TSTP Solution File: SWV722-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV722-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 : Thu Sep 29 15:24:14 EDT 2022
% Result : Unsatisfiable 87.85s 56.38s
% Output : Proof 88.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 117
% Syntax : Number of formulae : 272 ( 112 unt; 25 typ; 0 def)
% Number of atoms : 702 ( 179 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 771 ( 344 ~; 338 |; 0 &)
% ( 89 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 28 ( 28 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 14 >; 17 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 11 con; 0-3 aty)
% Number of variables : 798 ( 720 !; 0 ?; 798 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(c_Event_Oknows_type,type,
c_Event_Oknows: ( $i * $i ) > $i ).
tff(v_evs_type,type,
v_evs: $i ).
tff(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
tff(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(v_K_type,type,
v_K: $i ).
tff(c_Message_Omsg_OCrypt_type,type,
c_Message_Omsg_OCrypt: ( $i * $i ) > $i ).
tff(c_Message_Omsg_OMPair_type,type,
c_Message_Omsg_OMPair: ( $i * $i ) > $i ).
tff(v_X_type,type,
v_X: $i ).
tff(v_B_type,type,
v_B: $i ).
tff(v_NA_type,type,
v_NA: $i ).
tff(c_Public_OshrK_type,type,
c_Public_OshrK: $i > $i ).
tff(v_A_type,type,
v_A: $i ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
tff(c_List_Oset_type,type,
c_List_Oset: ( $i * $i ) > $i ).
tff(c_Event_Oevent_OSays_type,type,
c_Event_Oevent_OSays: ( $i * $i * $i ) > $i ).
tff(c_Message_Oagent_OServer_type,type,
c_Message_Oagent_OServer: $i ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(1,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
refl(
( ( c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)) )
<=> ( c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
tff(5,plain,
! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] : ( c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)) )
| ( c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)) = c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))) = c_Message_Oparts(c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
c_Message_Oparts(c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)) = c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
^ [V_H: $i,V_X: $i] :
refl(
( ( c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) )
<=> ( c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) )
<=> ! [V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) )
<=> ! [V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
! [V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert_0) ).
tff(17,plain,
! [V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ~ ! [V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) )
| ( c_Message_Oparts(c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs))),tc_fun(tc_Message_Omsg,tc_bool)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
c_Message_Oparts(c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs))),tc_fun(tc_Message_Omsg,tc_bool)),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs))),tc_fun(tc_Message_Omsg,tc_bool)) = c_Message_Oparts(c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
^ [V_H: $i] :
refl(
( ( c_Message_Oparts(c_Message_Oparts(V_H)) = c_Message_Oparts(V_H) )
<=> ( c_Message_Oparts(c_Message_Oparts(V_H)) = c_Message_Oparts(V_H) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [V_H: $i] : ( c_Message_Oparts(c_Message_Oparts(V_H)) = c_Message_Oparts(V_H) )
<=> ! [V_H: $i] : ( c_Message_Oparts(c_Message_Oparts(V_H)) = c_Message_Oparts(V_H) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [V_H: $i] : ( c_Message_Oparts(c_Message_Oparts(V_H)) = c_Message_Oparts(V_H) )
<=> ! [V_H: $i] : ( c_Message_Oparts(c_Message_Oparts(V_H)) = c_Message_Oparts(V_H) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
! [V_H: $i] : ( c_Message_Oparts(c_Message_Oparts(V_H)) = c_Message_Oparts(V_H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__idem_0) ).
tff(27,plain,
! [V_H: $i] : ( c_Message_Oparts(c_Message_Oparts(V_H)) = c_Message_Oparts(V_H) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [V_H: $i] : ( c_Message_Oparts(c_Message_Oparts(V_H)) = c_Message_Oparts(V_H) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [V_H: $i] : ( c_Message_Oparts(c_Message_Oparts(V_H)) = c_Message_Oparts(V_H) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ~ ! [V_H: $i] : ( c_Message_Oparts(c_Message_Oparts(V_H)) = c_Message_Oparts(V_H) )
| ( c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs))) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs))) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs))),tc_fun(tc_Message_Omsg,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs))),tc_fun(tc_Message_Omsg,tc_bool)),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
( ~ ! [V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) )
| ( c_Message_Oparts(c_Set_Oinsert(v_K,c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
c_Message_Oparts(c_Set_Oinsert(v_K,c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(unit_resolution,[status(thm)],[34,19]) ).
tff(36,plain,
( c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
<=> c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(38,plain,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
^ [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
refl(
( ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
<=> ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
^ [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
rewrite(
( ( c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__spies_0) ).
tff(45,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg) )
<=> ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[51,48,38]) ).
