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_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_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_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_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 ).
thf(sk4_decl,type,
sk4: $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i ).
thf(sk28_decl,type,
sk28: $i > $i ).
thf(sk34_decl,type,
sk34: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_ONonce @ A )
= B ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_ONumber @ A )
= B ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_List_Orev ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OKey @ A )
= B ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OHash @ A )
= B ) ) ) ).
thf(sk28_def,definition,
( sk28
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Public_OshrK @ A )
= B ) ) ) ).
thf(sk34_def,definition,
( sk34
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OAgent @ A )
= B ) ) ) ).
thf(194,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(809,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)],[194]) ).
thf(123,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(629,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)],[123]) ).
thf(19,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(364,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)],[19]) ).
thf(365,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)],[364]) ).
thf(175,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(760,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)],[175]) ).
thf(26,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(386,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(387,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(cnf,[status(esa)],[386]) ).
thf(388,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( A = c_0 ) ),
inference(lifteq,[status(thm)],[387]) ).
thf(245,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(936,plain,
tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(1632,plain,
! [A: $i] :
( ( A != c_Message_Oagent_OSpy )
| ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_0 @ c_in ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,936]) ).
thf(1633,plain,
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_0 @ c_in ) ) )
| ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1632:[bind(A,$thf( c_Message_Oagent_OSpy ))]]) ).
thf(14,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(347,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)],[14]) ).
thf(248,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(941,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)],[248]) ).
thf(136,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(666,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)],[136]) ).
thf(296,axiom,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(1058,plain,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(2,negated_conjecture,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(324,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(327,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[324]) ).
thf(1299,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1058,327]) ).
thf(1300,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1299]) ).
thf(1307,plain,
! [B: $i,A: $i] :
( ( B != tc_Message_Oagent )
| ( c_UNIV != c_Event_Obad )
| ( A != v_A ) ),
inference(simp,[status(thm)],[1300]) ).
thf(1313,plain,
c_UNIV != c_Event_Obad,
inference(simp,[status(thm)],[1307]) ).
thf(1490,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != c_Event_Obad )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,1313]) ).
thf(1491,plain,
( ( c_0 != c_Event_Obad )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1490:[bind(A,$thf( c_UNIV ))]]) ).
thf(33,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(408,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(409,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[408]) ).
thf(1950,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 != c_Event_Obad ) ),
inference(paramod_ordered,[status(thm)],[1491,409]) ).
thf(1951,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ( c_0 != c_Event_Obad ) ),
inference(simp,[status(thm)],[1950]) ).
thf(1952,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_UNIV != A )
| ( c_0 != A )
| ( c_0 != c_Event_Obad ) ),
inference(simp,[status(thm)],[1951]) ).
thf(1956,plain,
( ( c_UNIV != c_0 )
| ( c_0 != c_Event_Obad ) ),
inference(simp,[status(thm)],[1952]) ).
thf(62,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(479,plain,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(317,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
thf(1104,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(1105,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[1104]) ).
thf(236,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(909,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)],[236]) ).
thf(283,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(1029,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(1030,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) ) ),
inference(polarity_switch,[status(thm)],[1029]) ).
thf(1031,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) ) ),
inference(lifteq,[status(thm)],[1030]) ).
thf(7,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(332,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(333,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
= c_List_Olist_ONil ),
inference(lifteq,[status(thm)],[332]) ).
thf(122,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(628,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)],[122]) ).
thf(230,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(893,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)],[230]) ).
thf(47,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(441,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)],[47]) ).
thf(61,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(477,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(478,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[477]) ).
thf(7098,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)],[441,478]) ).
thf(7099,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)],[7098]) ).
thf(7131,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)],[7099]) ).
thf(7143,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[7131]) ).
thf(308,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(1083,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)],[308]) ).
thf(257,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(962,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)],[257]) ).
thf(180,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(776,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(777,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
= c_0 ),
inference(lifteq,[status(thm)],[776]) ).
thf(91,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(555,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)],[91]) ).
thf(63,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(480,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)],[63]) ).
thf(481,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)],[480]) ).
thf(15,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(352,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)],[15]) ).
thf(150,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(706,plain,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(204,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(837,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(838,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[837]) ).
thf(1190,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)],[706,838]) ).
thf(1191,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)],[1190]) ).
thf(1200,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_Message_Oagent )
| ( c_Finite__Set_OFinites != c_Event_Obad )
| ( c_Message_Oagent_OServer != c_emptyset ) ),
inference(simp,[status(thm)],[1191]) ).
thf(57,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(463,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)],[57]) ).
thf(54,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(454,plain,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(455,plain,
! [A: $i] :
~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[454]) ).
thf(1277,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)],[463,455]) ).
thf(1278,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)],[1277]) ).
thf(1284,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)],[1278]) ).
thf(1290,plain,
( ( ( tc_nat @ tc_set )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Finite__Set_OFinites ) ),
inference(simp,[status(thm)],[1284]) ).
thf(269,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(994,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)],[269]) ).
thf(167,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(741,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)],[167]) ).
thf(51,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(449,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)],[51]) ).
thf(3,negated_conjecture,
tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(325,plain,
tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1344,plain,
! [B: $i,A: $i] :
( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[325,1105]) ).
thf(1345,plain,
! [B: $i,A: $i] :
( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1344]) ).
thf(1366,plain,
! [B: $i,A: $i] :
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= B )
| ( c_emptyset != c_OtwayRees_Ootway )
| ( v_evs != A ) ),
inference(simp,[status(thm)],[1345]) ).
thf(1374,plain,
c_emptyset != c_OtwayRees_Ootway,
inference(simp,[status(thm)],[1366]) ).
thf(1622,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != c_OtwayRees_Ootway )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,1374]) ).
thf(1623,plain,
( ( c_0 != c_OtwayRees_Ootway )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1622:[bind(A,$thf( c_emptyset ))]]) ).
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(381,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(382,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[381]) ).
thf(4293,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)],[1623,382]) ).
thf(4294,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)],[4293]) ).
thf(4313,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_emptyset != c_0 )
| ( c_0 != A )
| ( c_0 != c_OtwayRees_Ootway ) ),
inference(simp,[status(thm)],[4294]) ).
thf(4326,plain,
( ( c_emptyset != c_0 )
| ( c_0 != c_OtwayRees_Ootway ) ),
inference(simp,[status(thm)],[4313]) ).
thf(117,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(614,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)],[117]) ).
thf(1,negated_conjecture,
tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ 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_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Event_Oevent_OGets ) @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(323,plain,
tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ 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_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Event_Oevent_OGets ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(1166,plain,
! [A: $i] :
( ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ 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_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Event_Oevent_OGets ) @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[323,455]) ).
thf(1167,plain,
! [A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ 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_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Event_Oevent_OGets ) @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1166]) ).
thf(1170,plain,
! [A: $i] :
( ( tc_Message_Omsg != tc_Event_Oevent )
| ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
!= ( c_emptyset @ c_Message_Oparts ) )
| ( ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ 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_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Event_Oevent_OGets ) )
!= A ) ),
inference(simp,[status(thm)],[1167]) ).
thf(1173,plain,
( ( tc_Message_Omsg != tc_Event_Oevent )
| ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
!= ( c_emptyset @ c_Message_Oparts ) ) ),
inference(simp,[status(thm)],[1170]) ).
thf(79,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(523,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(102,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(582,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)],[102]) ).
thf(1436,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,479]) ).
thf(1437,plain,
( ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1436:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).
thf(261,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(970,plain,
! [A: $i] :
( c_emptyset
= ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(971,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[970]) ).
