TPTP Problem File: SWV776-1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWV776-1 : TPTP v8.2.0. Released v4.1.0.
% Domain : Software Verification
% Problem : Needham-Schroeder shared-key protocol 401_1
% Version : Especial.
% English :
% Refs : [BAN89] Burrows et al. (1989), A Logic of Authentication
% : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
% : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source : [Nip10]
% Names : NS_Shared-401_1 [Nip10]
% Status : Unsatisfiable
% Rating : 0.35 v8.2.0, 0.33 v8.1.0, 0.37 v7.5.0, 0.32 v7.4.0, 0.29 v7.3.0, 0.42 v7.1.0, 0.33 v7.0.0, 0.47 v6.4.0, 0.40 v6.3.0, 0.36 v6.2.0, 0.50 v6.0.0, 0.60 v5.5.0, 0.75 v5.3.0, 0.78 v5.2.0, 0.69 v5.1.0, 0.71 v5.0.0, 0.64 v4.1.0
% Syntax : Number of clauses : 498 ( 163 unt; 100 nHn; 263 RR)
% Number of literals : 1032 ( 335 equ; 462 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 0 prp; 1-3 aty)
% Number of functors : 60 ( 60 usr; 10 con; 0-5 aty)
% Number of variables : 1530 ( 276 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments :
%------------------------------------------------------------------------------
cnf(cls_analz__insert__MPair_0,axiom,
c_Message_Oanalz(c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) ).
cnf(cls_analz_OSnd_0,axiom,
( 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) ) ).
cnf(cls_analz_OFst_0,axiom,
( c_in(V_X,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) ) ).
cnf(cls_MPair__synth__analz_1,axiom,
( c_in(V_Y,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) ) ).
cnf(cls_MPair__synth__analz_0,axiom,
( c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) ) ).
cnf(cls_parts_OSnd_0,axiom,
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) ) ).
cnf(cls_parts_OFst_0,axiom,
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) ) ).
cnf(cls_MPair__used_1,axiom,
( c_in(V_Y,c_Event_Oused(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Event_Oused(V_H),tc_Message_Omsg) ) ).
cnf(cls_MPair__used_0,axiom,
( c_in(V_X,c_Event_Oused(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Event_Oused(V_H),tc_Message_Omsg) ) ).
cnf(cls_synth_OMPair_0,axiom,
( c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(V_Y,c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg) ) ).
cnf(cls_NS3__msg__in__parts__spies_0,axiom,
( c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_S,V_A,c_Message_Omsg_OCrypt(V_KA,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) ).
cnf(cls_parts__insert__MPair_0,axiom,
c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(c_Set_Oinsert(V_X,c_Set_Oinsert(V_Y,V_H,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) ).
cnf(cls_MPair__synth_1,axiom,
( c_in(V_Y,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) ) ).
cnf(cls_MPair__synth_0,axiom,
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) ) ).
cnf(cls_MPair__synth__analz_2,axiom,
( c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(V_Y,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) ) ).
cnf(cls_msg_Osimps_I48_J_0,axiom,
c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) ).
cnf(cls_pushes_I12_J_0,axiom,
c_Set_Oinsert(c_Message_Omsg_OCrypt(V_X,V_K),c_Set_Oinsert(c_Message_Omsg_OMPair(V_X_H,V_Y),V_A,tc_Message_Omsg),tc_Message_Omsg) = c_Set_Oinsert(c_Message_Omsg_OMPair(V_X_H,V_Y),c_Set_Oinsert(c_Message_Omsg_OCrypt(V_X,V_K),V_A,tc_Message_Omsg),tc_Message_Omsg) ).
cnf(cls_msg_Osimps_I6_J_0,axiom,
( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H)
| V_msg1 = V_msg1_H ) ).
cnf(cls_msg_Osimps_I6_J_1,axiom,
( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H)
| V_msg2 = V_msg2_H ) ).
cnf(cls_msg_Osimps_I49_J_0,axiom,
c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) != c_Message_Omsg_OMPair(V_msg1,V_msg2) ).