tff(53,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
refl(
( ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
<=> ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
rewrite(
( ( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) )
<=> ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,axiom,
! [V_a: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
tff(59,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[61,54]) ).
tff(63,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg)
| ( c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg) = c_Event_Oknows(c_Message_Oagent_OSpy,v_evs) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg)
| ( c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg) = c_Event_Oknows(c_Message_Oagent_OSpy,v_evs) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg)
| ( c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg) = c_Event_Oknows(c_Message_Oagent_OSpy,v_evs) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg)
| ( c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg) = c_Event_Oknows(c_Message_Oagent_OSpy,v_evs) ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg) = c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),
inference(unit_resolution,[status(thm)],[65,62,52]) ).
tff(67,plain,
c_Set_Oinsert(v_K,c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg),tc_Message_Omsg) = c_Set_Oinsert(v_K,c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
c_Set_Oinsert(v_K,c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg) = c_Set_Oinsert(v_K,c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg),tc_Message_Omsg),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
c_Message_Oparts(c_Set_Oinsert(v_K,c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg)) = c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg),tc_Message_Omsg)),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg),tc_Message_Omsg)) = c_Message_Oparts(c_Set_Oinsert(v_K,c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg)),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
^ [V_Y: $i,V_H: $i,V_X: $i] :
refl(
( ( c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(V_Y,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) )
<=> ( c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(V_Y,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(V_Y,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(V_Y,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(V_Y,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(V_Y,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,axiom,
! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(V_Y,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert2_0) ).
tff(75,plain,
! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(V_Y,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(V_Y,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(V_Y,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(V_Y,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) )
| ( c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg),tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg),tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(unit_resolution,[status(thm)],[78,77]) ).
tff(80,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)) = c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg),tc_Message_Omsg)),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
^ [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
refl(
( ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
^ [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
rewrite(
( ( c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(85,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,axiom,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__parts__knows__Spy_0) ).
tff(87,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[89,82]) ).
tff(91,plain,
( ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) )
<=> ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[93,90,38]) ).
tff(95,plain,
^ [V_H: $i,V_X: $i,V_K: $i] :
refl(
( ( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
( ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,axiom,
! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts_OBody_0) ).
tff(99,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ( c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) )
<=> ( ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
| c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ) ),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
| c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ) ),
inference(transitivity,[status(thm)],[104,102]) ).
tff(106,plain,
( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
| c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[107,101,94]) ).
tff(109,plain,
^ [V_Y: $i,V_H: $i,V_X: $i] :
refl(
( ( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(110,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,axiom,
! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts_OSnd_0) ).
tff(113,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) )
<=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ( c_in(c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) )
<=> ( ~ c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) )
| c_in(c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) )
<=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ) ),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) )
| c_in(c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) )
<=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ) ),
inference(transitivity,[status(thm)],[118,116]) ).
tff(120,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) )
| c_in(c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
c_in(c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[121,115,108]) ).
tff(123,plain,
( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) )
| c_in(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) )
<=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) )
| c_in(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) )
| c_in(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) )
| c_in(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
c_in(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[125,115,122]) ).
tff(127,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ( c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ( c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ( c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ( c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)) ) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
( ~ c_in(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ( c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)) ) ),
inference(unit_resolution,[status(thm)],[129,62]) ).
tff(131,plain,
c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),
inference(unit_resolution,[status(thm)],[130,126]) ).
tff(132,plain,
c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)) = c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
^ [V_a: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) )
<=> ( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(136,plain,
( ! [V_a: $i,T_a: $i,V_B: $i,V_A: $i] : ( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) )
<=> ! [V_a: $i,T_a: $i,V_B: $i,V_A: $i] : ( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,plain,
( ! [V_a: $i,T_a: $i,V_B: $i,V_A: $i] : ( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) )
<=> ! [V_a: $i,T_a: $i,V_B: $i,V_A: $i] : ( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(138,axiom,
! [V_a: $i,T_a: $i,V_B: $i,V_A: $i] : ( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
tff(139,plain,
! [V_a: $i,T_a: $i,V_B: $i,V_A: $i] : ( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
! [V_a: $i,T_a: $i,V_B: $i,V_A: $i] : ( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
inference(skolemize,[status(sab)],[139]) ).
tff(141,plain,
! [V_a: $i,T_a: $i,V_B: $i,V_A: $i] : ( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
inference(modus_ponens,[status(thm)],[140,136]) ).
tff(142,plain,
( ~ ! [V_a: $i,T_a: $i,V_B: $i,V_A: $i] : ( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) )
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)) = c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)) = c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[142,141]) ).
