TSTP Solution File: SWV311-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV311-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:14:59 EDT 2023
% Result : Unsatisfiable 18.54s 4.26s
% Output : Refutation 18.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 474
% Syntax : Number of formulae : 815 ( 227 unt; 134 typ; 0 def)
% Number of atoms : 1237 ( 428 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 8490 ( 618 ~; 556 |; 0 &;7316 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 303 ( 303 >; 0 *; 0 +; 0 <<)
% Number of symbols : 136 ( 134 usr; 29 con; 0-6 aty)
% Number of variables : 2072 ( 0 ^;2072 !; 0 ?;2072 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_B_type,type,
v_B: $i ).
thf(c_Event_Obad_type,type,
c_Event_Obad: $i ).
thf(tc_Message_Oagent_type,type,
tc_Message_Oagent: $i ).
thf(v_evs3_type,type,
v_evs3: $i ).
thf(c_OtwayRees_Ootway_type,type,
c_OtwayRees_Ootway: $i ).
thf(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
thf(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
thf(v_NB_type,type,
v_NB: $i ).
thf(c_Message_Omsg_ONonce_type,type,
c_Message_Omsg_ONonce: $i > $i ).
thf(v_NBa_type,type,
v_NBa: $i ).
thf(v_K_type,type,
v_K: $i ).
thf(v_KAB_type,type,
v_KAB: $i ).
thf(c_Event_Oevent_OSays_type,type,
c_Event_Oevent_OSays: $i > $i > $i > $i ).
thf(v_Ba_type,type,
v_Ba: $i ).
thf(c_Message_Oagent_OServer_type,type,
c_Message_Oagent_OServer: $i ).
thf(c_Message_Omsg_OMPair_type,type,
c_Message_Omsg_OMPair: $i > $i > $i ).
thf(v_NAa_type,type,
v_NAa: $i ).
thf(c_Message_Omsg_OAgent_type,type,
c_Message_Omsg_OAgent: $i > $i ).
thf(v_Aa_type,type,
v_Aa: $i ).
thf(c_Message_Omsg_OCrypt_type,type,
c_Message_Omsg_OCrypt: $i > $i > $i ).
thf(c_Public_OshrK_type,type,
c_Public_OshrK: $i > $i ).
thf(c_List_Oset_type,type,
c_List_Oset: $i > $i > $i ).
thf(v_NA_type,type,
v_NA: $i ).
thf(v_A_type,type,
v_A: $i ).
thf(v_x_type,type,
v_x: $i ).
thf(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i > $i ).
thf(c_Event_Oused_type,type,
c_Event_Oused: $i > $i ).
thf(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
thf(c_Event_Oevent_OGets_type,type,
c_Event_Oevent_OGets: $i > $i > $i ).
thf(c_Wellfounded__Recursion_Oacyclic_type,type,
c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).
thf(c_Relation_Oconverse_type,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_0_type,type,
c_0: $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i ).
thf(c_List_Orev_type,type,
c_List_Orev: $i > $i > $i ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(c_Wellfounded__Relations_Oless__than_type,type,
c_Wellfounded__Relations_Oless__than: $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(c_less_type,type,
c_less: $i > $i > $i > $o ).
thf(c_Datatype__Universe_OIn1_type,type,
c_Datatype__Universe_OIn1: $i > $i > $i > $i ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(c_emptyset_type,type,
c_emptyset: $i ).
thf(c_Datatype__Universe_OIn0_type,type,
c_Datatype__Universe_OIn0: $i > $i > $i > $i ).
thf(c_Datatype__Universe_Odprod_type,type,
c_Datatype__Universe_Odprod: $i > $i > $i > $i > $i ).
thf(tc_Datatype__Universe_Onode_type,type,
tc_Datatype__Universe_Onode: $i > $i > $i ).
thf(c_Datatype__Universe_OScons_type,type,
c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__1_type,type,
c_Main_OdprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__2_type,type,
c_Main_OdprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__3_type,type,
c_Main_OdprodE__3: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__4_type,type,
c_Main_OdprodE__4: $i > $i > $i > $i > $i > $i ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_append_type,type,
c_append: $i > $i > $i > $i ).
thf(c_Finite__Set_OFinites_type,type,
c_Finite__Set_OFinites: $i ).
thf(c_insert_type,type,
c_insert: $i > $i > $i > $i ).
thf(c_SetInterval_OgreaterThanAtMost_type,type,
c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(c_SetInterval_OatLeastAtMost_type,type,
c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_Message_Oagent_OFriend_type,type,
c_Message_Oagent_OFriend: $i > $i ).
thf(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
thf(c_Nat_Osize_type,type,
c_Nat_Osize: $i > $i > $i ).
thf(c_Wellfounded__Recursion_Owf_type,type,
c_Wellfounded__Recursion_Owf: $i > $i > $o ).
thf(c_Wellfounded__Relations_Olex__prod_type,type,
c_Wellfounded__Relations_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_union_type,type,
c_union: $i > $i > $i > $i ).
thf(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
thf(c_Message_Osynth_type,type,
c_Message_Osynth: $i > $i ).
thf(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
thf(c_SetInterval_OatLeastLessThan_type,type,
c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_Message_Omsg_ONumber_type,type,
c_Message_Omsg_ONumber: $i > $i ).
thf(c_Pow_type,type,
c_Pow: $i > $i > $i ).
thf(c_Relation_Orel__comp_type,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_Public_OpublicKey_type,type,
c_Public_OpublicKey: $i > $i > $i ).
thf(c_SetInterval_OatMost_type,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(c_Message_OHPair_type,type,
c_Message_OHPair: $i > $i > $i ).
thf(c_UNIV_type,type,
c_UNIV: $i ).
thf(c_Message_OinvKey_type,type,
c_Message_OinvKey: $i > $i ).
thf(c_Message_OsymKeys_type,type,
c_Message_OsymKeys: $i ).
thf(c_minus_type,type,
c_minus: $i > $i > $i > $i ).
thf(c_List_Oremdups_type,type,
c_List_Oremdups: $i > $i > $i ).
thf(c_Event_Oevent_ONotes_type,type,
c_Event_Oevent_ONotes: $i > $i > $i ).
thf(c_Message_Omsg_OHash_type,type,
c_Message_Omsg_OHash: $i > $i ).
thf(c_Datatype__Universe_Odsum_type,type,
c_Datatype__Universe_Odsum: $i > $i > $i > $i > $i ).
thf(c_Relation_OId_type,type,
c_Relation_OId: $i ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Sum__Type_OInr_type,type,
c_Sum__Type_OInr: $i > $i > $i > $i ).
thf(c_Sum__Type_OInl_type,type,
c_Sum__Type_OInl: $i > $i > $i > $i ).
thf(c_inter_type,type,
c_inter: $i > $i > $i > $i ).
thf(c_List_Odistinct_type,type,
c_List_Odistinct: $i > $i > $o ).
thf(c_Transitive__Closure_Otrancl_type,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_SetInterval_OlessThan_type,type,
c_SetInterval_OlessThan: $i > $i > $i ).
thf(c_Main_OImageE__1_type,type,
c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Sum__Type_OPlus_type,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(tc_sum_type,type,
tc_sum: $i > $i > $i ).
thf(c_Main_OPlusE__1_type,type,
c_Main_OPlusE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OPlusE__2_type,type,
c_Main_OPlusE__2: $i > $i > $i > $i > $i ).
thf(c_Relation_Odiag_type,type,
c_Relation_Odiag: $i > $i > $i ).
thf(c_Datatype__Universe_Ouprod_type,type,
c_Datatype__Universe_Ouprod: $i > $i > $i > $i > $i ).
thf(c_SetInterval_OgreaterThanLessThan_type,type,
c_SetInterval_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(c_Datatype_Ooption_OSome_type,type,
c_Datatype_Ooption_OSome: $i > $i > $i ).
thf(c_Union_type,type,
c_Union: $i > $i > $i ).
thf(c_Main_OUnionE__1_type,type,
c_Main_OUnionE__1: $i > $i > $i > $i ).
thf(c_Relation_ORange_type,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Main_ORangeE__1_type,type,
c_Main_ORangeE__1: $i > $i > $i > $i > $i ).
thf(c_List_Olists_type,type,
c_List_Olists: $i > $i > $i ).
thf(c_Main_OsubsetI__1_type,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Event_Oknows_type,type,
c_Event_Oknows: $i > $i > $i ).
thf(c_Main_OconverseE__1_type,type,
c_Main_OconverseE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OconverseE__2_type,type,
c_Main_OconverseE__2: $i > $i > $i > $i > $i ).
thf(c_List_Olistrel_type,type,
c_List_Olistrel: $i > $i > $i ).
thf(c_Main_Olistrel__Cons1__1_type,type,
c_Main_Olistrel__Cons1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Event_OinitState_type,type,
c_Event_OinitState: $i > $i ).
thf(c_Main_Oin__listsI__1_type,type,
c_Main_Oin__listsI__1: $i > $i > $i > $i ).