cnf(cls_msg_Osimps_I40_J_0,axiom,
c_Message_Omsg_OKey(V_nat) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) ).
cnf(cls_msg_Osimps_I41_J_0,axiom,
c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) != c_Message_Omsg_OKey(V_nat) ).
cnf(cls_pushes_I5_J_0,axiom,
c_Set_Oinsert(c_Message_Omsg_OKey(V_K),c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),V_A,tc_Message_Omsg),tc_Message_Omsg) = c_Set_Oinsert(c_Message_Omsg_OMPair(V_X,V_Y),c_Set_Oinsert(c_Message_Omsg_OKey(V_K),V_A,tc_Message_Omsg),tc_Message_Omsg) ).
cnf(cls_initState__into__used_0,axiom,
( c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oparts(c_Event_OinitState(V_B)),tc_Message_Omsg) ) ).
cnf(cls_parts__subset__iff_0,axiom,
( c_lessequals(V_G,c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ) ).
cnf(cls_parts__subset__iff_1,axiom,
( c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_lessequals(V_G,c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ) ).
cnf(cls_parts__insert__Crypt_0,axiom,
c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),tc_Message_Omsg) ).
cnf(cls_parts__mono_0,axiom,
( c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_lessequals(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)) ) ).
cnf(cls_invKey__shrK_0,axiom,
c_Message_OinvKey(c_Public_OshrK(V_A)) = c_Public_OshrK(V_A) ).
cnf(cls_invKey__eq_0,axiom,
( c_Message_OinvKey(V_K) != c_Message_OinvKey(V_K_H)
| V_K = V_K_H ) ).
cnf(cls_parts__partsD_0,axiom,
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oparts(c_Message_Oparts(V_H)),tc_Message_Omsg) ) ).
cnf(cls_Crypt__notin__initState_0,axiom,
~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oparts(c_Event_OinitState(V_B)),tc_Message_Omsg) ).
cnf(cls_parts_OBody_0,axiom,
( 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) ) ).
cnf(cls_parts__increasing_0,axiom,
c_lessequals(V_H,c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_analz__parts_0,axiom,
c_Message_Oanalz(c_Message_Oparts(V_H)) = c_Message_Oparts(V_H) ).
cnf(cls_parts__idem_0,axiom,
c_Message_Oparts(c_Message_Oparts(V_H)) = c_Message_Oparts(V_H) ).
cnf(cls_parts_OInj_0,axiom,
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,V_H,tc_Message_Omsg) ) ).
cnf(cls_invKey_0,axiom,
c_Message_OinvKey(c_Message_OinvKey(V_K)) = V_K ).
cnf(cls_parts__insert__Key_0,axiom,
c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OKey(V_K),c_Message_Oparts(V_H),tc_Message_Omsg) ).
cnf(cls_parts__analz_0,axiom,
c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) ).
cnf(cls_analz__conj__parts_0,axiom,
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) ) ).
cnf(cls_analz__into__parts_0,axiom,
( c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg) ) ).
cnf(cls_not__parts__not__analz_0,axiom,
( ~ c_in(V_c,c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg) ) ).
cnf(cls_parts__cut__eq_0,axiom,
( c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)) = c_Message_Oparts(V_H)
| ~ c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ).
cnf(cls_parts__insertI_0,axiom,
( c_in(V_c,c_Message_Oparts(c_Set_Oinsert(V_a,V_G,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oparts(V_G),tc_Message_Omsg) ) ).
cnf(cls_parts__trans_0,axiom,
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_lessequals(V_G,c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(V_X,c_Message_Oparts(V_G),tc_Message_Omsg) ) ).
cnf(cls_analz__subset__parts_0,axiom,
c_lessequals(c_Message_Oanalz(V_H),c_Message_Oparts(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_parts__insert__subset_0,axiom,
c_lessequals(c_Set_Oinsert(V_X,c_Message_Oparts(V_H),tc_Message_Omsg),c_Message_Oparts(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_analz_ODecrypt_0,axiom,
( c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)),c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oanalz(V_H),tc_Message_Omsg) ) ).