thf(1175,plain,
! [A: $i] :
( ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
!= ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) ) )
| ( tc_Event_Oevent @ ( c_emptyset @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ 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_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Event_Oevent_OGets ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[971,323]) ).
thf(1177,plain,
! [A: $i] :
( ( A != tc_Event_Oevent )
| ( c_List_Olist_ONil != v_evs )
| ( tc_Event_Oevent @ ( c_emptyset @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ 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_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Event_Oevent_OGets ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1175]) ).
thf(1179,plain,
( ( c_List_Olist_ONil != v_evs )
| ( tc_Event_Oevent @ ( c_emptyset @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ 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_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Event_Oevent_OGets ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1177]) ).
thf(1342,plain,
( ( c_List_Olist_ONil != v_evs )
| $false ),
inference(rewrite,[status(thm)],[1179,1105]) ).
thf(1343,plain,
c_List_Olist_ONil != v_evs,
inference(simp,[status(thm)],[1342]) ).
thf(1523,plain,
! [A: $i] :
( ( A != c_List_Olist_ONil )
| ( c_0 != v_evs )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,1343]) ).
thf(1524,plain,
( ( c_0 != v_evs )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1523:[bind(A,$thf( c_List_Olist_ONil ))]]) ).
thf(3629,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_evs ) ),
inference(paramod_ordered,[status(thm)],[1524,409]) ).
thf(3630,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ( c_0 != v_evs ) ),
inference(simp,[status(thm)],[3629]) ).
thf(3648,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_List_Olist_ONil != A )
| ( c_0 != A )
| ( c_0 != v_evs ) ),
inference(simp,[status(thm)],[3630]) ).
thf(3651,plain,
( ( c_List_Olist_ONil != c_0 )
| ( c_0 != v_evs ) ),
inference(simp,[status(thm)],[3648]) ).
thf(3669,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_List_Olist_ONil != c_0 )
| ( A != v_evs )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,3651]) ).
thf(3670,plain,
! [A: $i] :
( ( c_List_Olist_ONil != c_0 )
| ( A != v_evs )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[3669:[]]) ).
thf(3679,plain,
( ( c_List_Olist_ONil != c_0 )
| ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[3670]) ).
thf(16,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(355,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(356,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[355]) ).
thf(4561,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_List_Olist_ONil != c_0 ) ),
inference(paramod_ordered,[status(thm)],[3679,356]) ).
thf(4562,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ( c_List_Olist_ONil != c_0 ) ),
inference(simp,[status(thm)],[4561]) ).
thf(4584,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( c_emptyset != v_evs )
| ( c_0 != A )
| ( c_List_Olist_ONil != c_0 ) ),
inference(simp,[status(thm)],[4562]) ).
thf(4592,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( c_emptyset != v_evs )
| ( c_List_Olist_ONil != c_0 ) ),
inference(simp,[status(thm)],[4584]) ).
thf(289,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(1041,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)],[289]) ).
thf(217,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(861,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)],[217]) ).
thf(27,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(389,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(390,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[389]) ).
thf(391,plain,
! [A: $i] :
( ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) )
| ( A = c_0 ) ),
inference(lifteq,[status(thm)],[390]) ).
thf(5423,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != c_0 )
| ( c_0 != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[391,1956]) ).
thf(5424,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5423]) ).
thf(5425,plain,
( ( c_0 != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5424:[bind(A,$thf( c_UNIV ))]]) ).
thf(306,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(1078,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)],[306]) ).
thf(25,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(383,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)],[25]) ).
thf(384,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONumber )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[383]) ).
thf(385,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONumber )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[384]) ).
thf(83,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(533,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)],[83]) ).
thf(89,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(550,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)],[89]) ).
thf(212,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(852,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)],[212]) ).
thf(4175,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)],[852,455]) ).
thf(4176,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)],[4175]) ).
thf(4205,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)],[4176]) ).
thf(4220,plain,
! [A: $i] :
( ( A @ c_Event_OinitState )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[4205]) ).
thf(190,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(797,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)],[190]) ).
thf(60,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(472,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)],[60]) ).
thf(238,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(913,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)],[238]) ).
thf(251,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(945,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)],[251]) ).
thf(196,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(814,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)],[196]) ).
thf(1321,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[628,327]) ).
thf(1322,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1321]) ).
thf(1327,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= tc_Message_Oagent )
| ( c_Finite__Set_OFinites != c_Event_Obad )
| ( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
!= v_A ) ),
inference(simp,[status(thm)],[1322]) ).
thf(299,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(1063,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)],[299]) ).
thf(11,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(340,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)],[11]) ).
thf(271,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
thf(1001,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(225,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(879,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Public_OshrK )
!= ( B @ c_Public_OshrK ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(880,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Public_OshrK )
!= ( B @ c_Public_OshrK ) ) ),
inference(cnf,[status(esa)],[879]) ).
thf(881,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Public_OshrK )
!= ( B @ c_Public_OshrK ) ) ),
inference(lifteq,[status(thm)],[880]) ).
thf(882,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Public_OshrK @ A )
= B ),
inference(detectInverse,[status(thm)],[881]) ).
thf(883,plain,
! [A: $i] :
( ( A @ c_Public_OshrK @ sk28 )
= A ),
inference(cnf,[status(esa)],[882]) ).
thf(1391,plain,
! [A: $i] :
( ( A @ c_Public_OshrK @ sk28 )
= A ),
inference(lifteq,[status(thm)],[883]) ).
thf(183,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(782,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)],[183]) ).
thf(152,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(709,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)],[152]) ).
thf(206,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(841,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)],[206]) ).
thf(211,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(851,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)],[211]) ).
thf(4088,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)],[851,455]) ).
thf(4089,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)],[4088]) ).
thf(4118,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)],[4089]) ).
thf(4137,plain,
! [A: $i] :
( ( A @ c_Event_Oused )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[4118]) ).
thf(132,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(651,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)],[132]) ).
thf(313,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(1095,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)],[313]) ).
thf(31,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(402,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)],[31]) ).
thf(403,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONonce ) ),
inference(polarity_switch,[status(thm)],[402]) ).
thf(404,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONonce ) ),
inference(lifteq,[status(thm)],[403]) ).
thf(227,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(885,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)],[227]) ).
thf(291,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(1046,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)],[291]) ).
thf(160,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(724,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)],[160]) ).
thf(96,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(570,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(156,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(719,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)],[156]) ).
thf(184,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(785,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)],[184]) ).
thf(321,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(1113,plain,
! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(1256,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)],[1113,327]) ).
thf(1257,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)],[1256]) ).
thf(1264,plain,
! [A: $i] :
( ( tc_nat != tc_Message_Oagent )
| ( c_Message_OsymKeys != c_Event_Obad )
| ( ( A @ c_Public_OshrK )
!= v_A ) ),
inference(simp,[status(thm)],[1257]) ).
thf(12,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(343,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)],[12]) ).
thf(344,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)],[343]) ).
thf(17,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(357,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)],[17]) ).
thf(297,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(1059,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)],[297]) ).
thf(105,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(587,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)],[105]) ).
thf(148,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(702,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)],[148]) ).
thf(171,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(751,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)],[171]) ).
thf(1131,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)],[936,327]) ).
thf(1132,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)],[1131]) ).
thf(1135,plain,
( ( tc_Message_Oagent != tc_Message_Oagent )
| ( c_Event_Obad != c_Event_Obad )
| ( c_Message_Oagent_OSpy != v_A ) ),
inference(simp,[status(thm)],[1132]) ).
thf(1138,plain,
c_Message_Oagent_OSpy != v_A,
inference(simp,[status(thm)],[1135]) ).
thf(1544,plain,
! [A: $i] :
( ( A != c_Message_Oagent_OSpy )
| ( c_0 != v_A )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,1138]) ).
thf(1545,plain,
( ( c_0 != v_A )
| ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1544:[bind(A,$thf( c_Message_Oagent_OSpy ))]]) ).
thf(233,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(902,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)],[233]) ).
thf(93,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(559,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)],[93]) ).
thf(310,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(1087,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)],[310]) ).
thf(38,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(421,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(113,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(606,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)],[113]) ).
thf(172,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(754,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)],[172]) ).
thf(755,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[754]) ).
thf(3521,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)],[1058,755]) ).
thf(3522,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)],[3521]) ).
thf(3545,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)],[3522]) ).
thf(3557,plain,
c_Message_OsymKeys != c_UNIV,
inference(simp,[status(thm)],[3545]) ).
thf(127,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(638,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)],[127]) ).
thf(213,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(853,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)],[213]) ).