thf(v_sko__u__1_type,type,
v_sko__u__1: $i > $i > $i > $i > $i > $i ).
thf(c_Inter_type,type,
c_Inter: $i > $i > $i ).
thf(c_Main_OInterI__1_type,type,
c_Main_OInterI__1: $i > $i > $i > $i ).
thf(c_Main_OuprodE__1_type,type,
c_Main_OuprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OuprodE__2_type,type,
c_Main_OuprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Datatype_Oo2s_type,type,
c_Datatype_Oo2s: $i > $i > $i ).
thf(c_Main_Olistrel__Cons2__1_type,type,
c_Main_Olistrel__Cons2__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Olistrel__Cons2__2_type,type,
c_Main_Olistrel__Cons2__2: $i > $i > $i > $i > $i > $i ).
thf(c_Infinite__Set_Oatmost__one_type,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_Main_Orel__compE__1_type,type,
c_Main_Orel__compE__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_Orel__compE__3_type,type,
c_Main_Orel__compE__3: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_Ofinite__Union__1_type,type,
c_Main_Ofinite__Union__1: $i > $i > $i ).
thf(v_sko__usf_type,type,
v_sko__usf: $i > $i > $i > $i ).
thf(c_Main_OdiagE__1_type,type,
c_Main_OdiagE__1: $i > $i > $i > $i ).
thf(c_Main_Orel__compE__2_type,type,
c_Main_Orel__compE__2: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_OIdE__1_type,type,
c_Main_OIdE__1: $i > $i > $i ).
thf(c_Main_Olistrel__Cons1__2_type,type,
c_Main_Olistrel__Cons1__2: $i > $i > $i > $i > $i > $i ).
thf(c_List_Olex_type,type,
c_List_Olex: $i > $i > $i ).
thf(c_Relation_ODomain_type,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_List_Olenlex_type,type,
c_List_Olenlex: $i > $i > $i ).
thf(c_Main_ODomainE__1_type,type,
c_Main_ODomainE__1: $i > $i > $i > $i > $i ).
thf(229,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
thf(892,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(289,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__1__iff1_0) ).
thf(1036,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_OHPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(61,axiom,
c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
thf(479,plain,
c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(13,negated_conjecture,
v_K = v_KAB,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_8) ).
thf(347,plain,
v_K = v_KAB,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(211,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ ( c_Main_OInterI__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
thf(846,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ ( c_Main_OInterI__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__2__iff1_0) ).
thf(1031,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_OHPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(77,axiom,
! [B: $i,A: $i] :
( A
= ( c_append @ A @ c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).
thf(518,plain,
! [B: $i,A: $i] :
( A
= ( c_append @ A @ c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(250,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_1) ).
thf(941,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(325,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
thf(1110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(11,negated_conjecture,
v_A = v_Aa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(352,plain,
v_A = v_Aa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(312,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
thf(1083,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Public_OpublicKey @ A @ B )
!= ( c_Public_OpublicKey @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject__iff1_0) ).
thf(468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Public_OpublicKey @ A @ B )
!= ( c_Public_OpublicKey @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(266,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_OHPair @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__6__iff1_0) ).
thf(977,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_OHPair @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).
thf(582,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ B @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(161,axiom,
! [A: $i] :
( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff2_0) ).
thf(730,plain,
! [A: $i] :
( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(305,axiom,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
thf(1068,plain,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(273,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_append @ D @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).
thf(994,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_append @ D @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(307,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ E @ A @ B @ C @ D ) @ C @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).
thf(1073,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__2 @ E @ A @ B @ C @ D ) @ C @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).
thf(1041,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(224,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Infinite__Set_Oatmost__one @ A @ B )
| ~ ( c_in @ C @ A @ B )
| ~ ( c_in @ D @ A @ B )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(878,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Infinite__Set_Oatmost__one @ A @ B )
| ~ ( c_in @ C @ A @ B )
| ~ ( c_in @ D @ A @ B )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) )
| ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).
thf(440,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) )
| ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Sum__Type_OInr @ A @ B @ C )
!= ( c_Sum__Type_OInr @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).
thf(655,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Sum__Type_OInr @ A @ B @ C )
!= ( c_Sum__Type_OInr @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OHash @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5__iff1_0) ).
thf(511,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_Omsg_OHash @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= B )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).
thf(614,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= B )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= A )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).
thf(677,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= A )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_less @ A @ B @ ( tc_set @ C ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(384,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_less @ A @ B @ ( tc_set @ C ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(58,axiom,
! [A: $i] : ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
thf(472,plain,
! [A: $i] : ( c_in @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(148,axiom,
! [A: $i] :
~ ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff1_0) ).
thf(698,plain,
! [A: $i] :
~ ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(238,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oset @ A @ B )
!= c_emptyset )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).
thf(913,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oset @ A @ B )
!= c_emptyset )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ C ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OCrypt_0) ).
thf(945,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ C ) @ B @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ c_Relation_OId @ ( tc_prod @ C @ C ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
thf(538,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ c_Relation_OId @ ( tc_prod @ C @ C ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
thf(670,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(332,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).
thf(1127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(417,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(293,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_List_Oset @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
thf(1046,plain,
! [B: $i,A: $i] : ( c_in @ ( c_List_Oset @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(95,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ C @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).
thf(565,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ C @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(318,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).
thf(1095,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(31,axiom,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).
thf(404,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).
thf(389,plain,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ C @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OSays__imp__analz__Spy__dest_0) ).
thf(785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ C @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_List_Orev @ A @ B ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv__iff1_0) ).
thf(372,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_List_Orev @ A @ B ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(72,axiom,
! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(504,plain,
! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(247,axiom,
! [A: $i] :
( ( c_Message_Oagent_OFriend @ A )
!= c_Message_Oagent_OServer ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__2__iff1_0) ).
thf(934,plain,
! [A: $i] :
( ( c_Message_Oagent_OFriend @ A )
!= c_Message_Oagent_OServer ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(300,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_minus @ D @ B @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).
thf(1059,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_minus @ D @ B @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(253,axiom,
! [B: $i,A: $i] :
( ( c_emptyset
!= ( c_List_Oset @ A @ B ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).
thf(949,plain,
! [B: $i,A: $i] :
( ( c_emptyset
!= ( c_List_Oset @ A @ B ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_ONonce__synth_0) ).
thf(1055,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(158,axiom,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(724,plain,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__5__iff1_0) ).
thf(619,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OHash @ A )
!= ( c_Message_OHPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(207,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).
thf(838,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
| ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
thf(802,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
| ( c_in @ ( c_Pair @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1,negated_conjecture,
~ ( c_in @ v_B @ c_Event_Obad @ tc_Message_Oagent ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(344,plain,
~ ( c_in @ v_B @ c_Event_Obad @ tc_Message_Oagent ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
thf(881,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ c_List_Olist_ONil @ A @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(327,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Main_OInterI__1 @ A @ B @ C ) @ C )
| ( c_in @ A @ ( c_Inter @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
thf(1115,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Main_OInterI__1 @ A @ B @ C ) @ C )
| ( c_in @ A @ ( c_Inter @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ~ ( c_Wellfounded__Recursion_Owf @ C @ D )
| ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ C @ A @ D @ B ) @ ( tc_prod @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
thf(448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ~ ( c_Wellfounded__Recursion_Owf @ C @ D )
| ( c_Wellfounded__Recursion_Owf @ ( c_Wellfounded__Relations_Olex__prod @ C @ A @ D @ B ) @ ( tc_prod @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).
thf(817,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(234,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__5__iff1_0) ).
thf(902,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(37,axiom,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(421,plain,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
thf(870,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(263,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/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(969,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= c_0 )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff1_0) ).
thf(606,plain,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
!= c_0 )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(107,axiom,
! [A: $i] :
( c_Message_Oagent_OSpy
!= ( c_Message_Oagent_OFriend @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__6__iff1_0) ).
thf(591,plain,
! [A: $i] :
( c_Message_Oagent_OSpy
!= ( c_Message_Oagent_OFriend @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(937,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(191,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ ( c_Main_Olistrel__Cons1__1 @ E @ D @ A @ B @ C ) @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).
thf(806,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ A @ ( c_Main_Olistrel__Cons1__1 @ E @ D @ A @ B @ C ) @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(8,negated_conjecture,
c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Aa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OAgent @ v_Ba ) ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NBa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OAgent @ v_Ba ) ) ) ) ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(353,plain,
c_in @ ( c_Event_Oevent_OGets @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Aa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OAgent @ v_Ba ) ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NBa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OAgent @ v_Ba ) ) ) ) ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(199,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_minus @ B @ C @ ( tc_set @ D ) ) @ D )
| ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).
thf(821,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_minus @ B @ C @ ( tc_set @ D ) ) @ D )
| ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(336,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
thf(1136,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) )
| ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(834,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) )
| ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(2,negated_conjecture,
c_in @ v_evs3 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(348,plain,
c_in @ v_evs3 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__iff1_1) ).