tff(144,plain,
c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
^ [V_N: $i,V_KA: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
refl(
( ( ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(146,plain,
( ! [V_N: $i,V_KA: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ! [V_N: $i,V_KA: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,plain,
( ! [V_N: $i,V_KA: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ! [V_N: $i,V_KA: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(148,plain,
^ [V_N: $i,V_KA: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
rewrite(
( ( c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(149,plain,
( ! [V_N: $i,V_KA: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ! [V_N: $i,V_KA: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[148]) ).
tff(150,axiom,
! [V_N: $i,V_KA: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NS3__msg__in__parts__spies_0) ).
tff(151,plain,
! [V_N: $i,V_KA: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
! [V_N: $i,V_KA: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[151,147]) ).
tff(153,plain,
! [V_N: $i,V_KA: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[152]) ).
tff(154,plain,
! [V_N: $i,V_KA: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[153,146]) ).
tff(155,plain,
( ( ~ ! [V_N: $i,V_KA: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) )
<=> ( ~ ! [V_N: $i,V_KA: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(156,plain,
( ~ ! [V_N: $i,V_KA: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(157,plain,
( ~ ! [V_N: $i,V_KA: $i,V_S: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[157,154,38]) ).
tff(159,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
refl(
( ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) )
<=> ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ) )),
inference(bind,[status(th)],]) ).
tff(160,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ) ),
inference(quant_intro,[status(thm)],[159]) ).
tff(161,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(162,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
rewrite(
( ( ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) )
<=> ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ) )),
inference(bind,[status(th)],]) ).
tff(163,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ) ),
inference(quant_intro,[status(thm)],[162]) ).
tff(164,axiom,
! [V_a: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
tff(165,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[165,161]) ).
tff(167,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ),
inference(skolemize,[status(sab)],[166]) ).
tff(168,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[167,160]) ).
tff(169,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) )
| ~ c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ( c_Set_Oinsert(v_X,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),c_Set_Oinsert(v_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) )
| ~ c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ( c_Set_Oinsert(v_X,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),c_Set_Oinsert(v_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(170,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) )
| ~ c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ( c_Set_Oinsert(v_X,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),c_Set_Oinsert(v_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ) )
| ~ c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ( c_Set_Oinsert(v_X,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),c_Set_Oinsert(v_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)) ) ),
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
c_Set_Oinsert(v_X,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),c_Set_Oinsert(v_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),
inference(unit_resolution,[status(thm)],[171,168,158]) ).
tff(173,plain,
c_Set_Oinsert(v_K,c_Set_Oinsert(v_X,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),c_Set_Oinsert(v_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_Message_Omsg) = c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(v_X,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),c_Set_Oinsert(v_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_Message_Omsg)) = c_Message_Oparts(c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
c_Message_Oparts(c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)) = c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(v_X,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),c_Set_Oinsert(v_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_Message_Omsg)),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)) = c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(v_X,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),c_Set_Oinsert(v_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_Message_Omsg)),
inference(transitivity,[status(thm)],[80,70,35,33,22,175]) ).
tff(177,plain,
c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) = c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(v_X,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),c_Set_Oinsert(v_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(v_X,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),c_Set_Oinsert(v_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) = c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_B,c_Message_Omsg_OMPair(v_K,v_X)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ( c_Set_Oinsert(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ( c_Set_Oinsert(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(180,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ( c_Set_Oinsert(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(181,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ( c_Set_Oinsert(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)) ) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
c_Set_Oinsert(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),
inference(unit_resolution,[status(thm)],[181,62,158]) ).
tff(183,plain,
c_Set_Oinsert(v_K,c_Set_Oinsert(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),tc_Message_Omsg) = c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),tc_Message_Omsg)) = c_Message_Oparts(c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
c_Message_Oparts(c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)) = c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),tc_Message_Omsg)),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(v_X,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),c_Set_Oinsert(v_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_Message_Omsg)) = c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),tc_Message_Omsg)),
inference(transitivity,[status(thm)],[174,185]) ).
tff(187,plain,
c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(v_X,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),c_Set_Oinsert(v_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) = c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) = c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(v_X,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),c_Set_Oinsert(v_X,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
^ [V_Y: $i,V_H: $i,V_X: $i] :
refl(
( ( c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) )
<=> ( c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(190,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[189]) ).
tff(191,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(192,axiom,
! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__MPair_0) ).
tff(193,plain,
! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[193]) ).
tff(195,plain,
! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[194,190]) ).
tff(196,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] : ( c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) )
| ( c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(197,plain,
c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Set_Oinsert(v_K,c_Set_Oinsert(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[196,195]) ).
tff(198,plain,
c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)) = c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs))),
inference(monotonicity,[status(thm)],[131]) ).
tff(199,plain,
c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs))) = c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OMPair(v_K,v_X),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)),
inference(symmetry,[status(thm)],[198]) ).