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(1013,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(177,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(770,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(4289,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)],[388,1623]) ).
thf(4290,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)],[4289:[]]) ).
thf(4317,plain,
( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[4290]) ).
thf(36,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(416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_append ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(242,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(924,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)],[242]) ).
thf(67,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(492,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)],[67]) ).
thf(173,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(756,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)],[173]) ).
thf(186,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(789,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)],[186]) ).
thf(6,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(331,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1350,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)],[936,1105]) ).
thf(1351,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)],[1350]) ).
thf(1365,plain,
! [B: $i,A: $i] :
( ( tc_Message_Oagent != B )
| ( c_emptyset != c_Event_Obad )
| ( c_Message_Oagent_OSpy != A ) ),
inference(simp,[status(thm)],[1351]) ).
thf(1373,plain,
c_emptyset != c_Event_Obad,
inference(simp,[status(thm)],[1365]) ).
thf(5593,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[391,1373]) ).
thf(5594,plain,
( ( c_0 != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5593:[bind(A,$thf( c_emptyset ))]]) ).
thf(7539,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)],[331,5594]) ).
thf(7540,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)],[7539]) ).
thf(7557,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_emptyset != c_0 )
| ( c_0 != c_Event_Obad ) ),
inference(simp,[status(thm)],[7540]) ).
thf(7564,plain,
( ( c_emptyset != c_0 )
| ( c_0 != c_Event_Obad ) ),
inference(simp,[status(thm)],[7557]) ).
thf(319,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(1109,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)],[319]) ).
thf(130,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(646,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(246,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(937,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)],[246]) ).
thf(1944,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != c_Event_Obad )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,1491]) ).
thf(1945,plain,
! [A: $i] :
( ( A != c_Event_Obad )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1944:[]]) ).
thf(1960,plain,
( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( c_Event_Obad @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1945]) ).
thf(259,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(966,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)],[259]) ).
thf(278,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(1018,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)],[278]) ).
thf(1019,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[1018]) ).
thf(1020,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OAgent )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[1019]) ).
thf(98,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(574,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)],[98]) ).
thf(293,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(1051,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)],[293]) ).
thf(199,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(821,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)],[199]) ).
thf(234,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(905,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)],[234]) ).
thf(9,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(337,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)],[9]) ).
thf(338,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)],[337]) ).
thf(1232,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)],[338,382]) ).
thf(1233,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)],[1232]) ).
thf(1234,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[1233:[bind(A,$thf( A )),bind(B,$thf( c_0 )),bind(C,$thf( A ))]]) ).
thf(6511,plain,
! [C: $i,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 @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1058,1234]) ).
thf(6512,plain,
! [C: $i,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 @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[6511]) ).
thf(6559,plain,
! [C: $i,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 @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[6512]) ).
thf(6591,plain,
c_UNIV != c_Wellfounded__Relations_Oless__than,
inference(simp,[status(thm)],[6559]) ).
thf(29,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(395,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)],[29]) ).
thf(396,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(cnf,[status(esa)],[395]) ).
thf(397,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(lifteq,[status(thm)],[396]) ).
thf(164,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(734,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)],[164]) ).
thf(74,axiom,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(507,plain,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(81,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(527,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)],[81]) ).
thf(111,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(602,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)],[111]) ).
thf(265,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(981,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)],[265]) ).
thf(224,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(877,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)],[224]) ).
thf(144,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(692,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)],[144]) ).
thf(41,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(428,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
| ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1198,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)],[706,327]) ).
thf(1199,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)],[1198]) ).
thf(1201,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_Message_Oagent )
| ( c_Finite__Set_OFinites != c_Event_Obad )
| ( c_emptyset != v_A ) ),
inference(simp,[status(thm)],[1199]) ).
thf(210,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(849,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)],[210]) ).
thf(304,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(1074,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)],[304]) ).
thf(3431,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[606,1105]) ).
thf(3432,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[3431]) ).
thf(3457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg != D )
| ( ( B @ c_Message_Osynth )
!= c_emptyset )
| ( ( A @ c_Message_Omsg_ONumber )
!= C ) ),
inference(simp,[status(thm)],[3432]) ).
thf(3459,plain,
! [A: $i] :
( ( A @ c_Message_Osynth )
!= c_emptyset ),
inference(simp,[status(thm)],[3457]) ).
thf(188,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(793,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)],[188]) ).
thf(20,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(366,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)],[20]) ).
thf(4,negated_conjecture,
~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ 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_NA @ 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(326,plain,
~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ 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_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ ( v_A @ c_Event_Oevent_OSays ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(328,plain,
~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ 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_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ ( v_A @ c_Event_Oevent_OSays ) ) @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[326]) ).
thf(1295,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ 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_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ ( v_A @ c_Event_Oevent_OSays ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1058,328]) ).
thf(1296,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ 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_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ ( v_A @ c_Event_Oevent_OSays ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1295]) ).
thf(1305,plain,
! [B: $i,A: $i] :
( ( B != tc_Event_Oevent )
| ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
!= c_UNIV )
| ( A
!= ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ 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_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ ( v_A @ c_Event_Oevent_OSays ) ) ) ) ),
inference(simp,[status(thm)],[1296]) ).
thf(1311,plain,
( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
!= c_UNIV ),
inference(simp,[status(thm)],[1305]) ).
thf(301,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(1067,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)],[301]) ).
thf(155,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(714,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)],[155]) ).
thf(1196,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)],[706,455]) ).
thf(1197,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)],[1196]) ).
thf(1204,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)],[1197]) ).
thf(1206,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Finite__Set_OFinites ) ),
inference(simp,[status(thm)],[1204]) ).
thf(53,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(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(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(249,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(942,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)],[249]) ).
thf(46,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(439,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)],[46]) ).
thf(8,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(334,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)],[8]) ).
thf(22,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(373,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)],[22]) ).
thf(374,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONumber )
!= ( B @ c_Message_Omsg_ONumber ) ) ),
inference(cnf,[status(esa)],[373]) ).
thf(375,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONumber )
!= ( B @ c_Message_Omsg_ONumber ) ) ),
inference(lifteq,[status(thm)],[374]) ).
thf(376,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_ONumber @ A )
= B ),
inference(detectInverse,[status(thm)],[375]) ).
thf(377,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_ONumber @ sk4 )
= A ),
inference(cnf,[status(esa)],[376]) ).
thf(1387,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_ONumber @ sk4 )
= A ),
inference(lifteq,[status(thm)],[377]) ).
thf(255,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(957,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)],[255]) ).
thf(348,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)],[347]) ).
