%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV727-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 : Sat Jun 21 05:35:59 AM UTC 2025
% Result : Unsatisfiable 177.45s 177.78s
% Output : Proof 177.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 53
% Syntax : Number of formulae : 130 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 454 ( 79 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 531 ( 224 ~; 252 |; 0 &)
% ( 55 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-3 aty)
% Number of variables : 234 ( 211 !; 0 ?; 234 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
tff(c_Event_Oknows_type,type,
c_Event_Oknows: ( $i * $i ) > $i ).
tff(v_evsf_type,type,
v_evsf: $i ).
tff(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Message_OinvKey_type,type,
c_Message_OinvKey: $i > $i ).
tff(v_K_type,type,
v_K: $i ).
tff(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Message_OsymKeys_type,type,
c_Message_OsymKeys: $i ).
tff(c_Event_Oused_type,type,
c_Event_Oused: $i > $i ).
tff(c_Message_OkeysFor_type,type,
c_Message_OkeysFor: $i > $i ).
tff(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(class_Lattices_Oupper__semilattice_type,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
tff(c_Message_Osynth_type,type,
c_Message_Osynth: $i > $i ).
tff(v_X_type,type,
v_X: $i ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(1,plain,
^ [V_H: $i] :
refl(( ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) )
<=> ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) )
<=> ! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) )
<=> ! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__analz_0) ).
tff(5,plain,
! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) )
| ( c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( c_in(v_K,c_Message_OsymKeys,tc_nat)
<=> c_in(v_K,c_Message_OsymKeys,tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
c_in(v_K,c_Message_OsymKeys,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(12,plain,
c_in(v_K,c_Message_OsymKeys,tc_nat),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [V_K: $i] :
refl(( ( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_K) = V_K ) )
<=> ( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_K) = V_K ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V_K: $i] :
( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_K) = V_K ) )
<=> ! [V_K: $i] :
( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_K) = V_K ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [V_K: $i] :
( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_K) = V_K ) )
<=> ! [V_K: $i] :
( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_K) = V_K ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
^ [V_K: $i] :
rewrite(( ( ( c_Message_OinvKey(V_K) = V_K )
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) )
<=> ( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_K) = V_K ) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [V_K: $i] :
( ( c_Message_OinvKey(V_K) = V_K )
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) )
<=> ! [V_K: $i] :
( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_K) = V_K ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [V_K: $i] :
( ( c_Message_OinvKey(V_K) = V_K )
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__K_0) ).
tff(19,plain,
! [V_K: $i] :
( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_K) = V_K ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_K: $i] :
( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_K) = V_K ) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [V_K: $i] :
( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_K) = V_K ) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [V_K: $i] :
( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_K) = V_K ) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [V_K: $i] :
( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_K) = V_K ) )
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(v_K) = v_K ) )
<=> ( ~ ! [V_K: $i] :
( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_K) = V_K ) )
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(v_K) = v_K ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [V_K: $i] :
( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_K) = V_K ) )
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(v_K) = v_K ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [V_K: $i] :
( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_K) = V_K ) )
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(v_K) = v_K ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
c_Message_OinvKey(v_K) = v_K,
inference(unit_resolution,[status(thm)],[25,22,12]) ).
tff(27,plain,
hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)) = hAPP(c_Message_Omsg_OKey,v_K),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
<=> c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
inference(monotonicity,[status(thm)],[27,9]) ).
tff(29,plain,
( c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
<=> c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( ~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
<=> ~ c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg)
<=> ~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(33,plain,
~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
^ [V_c: $i,V_evs: $i] :
refl(( ( c_in(V_c,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( c_in(V_c,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [V_c: $i,V_evs: $i] :
( c_in(V_c,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ! [V_c: $i,V_evs: $i] :
( c_in(V_c,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [V_c: $i,V_evs: $i] :
( c_in(V_c,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ! [V_c: $i,V_evs: $i] :
( c_in(V_c,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
! [V_c: $i,V_evs: $i] :
( c_in(V_c,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_usedI_0) ).
