%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV338-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:32:11 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 31
% Syntax : Number of formulae : 76 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 312 ( 35 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 378 ( 159 ~; 182 |; 0 &)
% ( 37 <=>; 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 : 0 ( 0 >; 0 *; 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(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(16,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(17,plain,
~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evsf),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,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)
| c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evsf),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,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(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) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,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)],[20,17]) ).
tff(22,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)],[21,14]) ).
tff(23,plain,
( c_in(v_K,c_Message_OsymKeys,tc_nat)
<=> c_in(v_K,c_Message_OsymKeys,tc_nat) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
c_in(v_K,c_Message_OsymKeys,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(25,plain,
c_in(v_K,c_Message_OsymKeys,tc_nat),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,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(27,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)],[26]) ).
tff(28,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(29,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(30,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)],[29,28]) ).
tff(31,plain,
! [V_y: $i] :
( ~ c_in(V_y,c_Message_OsymKeys,tc_nat)
| ( c_Message_OinvKey(V_y) = V_y ) ),
inference(skolemize,[status(sab)],[30]) ).
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)],[31,27]) ).
tff(33,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(34,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(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 ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
c_Message_OinvKey(v_K) = v_K,
inference(unit_resolution,[status(thm)],[35,32,25]) ).
tff(37,plain,
c_Message_Omsg_OKey(c_Message_OinvKey(v_K)) = c_Message_Omsg_OKey(v_K),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,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)],[37]) ).
tff(39,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)],[38]) ).
tff(40,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)],[39]) ).
tff(41,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(42,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)],[41]) ).
tff(43,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(44,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(45,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)],[44,43]) ).
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) ),
inference(skolemize,[status(sab)],[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) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,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(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) )
| ~ 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(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) )
| ~ 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)],[49,48]) ).
tff(51,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)],[50,47,17]) ).
tff(52,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)],[51,40]) ).
tff(53,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(54,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(55,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)],[54,53]) ).
tff(56,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(57,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(58,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)],[57,56]) ).
tff(59,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(60,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)],[59]) ).
tff(61,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(62,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(63,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)],[62]) ).
tff(64,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(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) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,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)],[65,61]) ).
tff(67,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)],[66]) ).
tff(68,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)],[67,60]) ).
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) )
| 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(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_insert(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_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(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_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(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_insert(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_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,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(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(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_insert(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_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
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) )
| 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(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(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_insert(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_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ) ),
inference(monotonicity,[status(thm)],[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) )
| 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(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(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_insert(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_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ) ),
inference(transitivity,[status(thm)],[71,69]) ).
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_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(74,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(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(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_insert(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_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,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)],[74,68,58,55,52]) ).
tff(76,plain,
$false,
inference(unit_resolution,[status(thm)],[75,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SWV338-2 : TPTP v9.0.0. Released v3.2.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n002.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 09:44:46 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.36 % SZS status Unsatisfiable
% 0.18/0.36 % SZS output start Proof
% See solution above
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------