%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV789-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:36:05 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.55s
% Output : Proof 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 26 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 79 ( 41 ~; 28 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 88 ( 78 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_Event_Oused_type,type,
c_Event_Oused: $i > $i ).
tff(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
tff(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
tff(c_Message_Omsg_OCrypt_type,type,
c_Message_Omsg_OCrypt: ( $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(v_K_type,type,
v_K: $i ).
tff(c_List_Oset_type,type,
c_List_Oset: ( $i * $i ) > $i ).
tff(c_Event_Oevent_OSays_type,type,
c_Event_Oevent_OSays: ( $i * $i * $i ) > $i ).
tff(v_A_type,type,
v_A: $i ).
tff(v_B_type,type,
v_B: $i ).
tff(1,plain,
^ [V_X: $i,V_K: $i] :
refl(( ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg)
<=> ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_X: $i,V_K: $i] : ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg)
<=> ! [V_X: $i,V_K: $i] : ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_X: $i,V_K: $i] : ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg)
<=> ! [V_X: $i,V_K: $i] : ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_X: $i,V_K: $i] : ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__notin__used__empty_0) ).
tff(5,plain,
! [V_X: $i,V_K: $i] : ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_X: $i,V_K: $i] : ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_X: $i,V_K: $i] : ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_X: $i,V_K: $i] : ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb)),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb)),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( c_in(c_Event_Oevent_OSays(v_B,v_A,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb))),c_List_Oset(c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
<=> c_in(c_Event_Oevent_OSays(v_B,v_A,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb))),c_List_Oset(c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
c_in(c_Event_Oevent_OSays(v_B,v_A,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb))),c_List_Oset(c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(12,plain,
c_in(c_Event_Oevent_OSays(v_B,v_A,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb))),c_List_Oset(c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
refl(( ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg) )
<=> ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
^ [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
rewrite(( ( c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__used_0) ).
tff(19,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(v_B,v_A,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb))),c_List_Oset(c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb)),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg) )
<=> ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(v_B,v_A,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb))),c_List_Oset(c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb)),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(v_B,v_A,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb))),c_List_Oset(c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb)),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(v_B,v_A,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb))),c_List_Oset(c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb)),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,22,12,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV789-1 : TPTP v9.0.0. Released v4.1.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 10:53:20 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.55 % SZS status Unsatisfiable
% 0.20/0.55 % SZS output start Proof
% See solution above
% 0.42/0.59 % E exiting
%------------------------------------------------------------------------------