tff(38,plain,
! [V_c: $i,V_evs: $i] :
( c_in(V_c,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [V_c: $i,V_evs: $i] :
( c_in(V_c,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [V_c: $i,V_evs: $i] :
( c_in(V_c,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ( ~ ! [V_c: $i,V_evs: $i] :
( c_in(V_c,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg)
| ~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) )
<=> ( ~ ! [V_c: $i,V_evs: $i] :
( c_in(V_c,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg)
| ~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [V_c: $i,V_evs: $i] :
( c_in(V_c,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg)
| ~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [V_c: $i,V_evs: $i] :
( c_in(V_c,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg)
| ~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[43,40,33]) ).
tff(45,plain,
~ c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[44,30]) ).
tff(46,plain,
^ [V_H: $i] :
refl(( c_lessequals(V_H,c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool))
<=> c_lessequals(V_H,c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool)) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [V_H: $i] : c_lessequals(V_H,c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool))
<=> ! [V_H: $i] : c_lessequals(V_H,c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [V_H: $i] : c_lessequals(V_H,c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool))
<=> ! [V_H: $i] : c_lessequals(V_H,c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
! [V_H: $i] : c_lessequals(V_H,c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__increasing_0) ).
tff(50,plain,
! [V_H: $i] : c_lessequals(V_H,c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool)),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [V_H: $i] : c_lessequals(V_H,c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool)),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [V_H: $i] : c_lessequals(V_H,c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool)),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ~ ! [V_H: $i] : c_lessequals(V_H,c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool))
| c_lessequals(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
c_lessequals(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
( class_Lattices_Olattice(tc_bool)
<=> class_Lattices_Olattice(tc_bool) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
tff(57,plain,
class_Lattices_Olattice(tc_bool),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
^ [T_1: $i,T_2: $i] :
refl(( ( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
<=> ( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
<=> ! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
<=> ! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
tff(62,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
( ( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Oupper__semilattice(tc_fun(tc_Message_Omsg,tc_bool))
| ~ class_Lattices_Olattice(tc_bool) )
<=> ( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Oupper__semilattice(tc_fun(tc_Message_Omsg,tc_bool))
| ~ class_Lattices_Olattice(tc_bool) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Oupper__semilattice(tc_fun(tc_Message_Omsg,tc_bool))
| ~ class_Lattices_Olattice(tc_bool) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [T_1: $i,T_2: $i] :
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) )
| class_Lattices_Oupper__semilattice(tc_fun(tc_Message_Omsg,tc_bool))
| ~ class_Lattices_Olattice(tc_bool) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
class_Lattices_Oupper__semilattice(tc_fun(tc_Message_Omsg,tc_bool)),
inference(unit_resolution,[status(thm)],[67,64,57]) ).
tff(69,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(( ( ~ class_Lattices_Oupper__semilattice(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y ) )
<=> ( ~ class_Lattices_Oupper__semilattice(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y ) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oupper__semilattice(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oupper__semilattice(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oupper__semilattice(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oupper__semilattice(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
rewrite(( ( ~ class_Lattices_Oupper__semilattice(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y )
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ( ~ class_Lattices_Oupper__semilattice(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y ) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oupper__semilattice(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y )
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oupper__semilattice(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oupper__semilattice(T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y )
| ~ c_lessequals(V_x,V_y,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
tff(75,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oupper__semilattice(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oupper__semilattice(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oupper__semilattice(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y ) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oupper__semilattice(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y ) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oupper__semilattice(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y ) )
| ~ class_Lattices_Oupper__semilattice(tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_lessequals(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool))
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)) = c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oupper__semilattice(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y ) )
| ~ class_Lattices_Oupper__semilattice(tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_lessequals(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool))
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)) = c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oupper__semilattice(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y ) )
| ~ class_Lattices_Oupper__semilattice(tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_lessequals(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool))
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)) = c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Lattices_Oupper__semilattice(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y ) )
| ~ class_Lattices_Oupper__semilattice(tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_lessequals(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool))
| ( c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)) = c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)) ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)) = c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),
inference(unit_resolution,[status(thm)],[81,78,68,54]) ).