thf(349,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)],[348]) ).
thf(109,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(598,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)],[109]) ).
thf(560,plain,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(polarity_switch,[status(thm)],[559]) ).
thf(561,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
inference(lifteq,[status(thm)],[560]) ).
thf(32,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(405,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)],[32]) ).
thf(406,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[405]) ).
thf(407,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_ONonce )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[406]) ).
thf(279,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(1021,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)],[279]) ).
thf(181,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(778,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(28,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(392,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(5718,plain,
! [A: $i] :
( ( A != c_Message_Oagent_OSpy )
| ( c_0 != v_A )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[391,1138]) ).
thf(5719,plain,
( ( c_0 != v_A )
| ~ ( tc_nat @ ( c_0 @ ( c_Message_Oagent_OSpy @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5718:[bind(A,$thf( c_Message_Oagent_OSpy ))]]) ).
thf(284,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(1032,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)],[284]) ).
thf(18,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(359,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)],[18]) ).
thf(360,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)],[359]) ).
thf(361,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)],[360]) ).
thf(121,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(625,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)],[121]) ).
thf(5,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(329,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)],[5]) ).
thf(141,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(682,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)],[141]) ).
thf(270,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(996,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)],[270]) ).
thf(997,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OAgent ) ) ),
inference(cnf,[status(esa)],[996]) ).
thf(998,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OAgent )
!= ( B @ c_Message_Omsg_OAgent ) ) ),
inference(lifteq,[status(thm)],[997]) ).
thf(999,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OAgent @ A )
= B ),
inference(detectInverse,[status(thm)],[998]) ).
thf(1000,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OAgent @ sk34 )
= A ),
inference(cnf,[status(esa)],[999]) ).
thf(1392,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OAgent @ sk34 )
= A ),
inference(lifteq,[status(thm)],[1000]) ).
thf(153,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(710,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)],[153]) ).
thf(55,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(456,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)],[55]) ).
thf(3991,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_A ) ),
inference(paramod_ordered,[status(thm)],[1545,356]) ).
thf(3992,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ( c_0 != v_A ) ),
inference(simp,[status(thm)],[3991]) ).
thf(4016,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( c_Message_Oagent_OSpy != c_emptyset )
| ( c_0 != A )
| ( c_0 != v_A ) ),
inference(simp,[status(thm)],[3992]) ).
thf(4027,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( c_Message_Oagent_OSpy != c_emptyset )
| ( c_0 != v_A ) ),
inference(simp,[status(thm)],[4016]) ).
thf(318,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(1106,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)],[318]) ).
thf(239,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(916,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)],[239]) ).
thf(59,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(467,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)],[59]) ).
thf(5591,plain,
! [A: $i] :
( ( A != c_Message_OsymKeys )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[391,3557]) ).
thf(5592,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Message_OsymKeys @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5591:[bind(A,$thf( c_Message_OsymKeys ))]]) ).
thf(7206,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)],[331,5592]) ).
thf(7207,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)],[7206]) ).
thf(7226,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_Message_OsymKeys != c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[7207]) ).
thf(7237,plain,
( ( c_Message_OsymKeys != c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[7226]) ).
thf(209,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(847,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)],[209]) ).
thf(65,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(484,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)],[65]) ).
thf(1966,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_UNIV != c_0 )
| ( A != c_Event_Obad )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,1956]) ).
thf(1967,plain,
! [A: $i] :
( ( c_UNIV != c_0 )
| ( A != c_Event_Obad )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1966:[]]) ).
thf(1968,plain,
( ( c_UNIV != c_0 )
| ( tc_nat @ ( c_Event_Obad @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1967]) ).
thf(44,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(435,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(7393,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)],[719,478]) ).
thf(7394,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)],[7393]) ).
thf(7418,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)],[7394]) ).
thf(7449,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[7418]) ).
thf(263,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(974,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)],[263]) ).
thf(223,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(874,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)],[223]) ).
thf(1267,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)],[338,409]) ).
thf(1268,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)],[1267]) ).
thf(1269,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[1268:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(1270,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)],[1269]) ).
thf(252,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(948,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)],[252]) ).
thf(320,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(1111,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)],[320]) ).
thf(273,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
thf(1006,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(221,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(869,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)],[221]) ).
thf(115,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(610,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)],[115]) ).
thf(215,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(857,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)],[215]) ).
thf(146,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(697,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)],[146]) ).
thf(311,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(1089,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)],[311]) ).
thf(1354,plain,
! [B: $i,A: $i] :
( ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ 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_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Event_Oevent_OGets ) @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[323,1105]) ).
thf(1355,plain,
! [B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ 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_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Event_Oevent_OGets ) @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1354]) ).
thf(1367,plain,
! [B: $i,A: $i] :
( ( tc_Event_Oevent != B )
| ( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
!= c_emptyset )
| ( ( v_B @ c_Message_Omsg_OAgent @ ( v_A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ 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_NA @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Event_Oevent_OGets ) )
!= A ) ),
inference(simp,[status(thm)],[1355]) ).
thf(1375,plain,
( ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) )
!= c_emptyset ),
inference(simp,[status(thm)],[1367]) ).
thf(1119,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[325,327]) ).
thf(1120,plain,
( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1119]) ).
thf(1121,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Oagent )
| ( c_OtwayRees_Ootway != c_Event_Obad )
| ( v_evs != v_A ) ),
inference(simp,[status(thm)],[1120]) ).
thf(71,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(499,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)],[71]) ).
thf(4159,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)],[852,1105]) ).
thf(4160,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)],[4159]) ).
thf(4203,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)],[4160]) ).
thf(4219,plain,
! [A: $i] :
( ( A @ c_Event_OinitState )
!= c_emptyset ),
inference(simp,[status(thm)],[4203]) ).
thf(226,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(884,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)],[226]) ).
thf(282,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(1028,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)],[282]) ).
thf(10,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).
thf(339,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(90,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(552,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)],[90]) ).
thf(553,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OKey ) ),
inference(polarity_switch,[status(thm)],[552]) ).
thf(554,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OKey ) ),
inference(lifteq,[status(thm)],[553]) ).
thf(128,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(640,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)],[128]) ).
thf(641,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[640]) ).
thf(642,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OHash )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[641]) ).
thf(66,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(489,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)],[66]) ).
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(1016,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(87,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(547,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)],[87]) ).
thf(139,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(679,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(288,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(1039,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)],[288]) ).
thf(322,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(1114,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)],[322]) ).
thf(1250,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1113,478]) ).
thf(1251,plain,
! [A: $i] :
( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1250]) ).
thf(1263,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= tc_nat )
| ( c_Message_OsymKeys != c_Finite__Set_OFinites )
| ( ( A @ c_Public_OshrK )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1251]) ).
thf(77,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(515,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)],[77]) ).
thf(1254,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)],[1113,455]) ).
thf(1255,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)],[1254]) ).
thf(1260,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg != tc_nat )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Message_OsymKeys )
| ( ( A @ c_Public_OshrK )
!= B ) ),
inference(simp,[status(thm)],[1255]) ).
thf(1266,plain,
( ( tc_Message_Omsg != tc_nat )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Message_OsymKeys ) ),
inference(simp,[status(thm)],[1260]) ).
thf(133,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(654,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)],[133]) ).
thf(158,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(721,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)],[158]) ).
thf(7721,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)],[941,1105]) ).
thf(7722,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)],[7721]) ).
thf(7773,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)],[7722]) ).
thf(7789,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Olists ) )
!= c_emptyset ),
inference(simp,[status(thm)],[7773]) ).
thf(95,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(567,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)],[95]) ).
