TSTP Solution File: SWV338-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV338-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 15:11:17 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 50
% Syntax : Number of formulae : 99 ( 29 unt; 18 typ; 0 def)
% Number of atoms : 323 ( 35 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 390 ( 165 ~; 184 |; 0 &)
% ( 41 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 11 >; 7 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 143 ( 130 !; 0 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Message_OkeysFor_type,type,
c_Message_OkeysFor: $i > $i ).
tff(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(c_union_type,type,
c_union: ( $i * $i * $i ) > $i ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $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(v_K_type,type,
v_K: $i ).
tff(c_Event_Oused_type,type,
c_Event_Oused: $i > $i ).
tff(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i > $i ).
tff(c_Message_OinvKey_type,type,
c_Message_OinvKey: $i > $i ).
tff(c_Message_OsymKeys_type,type,
c_Message_OsymKeys: $i ).
tff(c_insert_type,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(v_X_type,type,
v_X: $i ).
tff(c_Message_Osynth_type,type,
c_Message_Osynth: $i > $i ).
tff(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
tff(1,plain,
^ [T_a: $i,V_y: $i] :
refl(
( ( c_union(V_y,V_y,T_a) = V_y )
<=> ( c_union(V_y,V_y,T_a) = V_y ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [T_a: $i,V_y: $i] : ( c_union(V_y,V_y,T_a) = V_y )
<=> ! [T_a: $i,V_y: $i] : ( c_union(V_y,V_y,T_a) = V_y ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_a: $i,V_y: $i] : ( c_union(V_y,V_y,T_a) = V_y )
<=> ! [T_a: $i,V_y: $i] : ( c_union(V_y,V_y,T_a) = V_y ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [T_a: $i,V_y: $i] : ( c_union(V_y,V_y,T_a) = V_y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
tff(5,plain,
! [T_a: $i,V_y: $i] : ( c_union(V_y,V_y,T_a) = V_y ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T_a: $i,V_y: $i] : ( c_union(V_y,V_y,T_a) = V_y ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T_a: $i,V_y: $i] : ( c_union(V_y,V_y,T_a) = V_y ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_union(V_y,V_y,T_a) = V_y )
| ( c_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg) = c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
c_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg) = c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
c_Message_Oparts(c_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg)) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
c_Message_OkeysFor(c_Message_Oparts(c_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))) = c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),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_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,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_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat) ),
inference(symmetry,[status(thm)],[12]) ).
tff(14,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_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat) ),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,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(16,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(17,axiom,
~ c_in(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(18,plain,
( c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evsf),tc_Message_Omsg)
<=> $false ),
inference(iff_false,[status(thm)],[17]) ).
tff(19,plain,
( ( ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat)
| c_in(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)],[18]) ).
tff(20,plain,
( ( ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat)
| c_in(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)],[19,16]) ).
tff(21,axiom,
( ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat)
| c_in(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(22,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)],[21,20]) ).
tff(23,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)],[22,15]) ).
tff(24,plain,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat),
inference(modus_ponens,[status(thm)],[23,14]) ).
tff(25,plain,
( c_in(v_K,c_Message_OsymKeys,tc_nat)
<=> c_in(v_K,c_Message_OsymKeys,tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
c_in(v_K,c_Message_OsymKeys,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(27,plain,
c_in(v_K,c_Message_OsymKeys,tc_nat),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
^ [V_y: $i] :
refl(
( ( ~ c_in(V_y,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_y) = V_y ) )
<=> ( ~ c_in(V_y,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_y) = V_y ) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [V_y: $i] :
( ~ c_in(V_y,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_y) = V_y ) )
<=> ! [V_y: $i] :
( ~ c_in(V_y,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_y) = V_y ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [V_y: $i] :
( ~ c_in(V_y,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_y) = V_y ) )
<=> ! [V_y: $i] :
( ~ c_in(V_y,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_y) = V_y ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
! [V_y: $i] :
( ~ c_in(V_y,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_y) = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OinvKey__K_0) ).
tff(32,plain,
! [V_y: $i] :
( ~ c_in(V_y,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_y) = V_y ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [V_y: $i] :
( ~ c_in(V_y,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_y) = V_y ) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [V_y: $i] :
( ~ c_in(V_y,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_y) = V_y ) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ( ~ ! [V_y: $i] :
( ~ c_in(V_y,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_y) = V_y ) )
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(v_K) = v_K ) )
<=> ( ~ ! [V_y: $i] :
( ~ c_in(V_y,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_y) = V_y ) )
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(v_K) = v_K ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ~ ! [V_y: $i] :
( ~ c_in(V_y,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_y) = V_y ) )
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(v_K) = v_K ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
( ~ ! [V_y: $i] :
( ~ c_in(V_y,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_y) = V_y ) )
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(v_K) = v_K ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
c_Message_OinvKey(v_K) = v_K,
inference(unit_resolution,[status(thm)],[37,34,27]) ).
