%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV357-1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:32:16 AM UTC 2025
% Result : Unsatisfiable 0.71s 0.87s
% Output : Proof 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 37 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 171 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 238 ( 113 ~; 106 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 102 ( 93 !; 0 ?; 102 :)
% 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_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
tff(c_Event_Oknows_type,type,
c_Event_Oknows: ( $i * $i ) > $i ).
tff(v_evs2_type,type,
v_evs2: $i ).
tff(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
tff(c_Message_Omsg_OMPair_type,type,
c_Message_Omsg_OMPair: ( $i * $i ) > $i ).
tff(c_Message_Omsg_ONonce_type,type,
c_Message_Omsg_ONonce: $i > $i ).
tff(v_NB_type,type,
v_NB: $i ).
tff(c_Message_Omsg_OAgent_type,type,
c_Message_Omsg_OAgent: $i > $i ).
tff(v_Aa_type,type,
v_Aa: $i ).
tff(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
tff(c_List_Oset_type,type,
c_List_Oset: ( $i * $i ) > $i ).
tff(c_Event_Oevent_OGets_type,type,
c_Event_Oevent_OGets: ( $i * $i ) > $i ).
tff(v_Ba_type,type,
v_Ba: $i ).
tff(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
tff(c_Yahalom_Oyahalom_type,type,
c_Yahalom_Oyahalom: $i ).
tff(1,plain,
( ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg)
<=> ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
tff(3,plain,
~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_Y: $i,V_H: $i,V_X: $i] :
refl(( ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg) )
<=> ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV005-2.ax',cls_Message_OMPair__analz_0) ).
tff(8,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg) )
<=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( c_in(c_Event_Oevent_OGets(v_Ba,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB))),c_List_Oset(v_evs2,tc_Event_Oevent),tc_Event_Oevent)
<=> c_in(c_Event_Oevent_OGets(v_Ba,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB))),c_List_Oset(v_evs2,tc_Event_Oevent),tc_Event_Oevent) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
c_in(c_Event_Oevent_OGets(v_Ba,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB))),c_List_Oset(v_evs2,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(17,plain,
c_in(c_Event_Oevent_OGets(v_Ba,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB))),c_List_Oset(v_evs2,tc_Event_Oevent),tc_Event_Oevent),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( c_in(v_evs2,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
<=> c_in(v_evs2,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
c_in(v_evs2,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(20,plain,
c_in(v_evs2,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [V_X: $i,V_B: $i,V_evs: $i] :
refl(( ( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
<=> ( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
<=> ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
<=> ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [V_X: $i,V_B: $i,V_evs: $i] :
trans(monotonicity(rewrite(( ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ) )),
( ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
rewrite(( ( ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ) )),
( ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [V_X: $i,V_B: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [V_X: $i,V_B: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV005-4.ax',cls_Yahalom_OGets__imp__analz__Spy__dest_0) ).
tff(27,plain,
! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
| ~ c_in(v_evs2,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(v_Ba,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB))),c_List_Oset(v_evs2,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg) )
<=> ( ~ ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
| ~ c_in(v_evs2,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(v_Ba,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB))),c_List_Oset(v_evs2,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ( c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(v_Ba,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB))),c_List_Oset(v_evs2,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs2,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
<=> ( ~ c_in(v_evs2,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(v_Ba,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB))),c_List_Oset(v_evs2,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( ~ ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(v_Ba,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB))),c_List_Oset(v_evs2,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs2,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
<=> ( ~ ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
| ~ c_in(v_evs2,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(v_Ba,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB))),c_List_Oset(v_evs2,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(v_Ba,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB))),c_List_Oset(v_evs2,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs2,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
<=> ( ~ ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
| ~ c_in(v_evs2,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(v_Ba,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB))),c_List_Oset(v_evs2,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(v_Ba,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB))),c_List_Oset(v_evs2,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs2,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
| ~ c_in(v_evs2,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(v_Ba,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB))),c_List_Oset(v_evs2,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,30,20,17,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV357-1 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.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 : Fri Jun 20 09:44:09 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.71/0.87 % SZS status Unsatisfiable
% 0.71/0.87 % SZS output start Proof
% See solution above
% 0.78/0.96 % E exiting
%------------------------------------------------------------------------------