thf(568,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OKey )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(polarity_switch,[status(thm)],[567]) ).
thf(569,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OKey )
!= ( C @ ( B @ c_Message_OHPair ) ) ),
inference(lifteq,[status(thm)],[568]) ).
thf(21,axiom,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).
thf(371,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(120,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(622,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)],[120]) ).
thf(3623,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != v_evs )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,1524]) ).
thf(3624,plain,
! [A: $i] :
( ( A != v_evs )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[3623:[]]) ).
thf(3654,plain,
( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( v_evs @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[3624]) ).
thf(315,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(1099,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)],[315]) ).
thf(266,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(984,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)],[266]) ).
thf(237,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(911,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)],[237]) ).
thf(1325,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)],[628,478]) ).
thf(1326,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)],[1325]) ).
thf(1331,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)],[1326]) ).
thf(1333,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
!= c_UNIV ),
inference(simp,[status(thm)],[1331]) ).
thf(1224,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_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) )
| ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[325,338]) ).
thf(1225,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_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) )
| ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(simp,[status(thm)],[1224]) ).
thf(1241,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ tc_prod ) )
!= ( tc_Event_Oevent @ tc_List_Olist ) )
| ( c_Wellfounded__Relations_Oless__than != c_OtwayRees_Ootway )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) )
!= v_evs )
| ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(simp,[status(thm)],[1225]) ).
thf(125,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(633,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)],[125]) ).
thf(75,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(508,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)],[75]) ).
thf(241,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(921,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)],[241]) ).
thf(286,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(1035,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)],[286]) ).
thf(303,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(1071,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)],[303]) ).
thf(138,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(674,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)],[138]) ).
thf(82,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(530,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)],[82]) ).
thf(253,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(953,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)],[253]) ).
thf(243,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(926,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)],[243]) ).
thf(176,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(765,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)],[176]) ).
thf(294,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(1054,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)],[294]) ).
thf(179,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(773,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)],[179]) ).
thf(104,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(586,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)],[104]) ).
thf(3993,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_A ) ),
inference(paramod_ordered,[status(thm)],[1545,382]) ).
thf(3994,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ( c_0 != v_A ) ),
inference(simp,[status(thm)],[3993]) ).
thf(4013,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_Message_Oagent_OSpy != c_0 )
| ( c_0 != A )
| ( c_0 != v_A ) ),
inference(simp,[status(thm)],[3994]) ).
thf(4024,plain,
( ( c_Message_Oagent_OSpy != c_0 )
| ( c_0 != v_A ) ),
inference(simp,[status(thm)],[4013]) ).
thf(4035,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_Message_Oagent_OSpy != c_0 )
| ( A != v_A )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,4024]) ).
thf(4036,plain,
! [A: $i] :
( ( c_Message_Oagent_OSpy != c_0 )
| ( A != v_A )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[4035:[]]) ).
thf(4045,plain,
( ( c_Message_Oagent_OSpy != c_0 )
| ( tc_nat @ ( v_A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[4036]) ).
thf(4886,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( v_A @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_Message_Oagent_OSpy != c_0 ) ),
inference(paramod_ordered,[status(thm)],[4045,356]) ).
thf(4887,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( v_A @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ( c_Message_Oagent_OSpy != c_0 ) ),
inference(simp,[status(thm)],[4886]) ).
thf(4909,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( c_emptyset != v_A )
| ( c_0 != A )
| ( c_Message_Oagent_OSpy != c_0 ) ),
inference(simp,[status(thm)],[4887]) ).
thf(4919,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( c_emptyset != v_A )
| ( c_Message_Oagent_OSpy != c_0 ) ),
inference(simp,[status(thm)],[4909]) ).
thf(611,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)],[610]) ).
thf(3839,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)],[1058,611]) ).
thf(3840,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)],[3839]) ).
thf(3866,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)],[3840]) ).
thf(3888,plain,
! [A: $i] :
( ( A @ c_Event_OinitState @ c_Message_Oparts )
!= c_UNIV ),
inference(simp,[status(thm)],[3866]) ).
thf(143,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(689,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)],[143]) ).
thf(49,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(444,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1141,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)],[936,478]) ).
thf(1142,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)],[1141]) ).
thf(1146,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)],[1142]) ).
thf(42,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(430,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(94,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(562,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)],[94]) ).
thf(145,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(694,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)],[145]) ).
thf(350,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)],[349]) ).
thf(351,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) @ ( C @ ( B @ sk1 ) ) )
= A ),
inference(cnf,[status(esa)],[350]) ).
thf(1389,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) @ ( C @ ( B @ sk1 ) ) )
= A ),
inference(lifteq,[status(thm)],[351]) ).
thf(207,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(843,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)],[207]) ).
thf(473,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OKey )
!= ( B @ c_Message_Omsg_OKey ) ) ),
inference(cnf,[status(esa)],[472]) ).
thf(474,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OKey )
!= ( B @ c_Message_Omsg_OKey ) ) ),
inference(lifteq,[status(thm)],[473]) ).
thf(475,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OKey @ A )
= B ),
inference(detectInverse,[status(thm)],[474]) ).
thf(476,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OKey @ sk9 )
= A ),
inference(cnf,[status(esa)],[475]) ).
thf(1388,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OKey @ sk9 )
= A ),
inference(lifteq,[status(thm)],[476]) ).
thf(168,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(743,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)],[168]) ).
thf(100,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(579,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)],[100]) ).
thf(4291,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)],[1623,356]) ).
thf(4292,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)],[4291]) ).
thf(4315,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)],[4292]) ).
thf(4328,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( c_0 != c_OtwayRees_Ootway ) ),
inference(simp,[status(thm)],[4315]) ).
thf(35,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(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(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(200,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(826,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)],[200]) ).
thf(99,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(577,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)],[99]) ).
thf(154,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(711,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)],[154]) ).
thf(97,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(572,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)],[97]) ).
thf(1291,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)],[1058,478]) ).
thf(1292,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)],[1291]) ).
thf(1306,plain,
! [B: $i,A: $i] :
( ( B
!= ( tc_nat @ tc_set ) )
| ( c_UNIV != c_Finite__Set_OFinites )
| ( A != c_UNIV ) ),
inference(simp,[status(thm)],[1292]) ).
thf(1312,plain,
c_UNIV != c_Finite__Set_OFinites,
inference(simp,[status(thm)],[1306]) ).
thf(70,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(498,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)],[70]) ).
thf(192,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(804,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)],[192]) ).
thf(149,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(704,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)],[149]) ).
thf(185,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(787,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)],[185]) ).
thf(58,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__3__iff1_0) ).
thf(464,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(465,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(polarity_switch,[status(thm)],[464]) ).
thf(466,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(lifteq,[status(thm)],[465]) ).
thf(312,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(1092,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)],[312]) ).
thf(783,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OHash ) ),
inference(polarity_switch,[status(thm)],[782]) ).
thf(784,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OHash ) ),
inference(lifteq,[status(thm)],[783]) ).
thf(264,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(979,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)],[264]) ).
thf(112,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(604,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)],[112]) ).
thf(201,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(831,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)],[201]) ).
thf(5879,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[391,1312]) ).
thf(5880,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5879:[bind(A,$thf( c_UNIV ))]]) ).
thf(7902,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)],[331,5880]) ).
thf(7903,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)],[7902]) ).
thf(7922,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_UNIV != c_0 )
| ( c_Finite__Set_OFinites != c_0 ) ),
inference(simp,[status(thm)],[7903]) ).
thf(7933,plain,
( ( c_UNIV != c_0 )
| ( c_Finite__Set_OFinites != c_0 ) ),
inference(simp,[status(thm)],[7922]) ).