tff(39,plain,
c_Message_Omsg_OKey(c_Message_OinvKey(v_K)) = c_Message_Omsg_OKey(v_K),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( c_in(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(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)],[39]) ).
tff(41,plain,
( c_in(c_Message_Omsg_OKey(v_K),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
<=> c_in(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)],[40]) ).
tff(42,plain,
( ~ c_in(c_Message_Omsg_OKey(v_K),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
<=> ~ c_in(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)],[41]) ).
tff(43,plain,
( ~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evsf),tc_Message_Omsg)
<=> ~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evsf),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evsf),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[17,43]) ).
tff(45,plain,
^ [V_c: $i,V_evs: $i] :
refl(
( ( ~ 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)
| c_in(V_c,c_Event_Oused(V_evs),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [V_c: $i,V_evs: $i] :
( ~ 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) )
<=> ! [V_c: $i,V_evs: $i] :
( ~ 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) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [V_c: $i,V_evs: $i] :
( ~ 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) )
<=> ! [V_c: $i,V_evs: $i] :
( ~ 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) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
! [V_c: $i,V_evs: $i] :
( ~ 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0) ).
tff(49,plain,
! [V_c: $i,V_evs: $i] :
( ~ 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) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [V_c: $i,V_evs: $i] :
( ~ 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) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [V_c: $i,V_evs: $i] :
( ~ 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) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ( ~ ! [V_c: $i,V_evs: $i] :
( ~ 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(c_Message_Omsg_OKey(v_K),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evsf),tc_Message_Omsg) )
<=> ( ~ ! [V_c: $i,V_evs: $i] :
( ~ 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(c_Message_Omsg_OKey(v_K),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evsf),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ~ ! [V_c: $i,V_evs: $i] :
( ~ 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(c_Message_Omsg_OKey(v_K),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evsf),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
( ~ ! [V_c: $i,V_evs: $i] :
( ~ 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(c_Message_Omsg_OKey(v_K),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evsf),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
~ c_in(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)],[54,51,44]) ).
tff(56,plain,
~ c_in(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(modus_ponens,[status(thm)],[55,42]) ).
tff(57,plain,
( c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(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_insert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(58,axiom,
c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(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(59,plain,
c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat),
inference(modus_ponens,[status(thm)],[58,57]) ).
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_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],]) ).
tff(61,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(62,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)],[61,60]) ).
tff(63,plain,
^ [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
refl(
( ( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) )
<=> ( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) )
<=> ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) )
<=> ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
^ [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(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_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) ) )),
( ( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg))),tc_nat) )
<=> ( c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) ) )),
( ( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(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_union(V_G,V_H,tc_Message_Omsg))),tc_nat) )
<=> ( c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) ) )),
( ( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(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_union(V_G,V_H,tc_Message_Omsg))),tc_nat)
| c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
rewrite(
( ( c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat)
| c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) ) )),
( ( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(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_union(V_G,V_H,tc_Message_Omsg))),tc_nat)
| c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(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_union(V_G,V_H,tc_Message_Omsg))),tc_nat)
| c_in(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(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,axiom,
! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(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_union(V_G,V_H,tc_Message_Omsg))),tc_nat)
| c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)),c_Message_Oparts(V_H),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OkeysFor__parts__insert__dest_0) ).
tff(69,plain,
! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) ),
inference(modus_ponens,[status(thm)],[71,64]) ).
tff(73,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) )
| c_in(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(v_X,c_Message_Osynth(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_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),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_insert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) )
| c_in(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(v_X,c_Message_Osynth(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_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),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_insert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ( c_in(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(v_K,c_Message_OkeysFor(c_Message_Oparts(c_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),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_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat) )
<=> ( c_in(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(v_X,c_Message_Osynth(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_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),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_insert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) )
| c_in(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(v_K,c_Message_OkeysFor(c_Message_Oparts(c_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),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_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) )
| c_in(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(v_X,c_Message_Osynth(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_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),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_insert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat) ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) )
| c_in(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(v_K,c_Message_OkeysFor(c_Message_Oparts(c_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),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_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) )
| c_in(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(v_X,c_Message_Osynth(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_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),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_insert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,plain,
( ~ ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) )
| c_in(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(v_K,c_Message_OkeysFor(c_Message_Oparts(c_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),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_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg)
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [V_H: $i,V_X: $i,V_G: $i,V_K: $i] :
( c_in(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_union(V_G,V_H,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_insert(V_X,V_G,tc_Message_Omsg))),tc_nat) )
| c_in(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(v_X,c_Message_Osynth(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_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),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_insert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
( c_in(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(v_K,c_Message_OkeysFor(c_Message_Oparts(c_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat) ),
inference(unit_resolution,[status(thm)],[78,72,62,59]) ).
tff(80,plain,
c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_union(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat),
inference(unit_resolution,[status(thm)],[79,56]) ).
tff(81,plain,
$false,
inference(unit_resolution,[status(thm)],[80,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV338-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 02:33:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------