thf(574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz__iff1_0) ).
thf(905,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(62,axiom,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) @ c_Message_OsymKeys @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__priK__iff1_0) ).
thf(480,plain,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) @ c_Message_OsymKeys @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(28,axiom,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).
thf(397,plain,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_union @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).
thf(734,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ~ ( c_in @ C @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_union @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3__iff1_1) ).
thf(507,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ c_emptyset @ C )
= ( c_insert @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).
thf(602,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ c_emptyset @ C )
= ( c_insert @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(268,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
| ( A
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
thf(981,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
| ( A
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(329,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ A @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).
thf(1119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ A @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_0) ).
thf(774,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OFake__parts__insert__in__Un__dest_0) ).
thf(452,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn1 @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).
thf(380,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn1 @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(44,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
thf(439,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_ONonce @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3__iff1_0) ).
thf(761,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONonce @ A )
!= ( c_Message_Omsg_ONonce @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(193,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Ospies__pubK_0) ).
thf(810,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ A @ D @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).
thf(534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ A @ D @ C ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(155,axiom,
! [A: $i] :
( ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
| ( c_in @ ( c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff__iff2_0) ).
thf(714,plain,
! [A: $i] :
( ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
| ( c_in @ ( c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(294,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__into__parts__dest_0) ).
thf(1047,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(299,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ B ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_OSpy__see__shrK__D__dest_0) ).
thf(1057,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ B ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OKey @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__4__iff1_0) ).
thf(910,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_OKey @ A )
!= ( c_Message_OHPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Union @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
thf(1091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Union @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(283,axiom,
! [A: $i] :
( ( c_List_Oset @ c_List_Olist_ONil @ A )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).
thf(1021,plain,
! [A: $i] :
( ( c_List_Oset @ c_List_Olist_ONil @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(254,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
thf(952,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_OCons @ C @ D @ B ) )
| ( A
= ( c_append @ ( c_List_Orev @ D @ B ) @ ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff__iff1_0) ).
thf(429,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_OCons @ C @ D @ B ) )
| ( A
= ( c_append @ ( c_List_Orev @ D @ B ) @ ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(196,axiom,
! [A: $i] :
~ ( c_in @ A @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__emptyE_0) ).
thf(815,plain,
! [A: $i] :
~ ( c_in @ A @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__shrK_0) ).
thf(957,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_Main_Oin__listsI__1 @ B @ A @ C ) @ ( c_List_Oset @ A @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
thf(894,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_Main_Oin__listsI__1 @ B @ A @ C ) @ ( c_List_Oset @ A @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(218,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ G ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent )
| ( C = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_Ounique__NB__dest_0) ).
thf(862,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ G ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent )
| ( C = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(12,negated_conjecture,
( v_NA
= ( c_Message_Omsg_ONonce @ v_NAa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).
thf(349,plain,
( v_NA
= ( c_Message_Omsg_ONonce @ v_NAa ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(32,axiom,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).
thf(407,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(693,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).
thf(630,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ B @ C ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__usf @ B @ C @ A ) @ B @ C ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_OGets__imp__Says__dest_0) ).
thf(916,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ B @ C ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__usf @ B @ C @ A ) @ B @ C ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(64,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).
thf(484,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(120,axiom,
! [A: $i] :
( c_List_Olist_ONil
= ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).
thf(625,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).
thf(522,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( B = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).
thf(461,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( B = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(67,axiom,
! [B: $i,A: $i] :
( ( c_append @ A @ c_List_Olist_ONil @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).
thf(493,plain,
! [B: $i,A: $i] :
( ( c_append @ A @ c_List_Olist_ONil @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(310,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).
thf(1079,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(172,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_List_Olist_OCons @ A @ D @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
thf(757,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ ( c_List_Olist_OCons @ A @ D @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(153,axiom,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Public_OpublicKey @ A @ B ) @ c_Message_OsymKeys @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__pubK__iff1_0) ).
thf(710,plain,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Public_OpublicKey @ A @ B ) @ c_Message_OsymKeys @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(209,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) ),
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(842,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).
thf(1106,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
thf(852,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olistrel @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(43,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).
thf(435,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(315,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
thf(1089,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
thf(1143,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(330,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype_Oo2s @ B @ C ) @ C )
| ( B
= ( c_Datatype_Ooption_OSome @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).
thf(1121,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype_Oo2s @ B @ C ) @ C )
| ( B
= ( c_Datatype_Ooption_OSome @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(303,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpriK__in__initState_0) ).
thf(1064,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(159,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_Wellfounded__Recursion_Oacyclic @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).
thf(725,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_Wellfounded__Recursion_Oacyclic @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(267,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_ONumber_0) ).
thf(980,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(337,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Public_OshrK @ A )
!= ( c_Message_OinvKey @ ( c_Public_OpublicKey @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpriK__neq__shrK__iff1_0) ).
thf(1138,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Public_OshrK @ A )
!= ( c_Message_OinvKey @ ( c_Public_OpublicKey @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(220,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ A @ B ) @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).
thf(869,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Datatype_Oo2s @ ( c_Datatype_Ooption_OSome @ A @ B ) @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).
thf(783,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(216,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( A
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
thf(857,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( A
= ( c_Datatype__Universe_OScons @ ( c_Main_OuprodE__1 @ B @ C @ A @ D @ E ) @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(166,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn0 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ E @ F @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).
thf(742,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn0 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn0 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ E @ F @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( A
= ( c_append @ c_List_Olist_ONil @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).
thf(578,plain,
! [B: $i,A: $i] :
( A
= ( c_append @ c_List_Olist_ONil @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(226,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( A
= ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ F @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
thf(884,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( A
= ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ F @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(488,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Public_OpublicKey @ A @ B )
!= ( c_Public_OpublicKey @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject__iff1_1) ).
thf(637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Public_OpublicKey @ A @ B )
!= ( c_Public_OpublicKey @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(290,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ B @ ( c_Main_Olistrel__Cons1__2 @ E @ D @ A @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).
thf(1039,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( c_in @ ( c_Pair @ B @ ( c_Main_Olistrel__Cons1__2 @ E @ D @ A @ B @ C ) @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).
thf(547,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Oagent_OFriend @ A )
!= ( c_Message_Oagent_OFriend @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Oinject__iff1_0) ).
thf(706,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Oagent_OFriend @ A )
!= ( c_Message_Oagent_OFriend @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(143,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
| ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).
thf(686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ A @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
| ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__into__used_0) ).
thf(1075,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(622,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(320,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ E @ A @ B @ C @ D ) @ B @ D @ D ) @ E @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).
thf(1099,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_Olistrel__Cons2__1 @ E @ A @ B @ C @ D ) @ B @ D @ D ) @ E @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(150,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ F @ ( tc_prod @ C @ E ) )
| ( c_in @ D @ ( c_Relation_OImage @ F @ B @ C @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
thf(701,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ F @ ( tc_prod @ C @ E ) )
| ( c_in @ D @ ( c_Relation_OImage @ F @ B @ C @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).
thf(515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(334,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).
thf(1131,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ c_List_Olist_ONil @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olex @ C @ B ) @ ( tc_prod @ ( tc_List_Olist @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(269,axiom,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ B ) ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_ONonce__notin__initState__iff1_0) ).
thf(984,plain,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ B ) ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(276,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ C @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
thf(1002,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Ouprod @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) )
| ( c_in @ ( c_Main_OuprodE__2 @ B @ C @ A @ D @ E ) @ C @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(779,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(112,axiom,
! [A: $i] : ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
thf(605,plain,
! [A: $i] : ( c_in @ ( c_SetInterval_OlessThan @ A @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(14,negated_conjecture,
v_B = v_Ba,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_9) ).
thf(343,plain,
v_B = v_Ba,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
| ( A
= ( c_Pair @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
thf(938,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
| ( A
= ( c_Pair @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(123,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).
thf(633,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(85,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ~ ( c_in @ ( c_Pair @ F @ G @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ H @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ F @ A @ C @ D ) @ ( c_Datatype__Universe_OScons @ G @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odprod @ H @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).
thf(541,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ~ ( c_in @ ( c_Pair @ F @ G @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ H @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OScons @ F @ A @ C @ D ) @ ( c_Datatype__Universe_OScons @ G @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odprod @ H @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(175,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1__iff1_0) ).
thf(765,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(92,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_insert @ C @ c_emptyset @ D ) @ D @ E ) @ E )
| ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).
thf(558,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_insert @ C @ c_emptyset @ D ) @ D @ E ) @ E )
| ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(137,axiom,
! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
thf(674,plain,
! [A: $i] : ( c_in @ c_emptyset @ c_Finite__Set_OFinites @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(285,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E )
| ( A
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
thf(1026,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E )
| ( A
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(132,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).
thf(662,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(242,axiom,
c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OSpy_A_58_Abad_0) ).