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(1011,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(37,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(419,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1047,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OAgent ) ),
inference(polarity_switch,[status(thm)],[1046]) ).
thf(1048,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_OAgent ) ),
inference(lifteq,[status(thm)],[1047]) ).
thf(165,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(736,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)],[165]) ).
thf(3443,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[606,455]) ).
thf(3444,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[3443]) ).
thf(3455,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_ONumber )
!= C ) ),
inference(simp,[status(thm)],[3444]) ).
thf(3468,plain,
! [A: $i] :
( ( A @ c_Message_Osynth )
!= ( c_emptyset @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[3455]) ).
thf(367,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_ONonce ) ) ),
inference(cnf,[status(esa)],[366]) ).
thf(368,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_ONonce )
!= ( B @ c_Message_Omsg_ONonce ) ) ),
inference(lifteq,[status(thm)],[367]) ).
thf(369,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_ONonce @ A )
= B ),
inference(detectInverse,[status(thm)],[368]) ).
thf(370,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_ONonce @ sk3 )
= A ),
inference(cnf,[status(esa)],[369]) ).
thf(1376,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_ONonce @ sk3 )
= A ),
inference(lifteq,[status(thm)],[370]) ).
thf(1438,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,479]) ).
thf(1439,plain,
( ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1438:[bind(A,$thf( tc_nat ))]]) ).
thf(229,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(890,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)],[229]) ).
thf(195,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(811,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)],[195]) ).
thf(124,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(631,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)],[124]) ).
thf(174,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(758,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)],[174]) ).
thf(197,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(816,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)],[197]) ).
thf(114,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
thf(607,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(608,plain,
c_UNIV != c_emptyset,
inference(polarity_switch,[status(thm)],[607]) ).
thf(609,plain,
c_UNIV != c_emptyset,
inference(lifteq,[status(thm)],[608]) ).
thf(3989,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != v_A )
| ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,1545]) ).
thf(3990,plain,
! [A: $i] :
( ( A != v_A )
| ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[3989:[]]) ).
thf(4028,plain,
( ( tc_nat @ ( c_Message_Oagent_OSpy @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( v_A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[3990]) ).
thf(107,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(594,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(398,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_List_Orev ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[397]) ).
thf(399,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Orev ) @ ( B @ sk5 ) )
= A ),
inference(cnf,[status(esa)],[398]) ).
thf(7662,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Orev ) @ ( B @ sk5 ) )
= A ),
inference(lifteq,[status(thm)],[399]) ).
thf(7663,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 @ sk5 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[333,7662]) ).
thf(7664,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ ( A @ sk5 ) )
= c_List_Olist_ONil ),
inference(pattern_uni,[status(thm)],[7663:[bind(A,$thf( A )),bind(B,$thf( c_List_Olist_ONil )),bind(C,$thf( A ))]]) ).
thf(258,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(964,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)],[258]) ).
thf(40,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(427,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(6978,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[427,478]) ).
thf(6979,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)],[6978]) ).
thf(7002,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)],[6979]) ).
thf(7023,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[7002]) ).
thf(6648,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[421,478]) ).
thf(6649,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)],[6648]) ).
thf(6681,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)],[6649]) ).
thf(6692,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[6681]) ).
thf(330,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)],[329]) ).
thf(298,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(1061,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)],[298]) ).
thf(68,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(494,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(307,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(1080,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)],[307]) ).
thf(13,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(345,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(191,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(799,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)],[191]) ).
thf(1507,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)],[388,507]) ).
thf(1508,plain,
! [A: $i] :
( ( A @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1507:[bind(A,$thf( c_emptyset ))]]) ).
thf(1909,plain,
! [A: $i] :
( ( A @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1508]) ).
thf(161,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(726,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)],[161]) ).
thf(147,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(700,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)],[147]) ).
thf(78,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(520,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)],[78]) ).
thf(1162,plain,
! [A: $i] :
( ( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[325,455]) ).
thf(1163,plain,
! [A: $i] :
( ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
!= ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1162]) ).
thf(1168,plain,
! [A: $i] :
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_OtwayRees_Ootway )
| ( v_evs != A ) ),
inference(simp,[status(thm)],[1163]) ).
thf(1171,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_OtwayRees_Ootway ) ),
inference(simp,[status(thm)],[1168]) ).
thf(182,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(780,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)],[182]) ).
thf(393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
inference(polarity_switch,[status(thm)],[392]) ).
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(lifteq,[status(thm)],[393]) ).
thf(73,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(505,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)],[73]) ).
thf(126,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(636,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)],[126]) ).
thf(290,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(1044,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)],[290]) ).
thf(305,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(1076,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)],[305]) ).
thf(159,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(722,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)],[159]) ).
thf(106,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(589,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)],[106]) ).
thf(250,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(944,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(88,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(548,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)],[88]) ).
thf(131,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(648,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)],[131]) ).
thf(170,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(749,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)],[170]) ).
thf(118,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(617,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)],[118]) ).
thf(247,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(939,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)],[247]) ).
thf(341,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONumber ) ),
inference(polarity_switch,[status(thm)],[340]) ).
thf(342,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_OHPair ) )
!= ( C @ c_Message_Omsg_ONumber ) ),
inference(lifteq,[status(thm)],[341]) ).
thf(292,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(1049,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)],[292]) ).
thf(189,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(795,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)],[189]) ).
thf(140,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(680,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)],[140]) ).
thf(1139,plain,
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
!= ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[325,478]) ).
thf(1140,plain,
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
!= ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) ),
inference(simp,[status(thm)],[1139]) ).
thf(1145,plain,
( ( ( tc_nat @ tc_set )
!= ( tc_Event_Oevent @ tc_List_Olist ) )
| ( c_Finite__Set_OFinites != c_OtwayRees_Ootway )
| ( c_UNIV != v_evs ) ),
inference(simp,[status(thm)],[1140]) ).
thf(260,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(968,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)],[260]) ).
thf(56,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(458,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)],[56]) ).
thf(80,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(525,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)],[80]) ).
thf(214,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(855,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)],[214]) ).
thf(281,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(1025,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)],[281]) ).
thf(222,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(872,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)],[222]) ).
thf(228,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(887,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)],[228]) ).
thf(166,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(739,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)],[166]) ).
thf(1358,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)],[463,1105]) ).
thf(1359,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)],[1358]) ).
thf(1360,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)],[1359]) ).
thf(1368,plain,
c_Finite__Set_OFinites != c_emptyset,
inference(simp,[status(thm)],[1360]) ).
thf(92,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(557,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)],[92]) ).
thf(272,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_List_Oremdups ) )
= A )
| ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff1_0) ).
thf(1003,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_List_Oremdups ) )
= A )
| ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(5476,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)],[391,4326]) ).
thf(5477,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != c_OtwayRees_Ootway )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5476]) ).
thf(5478,plain,
( ( c_0 != c_OtwayRees_Ootway )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5477:[bind(A,$thf( c_emptyset ))]]) ).
thf(151,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(707,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)],[151]) ).
thf(1498,plain,
! [A: $i] :
( ( A
!= ( tc_Event_Oevent @ tc_List_Olist ) )
| ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,325]) ).
thf(1499,plain,
( ( c_0 @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) )
| ( tc_nat @ ( tc_Event_Oevent @ tc_List_Olist @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1498:[bind(A,$thf( tc_Event_Oevent @ tc_List_Olist ))]]) ).
thf(187,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(791,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)],[187]) ).