tff(83,plain,
c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool))) = c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool))) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),
inference(transitivity,[status(thm)],[83,9]) ).
tff(85,plain,
c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)))) = c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
( c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
<=> c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat) ),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
( c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat)
<=> c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat) ),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
( ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat)
<=> ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat) ),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ( ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg) )
<=> ( ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,axiom,
( ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
tff(91,plain,
( ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat),
inference(unit_resolution,[status(thm)],[91,33]) ).
tff(93,plain,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
^ [V_H: $i] :
refl(( ( c_Message_Oanalz(c_Message_Oanalz(V_H)) = c_Message_Oanalz(V_H) )
<=> ( c_Message_Oanalz(c_Message_Oanalz(V_H)) = c_Message_Oanalz(V_H) ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [V_H: $i] : ( c_Message_Oanalz(c_Message_Oanalz(V_H)) = c_Message_Oanalz(V_H) )
<=> ! [V_H: $i] : ( c_Message_Oanalz(c_Message_Oanalz(V_H)) = c_Message_Oanalz(V_H) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [V_H: $i] : ( c_Message_Oanalz(c_Message_Oanalz(V_H)) = c_Message_Oanalz(V_H) )
<=> ! [V_H: $i] : ( c_Message_Oanalz(c_Message_Oanalz(V_H)) = c_Message_Oanalz(V_H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
! [V_H: $i] : ( c_Message_Oanalz(c_Message_Oanalz(V_H)) = c_Message_Oanalz(V_H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__idem_0) ).
tff(98,plain,
! [V_H: $i] : ( c_Message_Oanalz(c_Message_Oanalz(V_H)) = c_Message_Oanalz(V_H) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [V_H: $i] : ( c_Message_Oanalz(c_Message_Oanalz(V_H)) = c_Message_Oanalz(V_H) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [V_H: $i] : ( c_Message_Oanalz(c_Message_Oanalz(V_H)) = c_Message_Oanalz(V_H) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
( ~ ! [V_H: $i] : ( c_Message_Oanalz(c_Message_Oanalz(V_H)) = c_Message_Oanalz(V_H) )
| ( c_Message_Oanalz(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))) = c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
c_Message_Oanalz(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))) = c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,plain,
c_Message_Osynth(c_Message_Oanalz(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)))) = c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
( c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)))),tc_Message_Omsg)
<=> c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
( c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
<=> c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)))),tc_Message_Omsg) ),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
( c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
<=> c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,axiom,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(108,plain,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)))),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[108,105]) ).
tff(110,plain,
( c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat)
<=> c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,axiom,
c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(112,plain,
c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
^ [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
refl(( ( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(114,plain,
( ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
^ [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
trans(monotonicity(rewrite(( ( c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) )
<=> ( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
( ( c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat) )
<=> ( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat) ) )),
rewrite(( ( ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat) )
<=> ( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
( ( c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat) )
<=> ( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(117,plain,
( ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat) )
<=> ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,axiom,
! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__parts__insert_0) ).
tff(119,plain,
! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[120]) ).
tff(122,plain,
! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[121,114]) ).
tff(123,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat)
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)))),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat)
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)))),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,plain,
( ( ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat)
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)))),tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) )
<=> ( ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat)
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)))),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat)
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)))),tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat)
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)))),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat) ) ),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat)
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)))),tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat)
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)))),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat) ) ),
inference(transitivity,[status(thm)],[125,123]) ).
tff(127,plain,
( ~ ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat)
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)))),tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
( ~ ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat)
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)))),tc_Message_Omsg)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
( c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat) ),
inference(unit_resolution,[status(thm)],[128,122,112,109]) ).
tff(130,plain,
$false,
inference(unit_resolution,[status(thm)],[129,93,45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SWV727-1 : TPTP v9.0.0. Released v4.1.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 10:43:55 EDT 2025
% 0.14/0.36 % CPUTime :
% 177.45/177.78 % SZS status Unsatisfiable
% 177.45/177.78 % SZS output start Proof
% See solution above
% 178.03/178.41 % E exiting
%------------------------------------------------------------------------------