thf(926,plain,
c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OHash_0) ).
thf(794,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).
thf(586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(322,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair__iff1_1) ).
thf(1103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(201,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__3__iff1_0) ).
thf(824,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
| ( c_less @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff1_0) ).
thf(375,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
| ( c_less @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(261,axiom,
! [A: $i] :
( c_emptyset
= ( c_List_Oset @ c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).
thf(965,plain,
! [A: $i] :
( c_emptyset
= ( c_List_Oset @ c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).
thf(750,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(104,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_Wellfounded__Recursion_Owf @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).
thf(584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_Wellfounded__Recursion_Owf @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B )
= ( c_Message_OHPair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair__iff2_0) ).
thf(819,plain,
! [B: $i,A: $i] :
( ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B )
= ( c_Message_OHPair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(265,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
thf(975,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__3 @ B @ C @ A @ D @ E @ F ) @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(38,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( A
= ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).
thf(423,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( A
= ( c_Pair @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__2 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( c_Datatype__Universe_OScons @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__4 @ A @ B @ C @ D @ E ) @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(278,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
thf(1007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(30,axiom,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).
thf(402,plain,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(162,axiom,
! [B: $i,A: $i] :
( ( c_append @ c_List_Olist_ONil @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).
thf(732,plain,
! [B: $i,A: $i] :
( ( c_append @ c_List_Olist_ONil @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(177,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(772,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(223,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( A
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ E @ A @ B @ C @ D ) @ ( c_Main_Olistrel__Cons2__2 @ E @ A @ B @ C @ D ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).
thf(875,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) @ ( c_List_Olistrel @ E @ D ) @ ( tc_prod @ ( tc_List_Olist @ D ) @ ( tc_List_Olist @ D ) ) )
| ( A
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons2__1 @ E @ A @ B @ C @ D ) @ ( c_Main_Olistrel__Cons2__2 @ E @ A @ B @ C @ D ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(331,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__2__iff1_0) ).
thf(1124,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_append @ ( c_List_Orev @ A @ B ) @ ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Olist_OCons @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff__iff2_0) ).
thf(545,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_append @ ( c_List_Orev @ A @ B ) @ ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Olist_OCons @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Orev @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv__iff1_0) ).
thf(413,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Orev @ C @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ c_emptyset @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(641,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ c_emptyset @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn0 @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).
thf(391,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn0 @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff2_0) ).
thf(445,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(99,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) )
| ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).
thf(572,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) )
| ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(184,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_ONotes @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__3__iff1_0) ).
thf(787,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_ONotes @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Public_OpublicKey @ A @ B )
!= ( c_Message_OinvKey @ ( c_Public_OpublicKey @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__neq__privateKey__iff1_0) ).
thf(498,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Public_OpublicKey @ A @ B )
!= ( c_Message_OinvKey @ ( c_Public_OpublicKey @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(56,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ F @ A @ G @ C ) @ H @ ( tc_prod @ G @ C ) )
| ( c_in @ ( c_Pair @ F @ B @ G @ D ) @ ( c_Relation_Orel__comp @ E @ H @ C @ D @ G ) @ ( tc_prod @ G @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
thf(466,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ F @ A @ G @ C ) @ H @ ( tc_prod @ G @ C ) )
| ( c_in @ ( c_Pair @ F @ B @ G @ D ) @ ( c_Relation_Orel__comp @ E @ H @ C @ D @ G ) @ ( tc_prod @ G @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
thf(804,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(252,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
thf(947,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(7,negated_conjecture,
~ ( c_in @ ( c_Message_Omsg_OKey @ v_KAB ) @ ( c_Event_Oused @ v_evs3 ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(350,plain,
~ ( c_in @ ( c_Message_Omsg_OKey @ v_KAB ) @ ( c_Event_Oused @ v_evs3 ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(136,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ~ ( c_in @ E @ F @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ E @ A @ C @ D ) @ ( c_Datatype__Universe_Ouprod @ F @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
thf(672,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ~ ( c_in @ E @ F @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) )
| ( c_in @ ( c_Datatype__Universe_OScons @ E @ A @ C @ D ) @ ( c_Datatype__Universe_Ouprod @ F @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(233,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
thf(900,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ A @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).
thf(1117,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(164,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_ONumber @ A )
!= ( c_Message_OHPair @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__3__iff1_0) ).
thf(736,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_Omsg_ONumber @ A )
!= ( c_Message_OHPair @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(96,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ c_Relation_OId @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
thf(567,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ c_Relation_OId @ ( tc_prod @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Sum__Type_OInl @ A @ B @ C )
!= ( c_Sum__Type_OInr @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).
thf(599,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Sum__Type_OInl @ A @ B @ C )
!= ( c_Sum__Type_OInr @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(280,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Relation_OId @ ( tc_prod @ B @ B ) )
| ( A
= ( c_Pair @ ( c_Main_OIdE__1 @ A @ B ) @ ( c_Main_OIdE__1 @ A @ B ) @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
thf(1011,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Relation_OId @ ( tc_prod @ B @ B ) )
| ( A
= ( c_Pair @ ( c_Main_OIdE__1 @ A @ B ) @ ( c_Main_OIdE__1 @ A @ B ) @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(419,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(20,axiom,
c_lessequals @ c_0 @ c_0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).
thf(377,plain,
c_lessequals @ c_0 @ c_0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(271,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
thf(990,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OAgent @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1__iff1_0) ).
thf(996,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OAgent @ A )
!= ( c_Message_Omsg_OAgent @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).
thf(649,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= ( c_append @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(292,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__4__iff1_0) ).
thf(1043,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(42,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
thf(434,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanAtMost @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(228,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Sum__Type_OInr @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ E @ B @ D @ C ) @ ( tc_sum @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
thf(890,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Sum__Type_OInr @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ E @ B @ D @ C ) @ ( tc_sum @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(60,axiom,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).
thf(477,plain,
~ ( c_in @ c_UNIV @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_ONumber @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_ANumber_AN_A_61_61_62_AR_0) ).
thf(609,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_ONumber @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(108,axiom,
! [A: $i] :
( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff2_0) ).
thf(594,plain,
! [A: $i] :
( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(286,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).
thf(1029,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(176,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( A
= ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair__iff1_0) ).
thf(769,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( A
= ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(326,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
thf(1112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(194,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OMPair__used_0) ).
thf(811,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(24,axiom,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).
thf(387,plain,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(6,negated_conjecture,
( ( c_in @ ( c_Event_Oevent_OSays @ v_B @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_B ) @ ( c_Message_Omsg_OMPair @ v_x @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ v_NB @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OAgent @ v_B ) ) ) ) ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ v_NB @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_13) ).
thf(345,plain,
( ( c_in @ ( c_Event_Oevent_OSays @ v_B @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_B ) @ ( c_Message_Omsg_OMPair @ v_x @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ v_NB @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OAgent @ v_B ) ) ) ) ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ v_NB @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).
thf(367,plain,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ( c_Wellfounded__Recursion_Oacyclic @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(90,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).
thf(552,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz__iff2_0) ).
thf(848,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(149,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(700,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(78,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn1 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ F @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).
thf(520,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ E @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Datatype__Universe_OIn1 @ A @ C @ D ) @ ( c_Datatype__Universe_OIn1 @ B @ C @ D ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) @ ( c_Datatype__Universe_Odsum @ F @ E @ C @ D ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(246,axiom,
! [B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
= ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair__iff2_0) ).
thf(932,plain,
! [B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
= ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OprivateKey__into__used_0) ).
thf(1061,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
thf(685,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= c_List_Olist_ONil )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv__iff1_0) ).
thf(399,plain,
! [B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= c_List_Olist_ONil )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(258,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ F @ D ) @ C @ ( tc_prod @ F @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
thf(959,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Orel__comp @ B @ C @ D @ E @ F ) @ ( tc_prod @ F @ E ) )
| ( c_in @ ( c_Pair @ ( c_Main_Orel__compE__1 @ B @ C @ A @ D @ E @ F ) @ ( c_Main_Orel__compE__2 @ B @ C @ A @ D @ E @ F ) @ F @ D ) @ C @ ( tc_prod @ F @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(202,axiom,
! [A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_OinitState @ A ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__in__initState_0) ).
thf(827,plain,
! [A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_OinitState @ A ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).
thf(695,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONumber @ A )
!= ( c_Message_Omsg_ONumber @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2__iff1_0) ).
thf(455,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_ONumber @ A )
!= ( c_Message_Omsg_ONumber @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(270,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6__iff1_0) ).
thf(986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OMPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ A @ C @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
thf(563,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ A @ C @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(275,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_union @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).
thf(1000,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_union @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(73,axiom,
! [A: $i] :
( ~ ( c_in @ ( c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat )
| ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff__iff1_0) ).
thf(505,plain,
! [A: $i] :
( ~ ( c_in @ ( c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat )
| ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
| ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).
thf(653,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B )
| ( c_in @ ( c_Pair @ D @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(241,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1__iff1_1) ).