thf(103,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(585,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(72,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(502,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)],[72]) ).
thf(309,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(1085,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)],[309]) ).
thf(129,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(643,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)],[129]) ).
thf(1248,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)],[1113,838]) ).
thf(1249,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)],[1248]) ).
thf(1262,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)],[1249]) ).
thf(86,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(544,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)],[86]) ).
thf(235,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(907,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)],[235]) ).
thf(335,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( B @ ( A @ c_List_Orev ) ) ) ),
inference(cnf,[status(esa)],[334]) ).
thf(336,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Orev ) )
!= c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[335]) ).
thf(3625,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_evs ) ),
inference(paramod_ordered,[status(thm)],[1524,356]) ).
thf(3626,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ( c_0 != v_evs ) ),
inference(simp,[status(thm)],[3625]) ).
thf(3649,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( c_emptyset != c_List_Olist_ONil )
| ( c_0 != A )
| ( c_0 != v_evs ) ),
inference(simp,[status(thm)],[3626]) ).
thf(3652,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( c_emptyset != c_List_Olist_ONil )
| ( c_0 != v_evs ) ),
inference(simp,[status(thm)],[3649]) ).
thf(280,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(1023,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)],[280]) ).
thf(5426,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)],[391,1956]) ).
thf(5427,plain,
! [A: $i] :
( ( c_UNIV != c_0 )
| ( A != c_Event_Obad )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5426:[]]) ).
thf(6262,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Event_Obad @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5427]) ).
thf(110,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(600,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)],[110]) ).
thf(218,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(864,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)],[218]) ).
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(1008,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(116,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(612,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)],[116]) ).
thf(216,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(859,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)],[216]) ).
thf(50,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(446,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)],[50]) ).
thf(571,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[570]) ).
thf(1356,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)],[1113,1105]) ).
thf(1357,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)],[1356]) ).
thf(1364,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != C )
| ( c_Message_OsymKeys != c_emptyset )
| ( ( A @ c_Public_OshrK )
!= B ) ),
inference(simp,[status(thm)],[1357]) ).
thf(1372,plain,
c_Message_OsymKeys != c_emptyset,
inference(simp,[status(thm)],[1364]) ).
thf(595,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
inference(lifteq,[status(thm)],[594]) ).
thf(208,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(845,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)],[208]) ).
thf(64,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(482,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)],[64]) ).
thf(137,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(671,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)],[137]) ).
thf(101,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(581,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)],[101]) ).
thf(495,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
inference(lifteq,[status(thm)],[494]) ).
thf(516,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OHash ) ) ),
inference(cnf,[status(esa)],[515]) ).
thf(517,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OHash )
!= ( B @ c_Message_Omsg_OHash ) ) ),
inference(lifteq,[status(thm)],[516]) ).
thf(518,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Message_Omsg_OHash @ A )
= B ),
inference(detectInverse,[status(thm)],[517]) ).
thf(519,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OHash @ sk12 )
= A ),
inference(cnf,[status(esa)],[518]) ).
thf(1390,plain,
! [A: $i] :
( ( A @ c_Message_Omsg_OHash @ sk12 )
= A ),
inference(lifteq,[status(thm)],[519]) ).
thf(178,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(771,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)],[178]) ).
thf(1107,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
inference(polarity_switch,[status(thm)],[1106]) ).
thf(1108,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Public_OshrK )
!= ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
inference(lifteq,[status(thm)],[1107]) ).
thf(4072,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)],[851,1105]) ).
thf(4073,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)],[4072]) ).
thf(4122,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)],[4073]) ).
thf(4138,plain,
! [A: $i] :
( ( A @ c_Event_Oused )
!= c_emptyset ),
inference(simp,[status(thm)],[4122]) ).
thf(52,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(450,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)],[52]) ).
thf(244,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(931,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)],[244]) ).
thf(85,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(539,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)],[85]) ).
thf(1273,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)],[463,478]) ).
thf(1274,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)],[1273]) ).
thf(1283,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)],[1274]) ).
thf(1289,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= c_UNIV ),
inference(simp,[status(thm)],[1283]) ).
thf(316,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(1101,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)],[316]) ).
thf(30,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(400,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)],[30]) ).
thf(401,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)],[400]) ).
thf(163,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(731,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)],[163]) ).
thf(231,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(896,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)],[231]) ).
thf(169,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(748,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
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(378,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(232,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(899,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)],[232]) ).
thf(142,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(684,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)],[142]) ).
thf(1297,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)],[1058,455]) ).
thf(1298,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)],[1297]) ).
thf(1303,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_Message_Omsg )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_UNIV )
| ( A != C ) ),
inference(simp,[status(thm)],[1298]) ).
thf(1309,plain,
( ( c_emptyset @ c_Message_Oparts )
!= c_UNIV ),
inference(simp,[status(thm)],[1303]) ).
thf(84,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(536,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)],[84]) ).
thf(8170,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)],[679,401]) ).
thf(8171,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)],[8170]) ).
thf(8172,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( A @ ( A @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[8171:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(43,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(433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( D @ ( C @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(76,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(510,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)],[76]) ).
thf(119,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(620,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)],[119]) ).
thf(198,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(818,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)],[198]) ).
thf(39,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(422,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(220,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(867,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)],[220]) ).
thf(219,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(865,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)],[219]) ).
thf(202,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(833,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)],[202]) ).
thf(34,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(410,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)],[34]) ).
thf(314,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(1097,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)],[314]) ).
thf(203,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(835,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)],[203]) ).
thf(240,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(918,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)],[240]) ).
thf(362,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)],[361]) ).
thf(363,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) @ ( C @ ( B @ sk2 ) ) )
= A ),
inference(cnf,[status(esa)],[362]) ).
thf(4350,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) @ ( C @ ( B @ sk2 ) ) )
= A ),
inference(lifteq,[status(thm)],[363]) ).
thf(1164,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)],[936,455]) ).
thf(1165,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)],[1164]) ).
thf(1169,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)],[1165]) ).
thf(1172,plain,
( ( tc_Message_Omsg != tc_Message_Oagent )
| ( ( c_emptyset @ c_Message_Oparts )
!= c_Event_Obad ) ),
inference(simp,[status(thm)],[1169]) ).
thf(256,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(960,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)],[256]) ).
thf(157,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(720,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)],[157]) ).
thf(254,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(955,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)],[254]) ).
thf(358,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)],[357]) ).
thf(193,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(807,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)],[193]) ).
thf(45,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(437,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)],[45]) ).
thf(295,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(1056,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)],[295]) ).
thf(135,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(664,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)],[135]) ).
thf(285,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(1033,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)],[285]) ).
thf(1279,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[463,327]) ).
thf(1280,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1279]) ).
thf(1288,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= tc_Message_Oagent )
| ( c_Finite__Set_OFinites != c_Event_Obad )
| ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= v_A ) ),
inference(simp,[status(thm)],[1280]) ).
thf(5641,plain,
! [A: $i] :
( ( A != c_List_Olist_ONil )
| ( c_0 != v_evs )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[391,1343]) ).
thf(5642,plain,
( ( c_0 != v_evs )
| ~ ( tc_nat @ ( c_0 @ ( c_List_Olist_ONil @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[5641:[bind(A,$thf( c_List_Olist_ONil ))]]) ).
thf(300,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(1065,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)],[300]) ).
thf(162,axiom,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__4__iff1_0) ).
thf(728,plain,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(267,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(987,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)],[267]) ).
thf(108,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(596,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)],[108]) ).
thf(268,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(992,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)],[268]) ).
