TSTP Solution File: SWV727-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV727-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 15:24:16 EDT 2022
% Result : Unsatisfiable 52.48s 32.76s
% Output : Proof 52.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 77
% Syntax : Number of formulae : 158 ( 51 unt; 24 typ; 0 def)
% Number of atoms : 430 ( 79 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 486 ( 207 ~; 220 |; 0 &)
% ( 59 <=>; 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 : 26 ( 15 >; 11 *; 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 : 218 ( 195 !; 0 ?; 218 :)
% 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_Osynth_type,type,
c_Message_Osynth: $i > $i ).
tff(v_X_type,type,
v_X: $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_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/sandbox/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(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,c_Message_OinvKey(v_K)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(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)],[10]) ).
tff(12,plain,
( c_in(v_K,c_Message_OsymKeys,tc_nat)
<=> c_in(v_K,c_Message_OsymKeys,tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
c_in(v_K,c_Message_OsymKeys,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(14,plain,
c_in(v_K,c_Message_OsymKeys,tc_nat),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,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(16,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)],[15]) ).
tff(17,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(18,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(19,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)],[18]) ).
tff(20,axiom,
! [V_K: $i] :
( ( c_Message_OinvKey(V_K) = V_K )
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_invKey__K_0) ).
tff(21,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)],[20,19]) ).
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)],[21,17]) ).
tff(23,plain,
! [V_K: $i] :
( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_K) = V_K ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,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)],[23,16]) ).
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 ) )
<=> ( ~ ! [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(26,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(27,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)],[26,25]) ).
tff(28,plain,
c_Message_OinvKey(v_K) = v_K,
inference(unit_resolution,[status(thm)],[27,24,14]) ).
tff(29,plain,
hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)) = hAPP(c_Message_Omsg_OKey,v_K),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)),c_Message_Oparts(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)],[29]) ).
tff(31,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_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
inference(symmetry,[status(thm)],[30]) ).
tff(32,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(transitivity,[status(thm)],[31,11]) ).
tff(33,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)],[32]) ).
tff(34,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(35,axiom,
~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(36,plain,
~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,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(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) )
<=> ! [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)],[37]) ).
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) )
<=> ! [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(40,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/sandbox/benchmark/theBenchmark.p',cls_usedI_0) ).
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) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
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) ),
inference(skolemize,[status(sab)],[41]) ).
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) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,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(45,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(46,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)],[45,44]) ).
tff(47,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)],[46,43,36]) ).
tff(48,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)],[47,33]) ).
tff(49,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(50,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)],[49]) ).
tff(51,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(52,axiom,
! [V_H: $i] : ( c_Message_Oanalz(c_Message_Oanalz(V_H)) = c_Message_Oanalz(V_H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__idem_0) ).
tff(53,plain,
! [V_H: $i] : ( c_Message_Oanalz(c_Message_Oanalz(V_H)) = c_Message_Oanalz(V_H) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [V_H: $i] : ( c_Message_Oanalz(c_Message_Oanalz(V_H)) = c_Message_Oanalz(V_H) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [V_H: $i] : ( c_Message_Oanalz(c_Message_Oanalz(V_H)) = c_Message_Oanalz(V_H) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,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(57,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)],[56,55]) ).
tff(58,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)],[57]) ).
tff(59,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)],[58]) ).
tff(60,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)],[59]) ).
tff(61,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(62,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(63,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)],[62,61]) ).
tff(64,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)],[63,60]) ).
tff(65,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(66,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)],[65]) ).
tff(67,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(68,axiom,
! [V_H: $i] : c_lessequals(V_H,c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__increasing_0) ).
tff(69,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)],[68,67]) ).
tff(70,plain,
! [V_H: $i] : c_lessequals(V_H,c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool)),
inference(skolemize,[status(sab)],[69]) ).
tff(71,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)],[70,66]) ).
tff(72,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(73,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)],[72,71]) ).
tff(74,plain,
( class_Lattices_Olattice(tc_bool)
<=> class_Lattices_Olattice(tc_bool) ),
inference(rewrite,[status(thm)],]) ).
tff(75,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
tff(76,plain,
class_Lattices_Olattice(tc_bool),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,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(78,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)],[77]) ).
tff(79,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(80,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/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
tff(81,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)],[80,79]) ).
tff(82,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)],[81]) ).
tff(83,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)],[82,78]) ).
tff(84,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(85,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(86,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)],[85,84]) ).
tff(87,plain,
class_Lattices_Oupper__semilattice(tc_fun(tc_Message_Omsg,tc_bool)),
inference(unit_resolution,[status(thm)],[86,83,76]) ).
tff(88,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(89,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)],[88]) ).
tff(90,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(91,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(92,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)],[91]) ).
tff(93,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/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
tff(94,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)],[93,92]) ).
tff(95,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)],[94,90]) ).
tff(96,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)],[95]) ).
tff(97,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)],[96,89]) ).
tff(98,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(99,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(100,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)],[99,98]) ).
tff(101,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)],[100,97,87,73]) ).
tff(102,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)],[101]) ).
tff(103,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)],[102,9]) ).
tff(104,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)],[103]) ).
tff(105,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)],[104]) ).
tff(106,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)],[105]) ).
tff(107,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)],[106]) ).
tff(108,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_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ( ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat)
| $false )
<=> ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg)
<=> $false ),
inference(iff_false,[status(thm)],[35]) ).
tff(111,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)
| $false ) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,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) ),
inference(transitivity,[status(thm)],[111,109]) ).
tff(113,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
tff(114,plain,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat),
inference(modus_ponens,[status(thm)],[114,108]) ).
tff(116,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)],[115,107]) ).
tff(117,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(118,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(119,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)],[118,117]) ).
tff(120,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(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) )
<=> ! [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)],[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) )
<=> ! [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(123,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(124,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)],[123]) ).
tff(125,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/sandbox/benchmark/theBenchmark.p',cls_keysFor__parts__insert_0) ).
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) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
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) ),
inference(modus_ponens,[status(thm)],[126,122]) ).
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) ),
inference(skolemize,[status(sab)],[127]) ).
tff(129,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)],[128,121]) ).
tff(130,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(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(rewrite,[status(thm)],]) ).
tff(131,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(132,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(modus_ponens,[status(thm)],[131,130]) ).
tff(133,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_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(unit_resolution,[status(thm)],[132,129,119]) ).
tff(134,plain,
$false,
inference(unit_resolution,[status(thm)],[133,116,64,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV727-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Sep 4 07:21:23 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 52.48/32.76 % SZS status Unsatisfiable
% 52.48/32.76 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------