thf(922,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(288,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).
thf(1034,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).
thf(675,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Pow @ B @ C ) @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn1 @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).
thf(426,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Datatype__Universe_OIn0 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn1 @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(82,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).
thf(531,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3__iff1_0) ).
thf(680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_ONotes @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).
thf(927,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(127,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(648,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(311,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
| ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
thf(1081,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( c_in @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ B @ D )
| ( c_in @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(117,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
thf(617,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ( c_in @ ( c_Pair @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(10,negated_conjecture,
( v_NA
= ( c_Message_Omsg_ONonce @ v_NAa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(342,plain,
( v_NA
= ( c_Message_Omsg_ONonce @ v_NAa ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(200,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__in__used_0) ).
thf(823,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(206,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_OSays @ B @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( v_sko__u__1 @ E @ B @ C @ D @ A ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) ) ) ) ) ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_OCrypt__imp__OR2__dest_0) ).
thf(836,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_OSays @ B @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( v_sko__u__1 @ E @ B @ C @ D @ A ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) ) ) ) ) ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Public_OshrK @ A )
!= ( c_Public_OpublicKey @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpubK__neq__shrK__iff1_0) ).
thf(1049,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Public_OshrK @ A )
!= ( c_Public_OpublicKey @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__iff1_0) ).
thf(473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_OHPair @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(309,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( D = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair__iff1_1) ).
thf(1076,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( D = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(340,axiom,
! [A: $i] : ( c_in @ ( c_Public_OshrK @ A ) @ c_Message_OsymKeys @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK_AX_A_58_AsymKeys_0) ).
thf(1145,plain,
! [A: $i] : ( c_in @ ( c_Public_OshrK @ A ) @ c_Message_OsymKeys @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_ONonce @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_ANonce_AN_A_61_61_62_AR_0) ).
thf(1018,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_ONonce @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(179,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= A )
| ( ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff2_0) ).
thf(776,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= A )
| ( ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(80,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).
thf(525,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
!= ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(154,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( c_Relation_Oconverse @ E @ C @ D ) @ ( tc_prod @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).
thf(712,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( c_Relation_Oconverse @ E @ C @ D ) @ ( tc_prod @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).
thf(690,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_union @ A @ B @ C )
!= c_emptyset )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__6__iff1_0) ).
thf(887,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_ONotes @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(264,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( C = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1__iff1_2) ).
thf(971,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( C = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(255,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Oanalz__spies__pubK_0) ).
thf(954,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OHash @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_AHash_AZ_A_61_61_62_AR_0) ).
thf(739,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OHash @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).
thf(580,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(215,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth_0) ).
thf(855,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(306,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OAgent @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_AAgent_AA_A_61_61_62_AR_0) ).
thf(1070,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OAgent @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(222,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
| ( A
= ( c_Pair @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
thf(872,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_prod @ D @ C ) )
| ( A
= ( c_Pair @ ( c_Main_OconverseE__2 @ B @ A @ C @ D ) @ ( c_Main_OconverseE__1 @ B @ A @ C @ D ) @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
thf(1053,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
| ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(17,axiom,
! [A: $i] :
( c_List_Olist_ONil
= ( c_List_Orev @ c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv__iff2_0) ).
thf(370,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( c_List_Orev @ c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ B @ A ) ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__privateKey_0) ).
thf(840,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ B @ A ) ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(313,axiom,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__4__iff1_0) ).
thf(1085,plain,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__analzD__dest_0) ).
thf(808,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(236,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( C
= ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair__iff1_0) ).
thf(907,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OMPair @ C @ D ) )
| ( C
= ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Datatype_Ooption_OSome @ A @ B )
!= ( c_Datatype_Ooption_OSome @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).
thf(744,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Datatype_Ooption_OSome @ A @ B )
!= ( c_Datatype_Ooption_OSome @ C @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ A @ C )
= ( c_insert @ B @ c_emptyset @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).
thf(703,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_insert @ B @ c_emptyset @ C ) @ ( tc_set @ C ) )
| ( ( c_insert @ B @ A @ C )
= ( c_insert @ B @ c_emptyset @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).
thf(1141,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(284,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ G ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent )
| ( E = G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_Ounique__NB__dest_1) ).
thf(1023,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ G ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent )
| ( E = G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(296,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ A @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__in__knows_0) ).
thf(1052,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ A @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).
thf(727,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ A @ B @ C ) )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(98,axiom,
! [B: $i,A: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).
thf(571,plain,
! [B: $i,A: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(115,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ B @ ( c_Relation_OImage @ E @ ( c_insert @ A @ c_emptyset @ C ) @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).
thf(612,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ( c_in @ B @ ( c_Relation_OImage @ E @ ( c_insert @ A @ c_emptyset @ C ) @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(69,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
thf(497,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(210,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OAgent_0) ).
thf(845,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( A = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).
thf(627,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( A = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).
thf(450,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_union @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(91,axiom,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).
thf(556,plain,
! [A: $i] :
( ( c_union @ c_emptyset @ c_emptyset @ A )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(245,axiom,
! [B: $i,A: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ A @ B ) @ ( tc_List_Olist @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
thf(931,plain,
! [B: $i,A: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ A @ B ) @ ( tc_List_Olist @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
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_in @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) )
| ( c_in @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ c_Finite__Set_OFinites @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(144,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).
thf(688,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Oacyclic @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ ( c_insert @ B @ C @ D ) @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).
thf(495,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_minus @ A @ ( c_insert @ B @ C @ D ) @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) )
| ( c_in @ ( c_minus @ A @ C @ ( tc_set @ D ) ) @ c_Finite__Set_OFinites @ ( tc_set @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OMPair_0) ).
thf(759,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ~ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(324,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Sum__Type_OInl @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ B @ E @ C @ D ) @ ( tc_sum @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
thf(1108,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( c_Sum__Type_OInl @ A @ C @ D ) @ ( c_Sum__Type_OPlus @ B @ E @ C @ D ) @ ( tc_sum @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(106,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
thf(588,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(260,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ( c_in @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
thf(963,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ( c_in @ ( c_Main_OImageE__1 @ C @ A @ B @ D @ E ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(302,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ~ ( c_in @ D @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ D @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).
thf(1062,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ~ ( c_in @ D @ ( c_Inter @ B @ C ) @ C )
| ( c_in @ D @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(321,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__partsD__dest_0) ).
thf(1101,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(3,negated_conjecture,
( v_NB
= ( c_Message_Omsg_ONonce @ v_NBa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_10) ).
thf(351,plain,
( v_NB
= ( c_Message_Omsg_ONonce @ v_NBa ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(181,axiom,
~ ( c_in @ c_Message_Oagent_OServer @ c_Event_Obad @ tc_Message_Oagent ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OServer_A_58_Abad_A_61_61_62_AR_0) ).
thf(781,plain,
~ ( c_in @ c_Message_Oagent_OServer @ c_Event_Obad @ tc_Message_Oagent ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(259,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OAgent @ F ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_Ono__nonce__OR1__OR2__dest_0) ).
thf(961,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OAgent @ F ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
| ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OBody__dest_0) ).
thf(813,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_OinitState @ C ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__in__initState_0) ).
thf(896,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_OinitState @ C ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ A @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
thf(748,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Union @ B @ C ) @ C )
| ( c_in @ A @ ( c_Main_OUnionE__1 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( c_lessequals @ D @ ( c_insert @ A @ c_emptyset @ B ) @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).
thf(568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ c_emptyset @ B )
!= ( c_insert @ C @ D @ B ) )
| ( c_lessequals @ D @ ( c_insert @ A @ c_emptyset @ B ) @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(21,axiom,
! [A: $i] :
( ( c_List_Orev @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv__iff2_0) ).
thf(378,plain,
! [A: $i] :
( ( c_List_Orev @ c_List_Olist_ONil @ A )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(134,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( A
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) )
| ( A
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
thf(667,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Sum__Type_OPlus @ B @ C @ D @ E ) @ ( tc_sum @ D @ E ) )
| ( A
= ( c_Sum__Type_OInl @ ( c_Main_OPlusE__1 @ B @ A @ D @ E ) @ D @ E ) )
| ( A
= ( c_Sum__Type_OInr @ ( c_Main_OPlusE__2 @ C @ A @ E @ D ) @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(244,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OMPair__used_1) ).
thf(929,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(9,negated_conjecture,
v_B = v_Ba,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(346,plain,
v_B = v_Ba,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).
thf(549,plain,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ A @ B @ C ) @ A @ C )
| ( c_in @ B @ ( c_List_Olists @ A @ C ) @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
thf(832,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ A @ B @ C ) @ A @ C )
| ( c_in @ B @ ( c_List_Olists @ A @ C ) @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(141,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
thf(684,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OgreaterThanLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Sum__Type_OInl @ A @ B @ C )
!= ( c_Sum__Type_OInl @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).