thf(6171,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_Message_Oagent_OSpy != c_0 )
| ( A != v_A )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[391,4024]) ).
thf(6172,plain,
! [A: $i] :
( ( c_Message_Oagent_OSpy != c_0 )
| ( A != v_A )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[6171:[]]) ).
thf(6233,plain,
( ( c_Message_Oagent_OSpy != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( v_A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[6172]) ).
thf(48,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(442,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)],[48]) ).
thf(4335,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)],[388,4326]) ).
thf(4336,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( A != c_OtwayRees_Ootway )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[4335:[]]) ).
thf(4345,plain,
( ( c_emptyset != c_0 )
| ( tc_nat @ ( c_OtwayRees_Ootway @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[4336]) ).
thf(205,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(839,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)],[205]) ).
thf(1125,plain,
( ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) )
!= ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[325,838]) ).
thf(1126,plain,
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) )
!= ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evs @ c_in ) ) ) ),
inference(simp,[status(thm)],[1125]) ).
thf(1129,plain,
( ( ( tc_Event_Oevent @ tc_List_Olist )
!= tc_Message_Oagent )
| ( c_OtwayRees_Ootway != c_Event_Obad )
| ( c_Message_Oagent_OServer != v_evs ) ),
inference(simp,[status(thm)],[1126]) ).
thf(353,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)],[352]) ).
thf(354,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)],[353]) ).
thf(134,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(659,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)],[134]) ).
thf(287,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(1037,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)],[287]) ).
thf(262,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(972,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)],[262]) ).
thf(69,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(496,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)],[69]) ).
thf(302,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(1069,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)],[302]) ).
thf(96948,plain,
$false,
inference(e,[status(thm)],[809,629,365,760,1633,347,941,666,1956,479,1105,909,1031,333,628,893,7143,1083,962,777,555,481,352,1200,408,1290,994,741,449,4326,614,1173,523,582,1437,4592,1041,861,5425,1078,385,533,550,4220,797,472,913,945,814,1327,1063,340,1001,1391,782,709,841,4137,1623,651,1095,404,885,1046,389,724,570,719,785,1264,344,1313,357,1059,587,838,702,751,1545,902,559,1087,421,606,325,3557,638,853,1013,770,4317,416,924,492,756,789,7564,1373,1109,646,937,1960,966,1020,574,1051,821,905,480,6591,397,734,507,527,602,981,877,692,428,1201,1104,849,1074,3459,793,381,366,1311,1067,714,3679,1206,452,942,439,334,1387,957,1343,349,598,561,407,5594,1021,778,392,5719,1032,361,625,329,682,1392,710,456,4027,1106,916,467,7237,847,484,1968,879,852,435,7449,324,974,874,1270,948,1111,1006,388,869,610,857,697,1089,1234,1375,1121,1138,356,499,4219,328,884,1028,339,554,642,489,1016,547,706,679,1039,970,1114,1263,515,1266,654,721,7789,569,371,622,837,3654,1099,984,911,1333,343,1241,633,508,921,1035,1071,674,530,953,926,765,1054,773,586,4919,3888,689,444,1374,375,1146,430,562,694,402,1389,843,1388,743,579,4328,413,826,577,711,391,936,382,572,1312,3651,498,1058,804,704,611,787,466,1092,784,1524,996,567,979,604,831,7933,1011,419,1048,736,3468,5880,1376,1439,890,477,811,631,758,816,609,323,4028,594,7664,1029,964,7023,6692,330,1061,494,1080,345,552,799,1909,726,700,520,1171,780,455,394,1113,851,505,636,1044,1076,722,589,944,548,648,749,617,939,342,355,754,1049,795,680,1145,1018,968,458,4045,776,525,855,640,1025,872,887,971,327,5592,739,1368,409,557,1003,5478,707,1499,791,331,441,585,502,463,338,1085,359,643,1262,7662,544,907,336,3652,1023,6262,600,864,386,1008,612,859,446,571,1372,595,845,482,671,581,495,1390,771,1108,4138,450,931,539,1289,368,1101,401,731,896,748,378,478,383,899,684,1309,536,8172,1491,433,510,620,818,405,422,867,865,373,833,410,1097,835,326,918,4350,1172,960,720,955,358,807,437,4024,1056,664,1033,1288,400,5642,1065,728,987,464,427,596,992,6233,442,4345,607,395,839,332,1129,337,354,659,1037,755,364,972,496,454,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV293-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % 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
% 0.12/0.39 % Computer : n013.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 13:28:06 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.88/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.45/1.42 % [INFO] Parsing done (443ms).
% 2.45/1.44 % [INFO] Running in sequential loop mode.
% 3.39/1.82 % [INFO] eprover registered as external prover.
% 3.39/1.83 % [INFO] Scanning for conjecture ...
% 4.11/2.04 % [INFO] Found a conjecture (or negated_conjecture) and 1472 axioms. Running axiom selection ...
% 4.78/2.26 % [INFO] Axiom selection finished. Selected 318 axioms (removed 1154 axioms).
% 5.74/2.44 % [INFO] Problem is propositional (TPTP CNF).
% 5.74/2.46 % [INFO] Type checking passed.
% 5.74/2.47 % [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 ...
% 257.80/68.97 % External prover 'e' found a proof!
% 257.80/68.97 % [INFO] Killing All external provers ...
% 257.80/68.97 % Time passed: 68435ms (effective reasoning time: 67523ms)
% 257.80/68.97 % Axioms used in derivation (318): 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_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_Message_OHash_91X_93_AY_A_61_AAgent_AA_A_61_61_62_AR_0, cls_Finite__Set_Ofinite__Pow__iff__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1, cls_Sum__Type_OInlI_0, 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_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_Owf__lex_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_List_Orev__is__Nil__conv__iff2_0, cls_Set_OUn__empty__iff1_1, cls_Public_OpublicKey__inject__iff1_1, cls_Relation_Orel__compE_2, cls_Relation_OImageE_1, cls_Relation_OdiagE_0, cls_Set_OsingletonD__dest_0, cls_SetInterval_Ofinite__atLeastAtMost_0, cls_Message_Omsg_Oinject__3__iff1_0, cls_SetInterval_Ofinite__atLeastLessThan_0, cls_Set_OUn__empty__iff1_0, cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, cls_Message_OHPair__neqs__4__iff1_0, cls_Wellfounded__Recursion_Owf__insert__iff2_0, cls_Set_Oempty__subsetI_0, cls_Finite__Set_Ofinite__Int_1, cls_List_Oappend__is__Nil__conv__iff2_0, cls_Relation_OIdI_0, cls_SetInterval_Ofinite__lessThan_0, cls_List_Olength__greater__0__conv__iff1_0, cls_List_Oappend1__eq__conv__iff1_1, cls_Set_OsubsetD_0, cls_Product__Type_OPair__eq__iff1_1, cls_Event_Oevent_Oinject__2__iff1_0, cls_List_Osame__append__eq__iff1_0, cls_Set_OsingletonI_0, cls_Message_Oparts__partsD__dest_0, cls_Wellfounded__Relations_Oless__than__iff__iff1_0, cls_Set_Osubset__antisym_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0, cls_List_Oself__append__conv__iff1_0, cls_List_Oin__listsI_1, cls_List_Orev__eq__Cons__iff__iff1_0, cls_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_OHash_91X_93_AY_A_61_ANumber_AN_A_61_61_62_AR_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_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
% 257.80/68.97 % No. of inferences in proof: 1048
% 257.80/68.98 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 68435 ms resp. 67523 ms w/o parsing
% 260.17/69.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 260.17/69.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------