tff(200,plain,
c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)) = c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs))),
inference(symmetry,[status(thm)],[31]) ).
tff(201,plain,
c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)) = c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))),
inference(transitivity,[status(thm)],[200,199,197,188,178,144,134,80,70,35,33,22,12]) ).
tff(202,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))
<=> c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))),tc_fun(tc_Message_Omsg,tc_bool))
<=> c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
^ [V_H: $i] :
refl(
( c_lessequals(V_H,c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool))
<=> c_lessequals(V_H,c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) )),
inference(bind,[status(th)],]) ).
tff(205,plain,
( ! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool))
<=> ! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(quant_intro,[status(thm)],[204]) ).
tff(206,plain,
( ! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool))
<=> ! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(rewrite,[status(thm)],]) ).
tff(207,axiom,
! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__increasing_0) ).
tff(208,plain,
! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),
inference(modus_ponens,[status(thm)],[207,206]) ).
tff(209,plain,
! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),
inference(skolemize,[status(sab)],[208]) ).
tff(210,plain,
! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)),
inference(modus_ponens,[status(thm)],[209,205]) ).
tff(211,plain,
( ~ ! [V_H: $i] : c_lessequals(V_H,c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(quant_inst,[status(thm)],]) ).
tff(212,plain,
c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))),tc_fun(tc_Message_Omsg,tc_bool)),
inference(unit_resolution,[status(thm)],[211,210]) ).
tff(213,plain,
c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(modus_ponens,[status(thm)],[212,203]) ).
tff(214,plain,
( c_in(v_K,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)
<=> c_in(v_K,c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),tc_Message_Omsg) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(215,plain,
( c_in(v_K,c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),tc_Message_Omsg)
<=> c_in(v_K,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) ),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
^ [V_x: $i,T_a: $i,V_B: $i] :
refl(
( c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)
<=> c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a) )),
inference(bind,[status(th)],]) ).
tff(217,plain,
( ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)
<=> ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a) ),
inference(quant_intro,[status(thm)],[216]) ).
tff(218,plain,
( ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)
<=> ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a) ),
inference(rewrite,[status(thm)],]) ).
tff(219,axiom,
! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
tff(220,plain,
! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a),
inference(modus_ponens,[status(thm)],[219,218]) ).
tff(221,plain,
! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a),
inference(skolemize,[status(sab)],[220]) ).
tff(222,plain,
! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a),
inference(modus_ponens,[status(thm)],[221,217]) ).
tff(223,plain,
( ~ ! [V_x: $i,T_a: $i,V_B: $i] : c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)
| c_in(v_K,c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(224,plain,
c_in(v_K,c_Set_Oinsert(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[223,222]) ).
tff(225,plain,
c_in(v_K,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[224,215]) ).
tff(226,plain,
( ~ c_in(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
<=> ~ c_in(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],]) ).
tff(227,axiom,
~ c_in(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(228,plain,
~ c_in(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[227,226]) ).
tff(229,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(230,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) ) ),
inference(quant_intro,[status(thm)],[229]) ).
tff(231,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(232,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
trans(
monotonicity(
rewrite(
( ( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) )
<=> ( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) ) )),
( ( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) )),
rewrite(
( ( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) ) )),
( ( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(233,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) ) ),
inference(quant_intro,[status(thm)],[232]) ).
tff(234,axiom,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
tff(235,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) ),
inference(modus_ponens,[status(thm)],[234,233]) ).
tff(236,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) ),
inference(modus_ponens,[status(thm)],[235,231]) ).
tff(237,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) ),
inference(skolemize,[status(sab)],[236]) ).
tff(238,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) ),
inference(modus_ponens,[status(thm)],[237,230]) ).
tff(239,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) )
| c_in(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(v_K,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) )
| c_in(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(v_K,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(240,plain,
( ( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(v_K,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)
| c_in(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) )
<=> ( c_in(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(v_K,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(241,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) )
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(v_K,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)
| c_in(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) )
| c_in(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(v_K,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) ) ),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) )
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(v_K,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)
| c_in(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) )
| c_in(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(v_K,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) ) ),
inference(transitivity,[status(thm)],[241,239]) ).
tff(243,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) )
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(v_K,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)
| c_in(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(244,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) )
| c_in(v_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(v_K,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[243,242]) ).
tff(245,plain,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(v_K,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg) ),
inference(unit_resolution,[status(thm)],[244,238,228]) ).
tff(246,plain,
~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_K,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(unit_resolution,[status(thm)],[245,225]) ).
tff(247,plain,
$false,
inference(unit_resolution,[status(thm)],[246,213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV722-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 07:32:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 87.85/56.38 % SZS status Unsatisfiable
% 87.85/56.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------