thf(716,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Sum__Type_OInl @ A @ B @ C )
!= ( c_Sum__Type_OInl @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(188,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
thf(800,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(335,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( D
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ E @ D @ A @ B @ C ) @ ( c_Main_Olistrel__Cons1__2 @ E @ D @ A @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).
thf(1133,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_List_Olistrel @ E @ C ) @ ( tc_prod @ ( tc_List_Olist @ C ) @ ( tc_List_Olist @ C ) ) )
| ( D
= ( c_List_Olist_OCons @ ( c_Main_Olistrel__Cons1__1 @ E @ D @ A @ B @ C ) @ ( c_Main_Olistrel__Cons1__2 @ E @ D @ A @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(170,axiom,
! [A: $i] :
( c_Message_Oagent_OServer
!= ( c_Message_Oagent_OFriend @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__1__iff1_0) ).
thf(752,plain,
! [A: $i] :
( c_Message_Oagent_OServer
!= ( c_Message_Oagent_OFriend @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_insert @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
thf(432,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_insert @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(319,axiom,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
thf(1097,plain,
! [B: $i,A: $i] :
( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
| ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(185,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2__iff1_0) ).
thf(790,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(219,axiom,
! [B: $i,A: $i] :
( ( ( c_Public_OshrK @ A )
!= ( c_Public_OshrK @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__injective__iff1_0) ).
thf(865,plain,
! [B: $i,A: $i] :
( ( ( c_Public_OshrK @ A )
!= ( c_Public_OshrK @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn0 @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).
thf(410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Datatype__Universe_OIn1 @ A @ B @ C )
!= ( c_Datatype__Universe_OIn0 @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz__iff1_1) ).
thf(967,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
| ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(240,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_1) ).
thf(918,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(5,negated_conjecture,
! [A: $i] :
~ ( c_in @ ( c_Event_Oevent_OSays @ v_Ba @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Ba ) @ ( c_Message_Omsg_OMPair @ A @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NBa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OAgent @ v_Ba ) ) ) ) ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_12) ).
thf(341,plain,
! [A: $i] :
~ ( c_in @ ( c_Event_Oevent_OSays @ v_Ba @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Ba ) @ ( c_Message_Omsg_OMPair @ A @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NBa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_OAgent @ v_Ba ) ) ) ) ) ) ) ) ) ) @ ( c_List_Oset @ v_evs3 @ tc_Event_Oevent ) @ tc_Event_Oevent ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OKey @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X_93_AY_A_61_AKey_AK_A_61_61_62_AR_0) ).
thf(897,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Message_OHPair @ A @ B )
!= ( c_Message_Omsg_OKey @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).
thf(664,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_append @ A @ B @ C )
!= c_List_Olist_ONil )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(203,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OKey @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4__iff1_0) ).
thf(828,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Omsg_OKey @ A )
!= ( c_Message_Omsg_OKey @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(304,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OGets @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__1__iff1_0) ).
thf(1065,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OGets @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(157,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( B = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).
thf(720,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Datatype__Universe_OScons @ A @ B @ C @ D )
!= ( c_Datatype__Universe_OScons @ E @ F @ C @ D ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
thf(955,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_Odiag @ B @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Main_OdiagE__1 @ B @ A @ C ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7__iff1_0) ).
thf(796,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Omsg_OCrypt @ A @ B )
!= ( c_Message_Omsg_OCrypt @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).
thf(464,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Pow @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(333,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
| ( c_in @ ( c_Pair @ A @ ( c_Main_ODomainE__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
thf(1129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
| ( c_in @ ( c_Pair @ A @ ( c_Main_ODomainE__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(217,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ~ ( c_in @ D @ ( c_List_Oset @ A @ C ) @ C )
| ( c_in @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
thf(860,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
| ~ ( c_in @ D @ ( c_List_Oset @ A @ C ) @ C )
| ( c_in @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).
thf(596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ B @ A @ C ) )
| ( B = c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff1_0) ).
thf(528,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_append @ B @ A @ C ) )
| ( B = c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(126,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).
thf(644,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(272,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth__synthD__dest_0) ).
thf(992,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(213,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).
thf(850,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(277,axiom,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) )
| ( ( c_List_Oremdups @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff1_0) ).
thf(1004,plain,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) )
| ( ( c_List_Oremdups @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(46,axiom,
! [A: $i] :
( ( c_Message_Oagent_OFriend @ A )
!= c_Message_Oagent_OSpy ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__5__iff1_0) ).
thf(442,plain,
! [A: $i] :
( ( c_Message_Oagent_OFriend @ A )
!= c_Message_Oagent_OSpy ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) )
!= ( c_Public_OpublicKey @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OprivateKey_Ab_AA_A_61_ApublicKey_Ac_AA_H_A_61_61_62_AR_0) ).
thf(501,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) )
!= ( c_Public_OpublicKey @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(16,axiom,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(369,plain,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(317,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
thf(1093,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_set @ B ) ) )
| ~ ( c_in @ ( c_Main_Ofinite__Union__1 @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_Union @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff2_0) ).
thf(395,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(4,negated_conjecture,
v_K = v_KAB,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_11) ).
thf(354,plain,
v_K = v_KAB,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(279,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OKey__synth_0) ).
thf(1009,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(131,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( c_lessequals @ B @ ( c_insert @ D @ c_emptyset @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).
thf(659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_insert @ A @ B @ C )
!= ( c_insert @ D @ c_emptyset @ C ) )
| ( c_lessequals @ B @ ( c_insert @ D @ c_emptyset @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(86,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ B @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).
thf(543,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Datatype__Universe_Odprod @ B @ C @ D @ E ) @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) )
| ( c_in @ ( c_Pair @ ( c_Main_OdprodE__1 @ A @ B @ C @ D @ E ) @ ( c_Main_OdprodE__3 @ A @ B @ C @ D @ E ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) @ B @ ( tc_prod @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) @ ( tc_set @ ( tc_Datatype__Universe_Onode @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Sum__Type_OInr @ A @ B @ C )
!= ( c_Sum__Type_OInl @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).
thf(560,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Sum__Type_OInr @ A @ B @ C )
!= ( c_Sum__Type_OInl @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
| ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ A @ B @ D @ C ) @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
thf(755,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
| ( c_in @ ( c_Pair @ ( c_Main_ORangeE__1 @ A @ B @ D @ C ) @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(51,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
thf(454,plain,
! [B: $i,A: $i] : ( c_in @ ( c_SetInterval_OatLeastLessThan @ A @ B @ tc_nat ) @ c_Finite__Set_OFinites @ ( tc_set @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(281,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2__iff1_1) ).
thf(1014,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).
thf(491,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Relation_Oconverse @ A @ B @ C ) @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ C @ B ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(314,axiom,
! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(1088,plain,
! [B: $i,A: $i] : ( c_in @ A @ c_UNIV @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(1954,plain,
$false,
inference(e,[status(thm)],[892,1036,479,347,846,1031,518,941,1110,352,1083,468,977,582,730,1068,994,1073,1041,878,440,655,511,614,677,384,472,698,913,945,538,670,1127,417,1046,565,1095,404,389,785,372,504,934,1059,949,1055,724,619,838,802,344,881,1115,448,817,902,421,870,969,606,591,937,806,353,821,1136,834,348,574,905,480,397,734,507,602,981,1119,774,452,380,439,761,810,534,714,1047,1057,910,1091,1021,952,429,815,957,894,862,349,407,693,630,916,484,625,522,461,493,1079,757,710,842,1106,852,435,1089,1143,1121,1064,725,980,1138,869,783,857,742,578,884,488,637,1039,547,706,686,1075,622,1099,701,515,1131,984,1002,779,605,343,938,633,541,765,558,674,1026,662,926,794,586,1103,824,375,965,750,584,819,975,423,1007,402,732,772,875,1124,545,413,641,391,445,572,787,498,466,804,947,350,672,900,1117,736,567,599,1011,419,377,990,996,649,1043,434,890,477,609,594,1029,769,1112,811,387,345,367,552,848,700,520,932,1061,685,399,959,827,695,455,986,563,1000,505,653,922,1034,675,426,531,680,927,648,1081,617,342,823,836,1049,473,1076,1145,1018,776,525,712,690,887,971,954,739,580,855,1070,872,1053,370,840,1085,808,907,744,703,1141,1023,1052,727,571,612,497,845,627,450,556,931,482,688,495,759,1108,588,963,1062,1101,351,781,961,813,896,748,568,378,667,929,346,549,832,684,716,800,1133,752,432,1097,790,865,410,967,918,341,897,664,828,1065,720,955,796,464,1129,860,596,528,644,459,992,850,1004,442,501,369,1093,395,354,1009,659,543,560,755,454,1014,491,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV311-1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n018.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 19 02:38:29 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.86/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.87/1.10 % [INFO] Parsing done (259ms).
% 1.87/1.11 % [INFO] Running in sequential loop mode.
% 2.37/1.32 % [INFO] eprover registered as external prover.
