%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV334-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:32:10 AM UTC 2025
% Result : Unsatisfiable 0.23s 0.40s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 13 ~; 1 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 10 ( 9 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
tff(c_List_Oset_type,type,
c_List_Oset: ( $i * $i ) > $i ).
tff(v_evs4_type,type,
v_evs4: $i ).
tff(c_Event_Oevent_OSays_type,type,
c_Event_Oevent_OSays: ( $i * $i * $i ) > $i ).
tff(c_Message_Omsg_OMPair_type,type,
c_Message_Omsg_OMPair: ( $i * $i ) > $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(v_Xa_type,type,
v_Xa: $i ).
tff(v_B_type,type,
v_B: $i ).
tff(v_A_type,type,
v_A: $i ).
tff(1,plain,
( c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(v_Xa,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
<=> c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(v_Xa,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(v_Xa,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).
tff(3,plain,
c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(v_Xa,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_U: $i] :
refl(( ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(V_U,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
<=> ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(V_U,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_U: $i] : ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(V_U,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
<=> ! [V_U: $i] : ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(V_U,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_U: $i] : ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(V_U,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
<=> ! [V_U: $i] : ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(V_U,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V_U: $i] : ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(V_U,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_11) ).
tff(8,plain,
! [V_U: $i] : ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(V_U,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_U: $i] : ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(V_U,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_U: $i] : ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(V_U,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ ! [V_U: $i] : ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(V_U,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(v_Xa,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
$false,
inference(unit_resolution,[status(thm)],[11,10,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SWV334-2 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 09:43:24 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.23/0.40 % SZS status Unsatisfiable
% 0.23/0.40 % SZS output start Proof
% See solution above
% 0.23/0.40 % E exiting
%------------------------------------------------------------------------------