%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV793-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:36:06 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.57s
% Output : Proof 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 29
% Syntax : Number of formulae : 70 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 232 ( 16 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 276 ( 126 ~; 120 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 10 con; 0-5 aty)
% Number of variables : 175 ( 159 !; 0 ?; 175 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(c_Event_Oknows_type,type,
c_Event_Oknows: ( $i * $i ) > $i ).
tff(v_evs4_type,type,
v_evs4: $i ).
tff(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
tff(c_List_OtakeWhile_type,type,
c_List_OtakeWhile: ( $i * $i * $i ) > $i ).
tff(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
tff(c_List_Orev_type,type,
c_List_Orev: ( $i * $i ) > $i ).
tff(c_COMBB_type,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_COMBC_type,type,
c_COMBC: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Event_Oevent_OSays_type,type,
c_Event_Oevent_OSays: ( $i * $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_Ka_type,type,
v_Ka: $i ).
tff(v_Aa_type,type,
v_Aa: $i ).
tff(v_Ba_type,type,
v_Ba: $i ).
tff(c_fequal_type,type,
c_fequal: $i > $i ).
tff(c_Not_type,type,
c_Not: $i ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(c_Event_Oused_type,type,
c_Event_Oused: $i > $i ).
tff(1,plain,
^ [V_evs: $i] :
refl(( ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) )
<=> ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) )
<=> ! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) )
<=> ! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__evs__rev_0) ).
tff(5,plain,
! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) )
| ( c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs4,tc_Event_Oevent)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs4,tc_Event_Oevent)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs4,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs4,tc_Event_Oevent))) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs4,tc_Event_Oevent))),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_fun(tc_Message_Omsg,tc_bool))
<=> c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs4,tc_Event_Oevent))),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs4,tc_Event_Oevent))),tc_fun(tc_Message_Omsg,tc_bool))
<=> c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
^ [V_P: $i,V_evs: $i] :
refl(( c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool))
<=> c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool)) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool))
<=> ! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool))
<=> ! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__spies__takeWhile__mono_0) ).
tff(19,plain,
! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool))
| c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs4,tc_Event_Oevent))),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs4,tc_Event_Oevent))),tc_fun(tc_Message_Omsg,tc_bool)),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(modus_ponens,[status(thm)],[23,14]) ).
tff(25,plain,
( c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
<=> c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_11) ).
tff(27,plain,
c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
^ [V_H: $i,V_X: $i,V_K: $i] :
refl(( ( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OBody_0) ).
tff(32,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ( c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) )
<=> ( ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) ) ),
inference(transitivity,[status(thm)],[37,35]) ).
tff(39,plain,
( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[40,34,27]) ).
tff(42,plain,
( ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Event_Oused(v_evs4),tc_Message_Omsg)
<=> ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Event_Oused(v_evs4),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
~ c_in(c_Message_Omsg_ONonce(v_NB),c_Event_Oused(v_evs4),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(44,plain,
~ c_in(c_Message_Omsg_ONonce(v_NB),c_Event_Oused(v_evs4),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
^ [V_c: $i,V_evs: $i] :
refl(( ( 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)
| ~ c_in(V_c,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(46,plain,
( ! [V_c: $i,V_evs: $i] :
( 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) )
<=> ! [V_c: $i,V_evs: $i] :
( 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) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [V_c: $i,V_evs: $i] :
( 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) )
<=> ! [V_c: $i,V_evs: $i] :
( 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) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
! [V_c: $i,V_evs: $i] :
( 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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_usedI_0) ).
tff(49,plain,
! [V_c: $i,V_evs: $i] :
( 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) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [V_c: $i,V_evs: $i] :
( 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) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [V_c: $i,V_evs: $i] :
( 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) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ( ~ ! [V_c: $i,V_evs: $i] :
( 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(c_Message_Omsg_ONonce(v_NB),c_Event_Oused(v_evs4),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg) )
<=> ( ~ ! [V_c: $i,V_evs: $i] :
( 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(c_Message_Omsg_ONonce(v_NB),c_Event_Oused(v_evs4),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [V_c: $i,V_evs: $i] :
( 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(c_Message_Omsg_ONonce(v_NB),c_Event_Oused(v_evs4),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [V_c: $i,V_evs: $i] :
( 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(c_Message_Omsg_ONonce(v_NB),c_Event_Oused(v_evs4),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[54,51,44]) ).
tff(56,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(( ( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
trans(monotonicity(rewrite(( ( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) )
<=> ( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) ) )),
( ( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) )),
rewrite(( ( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) )),
( ( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,axiom,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).
tff(62,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_fun(tc_Message_Omsg,tc_bool)) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_fun(tc_Message_Omsg,tc_bool)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) )
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
~ c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Ba,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NB))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs4,tc_Event_Oevent),tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(unit_resolution,[status(thm)],[68,65,55,41]) ).
tff(70,plain,
$false,
inference(unit_resolution,[status(thm)],[69,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV793-1 : TPTP v9.0.0. Released v4.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 10:52:20 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.57 % SZS status Unsatisfiable
% 0.21/0.57 % SZS output start Proof
% See solution above
% 0.45/0.62 % E exiting
%------------------------------------------------------------------------------