% 2.37/1.32 % [INFO] cvc4 registered as external prover.
% 2.37/1.32 % [INFO] Scanning for conjecture ...
% 2.80/1.45 % [INFO] Found a conjecture and 1475 axioms. Running axiom selection ...
% 3.35/1.58 % [INFO] Axiom selection finished. Selected 326 axioms (removed 1149 axioms).
% 3.80/1.69 % [INFO] Problem is propositional (TPTP CNF).
% 3.96/1.70 % [INFO] Type checking passed.
% 3.96/1.70 % [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 ...
% 18.54/4.25 % External prover 'e' found a proof!
% 18.54/4.25 % [INFO] Killing All external provers ...
% 18.54/4.26 % Time passed: 3741ms (effective reasoning time: 3145ms)
% 18.54/4.26 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 18.54/4.26 % Axioms used in derivation (326): cls_List_Olistrel__Cons1_0, cls_Message_Omsg_Oinject__7__iff1_0, cls_Finite__Set_Ofinite__Union_0, cls_List_Oset__empty2__iff2_0, cls_Public_Onot__symKeys__pubK__iff1_0, cls_Datatype__Universe_OuprodI_0, cls_Nat_Ole__0__eq__iff1_0, cls_Finite__Set_Ofinite__converse__iff1_0, cls_Message_Oanalz_OInj_0, cls_List_Ofinite__set_0, cls_List_Orev__is__Nil__conv__iff1_0, cls_Finite__Set_Ofinite__Un__iff1_1, cls_Datatype__Universe_OdprodE_0, cls_List_Oappend__in__lists__conv__iff2_0, cls_List_Oset__empty2__iff1_0, cls_Event_OSays__imp__analz__Spy__dest_0, cls_Public_OpublicKey__into__used_0, cls_List_ONil__notin__lex__iff1_0, cls_Relation_OImageI_0, cls_List_Olistrel__Cons2_1, cls_Public_ONonce__notin__initState__iff1_0, cls_Event_Oevent_Odistinct__3__iff1_0, cls_Message_Oanalz__analzD__dest_0, cls_Set_OsubsetI_1, cls_Sum__Type_OInr__not__Inl__iff1_0, cls_Datatype__Universe_Odsum__In0I_0, cls_List_Olength__remdups__eq__iff2_0, cls_List_Olists_ONil_0, cls_Set_OInterD_0, cls_Message_OMPair__eq__HPair__iff1_1, cls_List_ONil__is__append__conv__iff2_0, cls_Message_Osynth_OAgent_0, cls_Event_Oevent_Odistinct__1__iff1_0, cls_Sum__Type_OInr__eq__iff1_0, cls_Set_OemptyE_0, cls_Set_OUNIV__not__empty__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0, cls_Finite__Set_OFinites_OemptyI_0, cls_List_Oappend__self__conv2__iff1_0, cls_Relation_OImageE_0, cls_Event_Oevent_Oinject__3__iff1_0, cls_Message_Oagent_Odistinct__5__iff1_0, cls_Message_Oagent_Oinject__iff1_0, cls_Set_Osingleton__insert__inj__eq__iff1_1, cls_List_Orev__eq__Cons__iff__iff2_0, cls_Wellfounded__Recursion_Owf__insert__iff1_0, cls_Public_OpriK__neq__shrK__iff1_0, cls_Datatype_Ooption_Oinject__iff1_0, cls_Transitive__Closure_Otrancl_Or__into__trancl_0, cls_Message_OHPair__neqs__1__iff1_0, cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0, cls_Set_Osingleton__inject__dest_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_1, cls_Set_OUnionE_1, cls_Message_OHPair__neqs__3__iff1_0, cls_Nat_Oless__irrefl_0, cls_Event_Oevent_Oinject__1__iff1_2, cls_List_Olistrel__Nil1_0, cls_Nat_Onot__less0__iff1_0, cls_Finite__Set_OFinites_OinsertI_0, cls_Wellfounded__Relations_Owf__lex__prod_0, cls_Datatype__Universe_OIn1__eq__iff1_0, cls_Message_OMPair__synth__analz__iff1_1, cls_Public_OshrK_AX_A_58_AsymKeys_0, cls_Message_OHPair__eq__iff1_0, cls_Finite__Set_Ofinite__Int_0, cls_Message_OHash__synth_0, cls_Relation_OconverseE_1, cls_Nat_Oneq0__conv__iff2_0, cls_Sum__Type_OPlusE_0, cls_List_ONil__is__append__conv__iff1_0, cls_Relation_Orel__compE_0, cls_Finite__Set_Ofinite__Pow__iff__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1, cls_Sum__Type_OInlI_0, cls_Infinite__Set_Onat__not__finite_0, cls_Message_Osynth_OHash_0, cls_Message_OMPair__eq__HPair__iff1_0, cls_Set_OpsubsetI_0, cls_Relation_Oconverse__iff__iff2_0, cls_Set_Osubset__refl_0, cls_List_Olist_Oinject__iff1_0, cls_Message_Oagent_Odistinct__6__iff1_0, cls_Message_OHash_91X_93_AY_A_61_AAgent_AA_A_61_61_62_AR_0, cls_Relation_ORangeE_0, cls_Message_Osynth_ONumber_0, cls_Set_OInterI_1, cls_Message_Omsg_Oinject__7__iff1_1, cls_List_Oset__empty__iff2_0, cls_SetInterval_Ofinite__greaterThanAtMost_0, cls_Product__Type_OPair__eq__iff1_0, cls_Set_OinsertCI_0, cls_Message_OHash_91X_93_AY_A_61_AHash_AZ_A_61_61_62_AR_0, cls_Set_OUnCI_1, cls_Set_Osingleton__insert__inj__eq_H__iff2_0, cls_Message_Oparts_OInj_0, cls_List_Oappend__in__lists__conv__iff1_0, cls_Finite__Set_Ofinite__converse__iff2_0, cls_List_Olength__remdups__leq_0, cls_Nat_Ole__0__eq__iff2_0, cls_Relation_OdiagI_0, cls_Event_Oevent_Oinject__3__iff1_1, cls_Datatype__Universe_OIn0__not__In1__iff1_0, cls_Public_OMPair__used_1, cls_Set_OPow__iff__iff2_0, cls_Message_OHPair__eq__MPair__iff1_0, cls_Datatype__Universe_OdprodE_1, cls_Set_OUNIV__I_0, cls_Message_OCrypt__synth_1, cls_Set_OsubsetI_0, cls_Sum__Type_OPlusE_3, cls_Public_OsymKeys__invKey__iff__iff1_0, cls_Finite__Set_Ofinite__Diff__insert__iff1_0, cls_List_OlistsE_0, cls_List_Olength__0__conv__iff2_0, cls_Finite__Set_Ofinite__Un__iff1_0, cls_List_Oself__append__conv__iff2_0, cls_Relation_ODomainI_0, cls_Set_Onot__psubset__empty__iff1_0, cls_Message_Osynth_OMPair_0, cls_Set_OUnE_0, cls_List_Olistrel__Cons2_0, cls_Message_OHPair__eq__MPair__iff2_0, cls_Message_Omsg_Oinject__4__iff1_0, cls_Set_OinsertE_0, cls_Message_Oagent_Odistinct__2__iff1_0, cls_List_Owf__lex_0, cls_List_Orev__is__Nil__conv__iff2_0, cls_Set_OUn__empty__iff1_1, cls_Public_OpublicKey__inject__iff1_1, cls_Relation_Orel__compE_2, cls_Relation_OImageE_1, cls_Relation_OdiagE_0, cls_Set_OsingletonD__dest_0, cls_SetInterval_Ofinite__atLeastAtMost_0, cls_Message_Omsg_Oinject__3__iff1_0, cls_SetInterval_Ofinite__atLeastLessThan_0, cls_Set_OUn__empty__iff1_0, cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, cls_Message_OHPair__neqs__4__iff1_0, cls_Wellfounded__Recursion_Owf__insert__iff2_0, cls_Set_Oempty__subsetI_0, cls_Finite__Set_Ofinite__Int_1, cls_List_Oappend__is__Nil__conv__iff2_0, cls_Relation_OIdI_0, cls_SetInterval_Ofinite__lessThan_0, cls_List_Olength__greater__0__conv__iff1_0, cls_List_Oappend1__eq__conv__iff1_1, cls_Set_OsubsetD_0, cls_Product__Type_OPair__eq__iff1_1, cls_Event_Oevent_Oinject__2__iff1_0, cls_List_Osame__append__eq__iff1_0, cls_Set_OsingletonI_0, cls_Message_Oparts__partsD__dest_0, cls_Wellfounded__Relations_Oless__than__iff__iff1_0, cls_Set_Osubset__antisym_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0, cls_List_Oself__append__conv__iff1_0, cls_List_Oin__listsI_1, cls_List_Orev__eq__Cons__iff__iff1_0, cls_Message_Oagent_Odistinct__1__iff1_0, cls_Public_OprivateKey_Ab_AA_A_61_ApublicKey_Ac_AA_H_A_61_61_62_AR_0, cls_Datatype_Oelem__o2s__iff1_0, cls_Message_OMPair__eq__HPair__iff2_0, cls_Message_Oparts_OBody__dest_0, cls_Datatype__Universe_OuprodE_2, cls_Relation_Oconverse__iff__iff1_0, cls_Relation_OconverseE_0, cls_List_Olength__greater__0__conv__iff2_0, cls_Datatype__Universe_OIn1__not__In0__iff1_0, cls_Datatype__Universe_OScons__Scons__eq__iff1_0, cls_Datatype_Oelem__o2s__iff2_0, cls_List_Olist_Oinject__iff1_1, cls_Public_OshrK__in__used_0, cls_Message_Omsg_Oinject__5__iff1_0, cls_Datatype__Universe_OuprodE_0, cls_Public_OMPair__used_0, cls_Set_ODiffE_0, cls_Public_OshrK__in__initState_0, cls_Message_OHash_91X_93_AY_A_61_ACrypt_AK_AX_H_A_61_61_62_AR_0, cls_Sum__Type_OInl__not__Inr__iff1_0, cls_Infinite__Set_Oatmost__one__unique_0, cls_Message_OHPair__neqs__6__iff1_0, cls_Message_Oin__parts__UnE_0, cls_OtwayRees_OGets__imp__Says__dest_0, cls_Relation_ORangeI_0, cls_List_Oset__empty__iff1_0, cls_Message_Omsg_Oinject__1__iff1_0, cls_Message_OMPair__analz_1, cls_Datatype__Universe_OdprodE_2, cls_Public_OpublicKey__inject__iff1_0, cls_List_Oself__append__conv2__iff2_0, cls_Set_OIntE_1, cls_Message_OCrypt__synth_0, cls_List_Odistinct__remdups_0, cls_Finite__Set_Ofinite__Union_1, cls_Message_Omsg_Oinject__2__iff1_0, cls_Event_Oevent_Oinject__1__iff1_0, cls_Relation_Opair__in__Id__conv__iff1_0, cls_Set_OIntI_0, cls_Message_OHash_91X_93_AY_A_61_AKey_AK_A_61_61_62_AR_0, cls_Sum__Type_OPlusE_2, cls_Set_Osingleton__insert__inj__eq__iff2_0, cls_Wellfounded__Relations_Oless__than__iff__iff2_0, cls_Message_Omsg_Oinject__6__iff1_0, cls_Public_Oanalz__spies__pubK_0, cls_Wellfounded__Relations_Owf__less__than_0, cls_List_Olist_Odistinct__2__iff1_0, cls_Transitive__Closure_Or__into__rtrancl_0, cls_Finite__Set_Ofinite__Diff__insert__iff2_0, cls_Public_Onot__symKeys__priK__iff1_0, cls_Event_Oevent_Odistinct__5__iff1_0, cls_Message_OMPair__parts_1, cls_Wellfounded__Recursion_Owf__empty_0, cls_Message_OMPair__synth__analz__iff1_0, cls_Message_Osynth_OCrypt_0, cls_Datatype__Universe_OdprodI_0, cls_Message_Oagent_Odistinct__4__iff1_0, cls_SetInterval_Ofinite__greaterThanLessThan_0, cls_Message_Osynth__synthD__dest_0, cls_List_Olistrel__Cons1_2, cls_List_OlistsE_1, cls_List_Oappend__self__conv2__iff2_0, cls_Public_OSpy__spies__bad__shrK_0, cls_List_Oappend__self__conv__iff2_0, cls_Set_OUn__empty__iff2_0, cls_List_Oappend__same__eq__iff1_0, cls_OtwayRees_OCrypt__imp__OR2__dest_0, cls_Set_ODiffI_0, cls_Public_OpublicKey__neq__privateKey__iff1_0, cls_Sum__Type_OInrI_0, cls_Datatype__Universe_Odsum__In1I_0, cls_Message_ONonce__synth_0, cls_List_Orev__is__rev__conv__iff1_0, cls_Datatype__Universe_OuprodE_1, cls_Set_OpsubsetE_0, cls_Set_OUnionI_0, cls_List_Olistrel__Nil2_0, cls_Message_OHPair__neqs__5__iff1_0, cls_Relation_Orel__compI_0, cls_Finite__Set_Ofinite__Pow__iff__iff2_0, cls_List_Oappend__is__Nil__conv__iff1_0, cls_Public_OSpy__spies__bad__privateKey_0, cls_Datatype__Universe_OScons__Scons__eq__iff1_1, cls_OtwayRees_Ounique__NB__dest_1, cls_Datatype__Universe_OIn0__eq__iff1_0, cls_Event_Oevent_Oinject__2__iff1_1, cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0, cls_Message_OMPair__synth__analz__iff2_0, cls_Relation_OdiagE_1, cls_Message_Oanalz__into__parts__dest_0, cls_Relation_OImage__singleton__iff__iff1_0, cls_List_ONil2__notin__lex__iff1_0, cls_List_Oself__append__conv2__iff1_0, cls_Nat_Oneq0__conv__iff1_0, cls_Message_OMPair__synth_1, cls_Message_OHPair__eq__MPair__iff1_1, cls_List_Olist_Odistinct__1__iff1_0, cls_Public_Ospies__pubK_0, cls_Message_OHash_91X_93_AY_A_61_ANonce_AN_A_61_61_62_AR_0, cls_List_Olistrel__Cons1_1, cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0, cls_Set_OInterI_0, cls_List_Olistrel__Cons2_2, cls_Message_Osynth_OInj_0, cls_List_ONil__is__rev__conv__iff2_0, cls_Relation_ODomainE_0, cls_List_Oin__listsI_0, cls_Message_OMPair__analz_0, cls_Public_OprivateKey__into__used_0, cls_Sum__Type_OPlusE_1, cls_Event_Oevent_Odistinct__4__iff1_0, cls_Wellfounded__Recursion_Owf__insert__iff1_1, cls_Set_OUnionE_0, cls_Event_Oevent_Odistinct__6__iff1_0, cls_Message_Omsg_Oinject__6__iff1_1, cls_Message_Oagent_Odistinct__3__iff1_0, cls_Message_OFake__parts__insert__in__Un__dest_0, cls_Message_OHPair__neqs__2__iff1_0, cls_Public_OpriK__in__initState_0, cls_Message_OHPair__eq__iff1_1, cls_List_Oappend1__eq__conv__iff1_0, cls_Message_OKey__synth_0, cls_Message_Oanalz_ODecrypt__dest_0, cls_Public_OpublicKey__in__initState_0, cls_Message_OHash_91X_93_AY_A_61_ANumber_AN_A_61_61_62_AR_0, cls_OtwayRees_Ono__nonce__OR1__OR2__dest_0, cls_List_Oin__listsD__dest_0, cls_Set_OPow__iff__iff1_0, cls_Nat_Ole0_0, cls_Event_OSpy_A_58_Abad_0, cls_Set_Osingleton__insert__inj__eq__iff1_0, cls_Sum__Type_OInl__eq__iff1_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_0, cls_List_ONil__is__rev__conv__iff1_0, cls_Event_Oevent_Oinject__1__iff1_1, cls_Message_OMPair__parts_0, cls_Relation_OImage__singleton__iff__iff2_0, cls_OtwayRees_OSpy__see__shrK__D__dest_0, cls_List_Olength__0__conv__iff1_0, cls_List_Owf__lenlex_0, cls_Relation_OIdE_0, cls_Message_Oparts__emptyE_0, cls_Set_OpsubsetE_1, cls_Public_OshrK__injective__iff1_0, cls_SetInterval_Ofinite__atMost_0, cls_Set_OIntE_0, cls_OtwayRees_Ounique__NB__dest_0, cls_Relation_Orel__compE_1, cls_List_Oappend__is__Nil__conv__iff1_1, cls_Event_Oevent_Odistinct__2__iff1_0, cls_Finite__Set_Ofinite__Un__iff2_0, cls_Public_OsymKeys__invKey__iff__iff2_0, cls_List_Olength__remdups__eq__iff1_0, cls_Message_OMPair__synth_0, cls_List_Oappend__in__lists__conv__iff1_1, cls_Set_OinsertCI_1, cls_Set_ODiffE_1, cls_List_ONil__is__append__conv__iff1_1, cls_Transitive__Closure_Otrancl__into__rtrancl_0, cls_List_Oappend__self__conv__iff1_0, cls_Public_OpubK__neq__shrK__iff1_0, cls_Event_OServer_A_58_Abad_A_61_61_62_AR_0, cls_Public_OshrK__in__knows_0, cls_Set_OUnCI_0, cls_List_Olists_OCons_0
% 18.54/4.26 % No. of inferences in proof: 681
% 18.54/4.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3741 ms resp. 3145 ms w/o parsing
% 18.99/4.41 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.99/4.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------