cnf(cls_usedI_0,axiom,
( 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) ) ).
cnf(cls_parts__knows__Spy__subset__used_0,axiom,
c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),c_Event_Oused(V_evs),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_Oops__parts__spies_0,axiom,
( c_in(V_K,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_B,c_Message_Omsg_OMPair(V_K,V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) ).
cnf(cls_analz__Crypt__if_1,axiom,
( c_Message_Oanalz(c_Set_Oinsert(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)),c_Message_Oanalz(V_H),tc_Message_Omsg) ) ).
cnf(cls_analz__Crypt__if_0,axiom,
( c_Message_Oanalz(c_Set_Oinsert(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oanalz(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)),c_Message_Oanalz(V_H),tc_Message_Omsg) ) ).
cnf(cls_Crypt__synth__analz_0,axiom,
( c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)),c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(V_H),tc_Message_Omsg) ) ).
cnf(cls_Crypt__synth__analz_1,axiom,
( c_in(c_Message_Omsg_OCrypt(V_K,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(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)),c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(V_H),tc_Message_Omsg) ) ).
cnf(cls_synth__subset__iff_0,axiom,
( c_lessequals(V_G,c_Message_Osynth(V_H),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ) ).
cnf(cls_msg_Osimps_I7_J_0,axiom,
( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H)
| V_nat = V_nat_H ) ).
cnf(cls_msg_Osimps_I7_J_1,axiom,
( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H)
| V_msg = V_msg_H ) ).
cnf(cls_Crypt__notin__used__empty_0,axiom,
~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg) ).
cnf(cls_distinct1__rotate_1,axiom,
( c_List_Odistinct(c_List_Orotate1(V_xs,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a) ) ).
cnf(cls_distinct1__rotate_0,axiom,
( c_List_Odistinct(V_xs,T_a)
| ~ c_List_Odistinct(c_List_Orotate1(V_xs,T_a),T_a) ) ).
cnf(cls_distinct__filter_0,axiom,
( c_List_Odistinct(c_List_Ofilter(V_P,V_xs,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a) ) ).
cnf(cls_synth_OInj_0,axiom,
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(V_X,V_H,tc_Message_Omsg) ) ).
cnf(cls_Crypt__synth__eq_1,axiom,
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| c_in(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg) ) ).
cnf(cls_Crypt__synth__eq_0,axiom,
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg) ) ).
cnf(cls_Crypt__synth_1,axiom,
( c_in(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg) ) ).
cnf(cls_synth__synthD_0,axiom,
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Osynth(c_Message_Osynth(V_H)),tc_Message_Omsg) ) ).
cnf(cls_shrK__in__used_0,axiom,
c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Event_Oused(V_evs),tc_Message_Omsg) ).
cnf(cls_neq__shrK_0,axiom,
c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_B)),c_Event_Oused(V_evs),tc_Message_Omsg) ).
cnf(cls_distinct__rev_1,axiom,
( c_List_Odistinct(c_List_Orev(V_xs,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a) ) ).
cnf(cls_distinct__rev_0,axiom,
( c_List_Odistinct(V_xs,T_a)
| ~ c_List_Odistinct(c_List_Orev(V_xs,T_a),T_a) ) ).
cnf(cls_synth__idem_0,axiom,
c_Message_Osynth(c_Message_Osynth(V_H)) = c_Message_Osynth(V_H) ).
cnf(cls_remdups__id__iff__distinct_0,axiom,
( c_List_Oremdups(V_xs,T_a) != V_xs
| c_List_Odistinct(V_xs,T_a) ) ).
cnf(cls_distinct__remdups__id_0,axiom,
( c_List_Oremdups(V_xs,T_a) = V_xs
| ~ c_List_Odistinct(V_xs,T_a) ) ).
cnf(cls_Crypt__synth_0,axiom,
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg) ) ).
cnf(cls_takeWhile__cong_2,axiom,
( c_List_OtakeWhile(V_P,V_x,T_a) = c_List_OtakeWhile(V_Q,V_x,T_a)
| ~ hBOOL(hAPP(V_Q,c_List_Osko__List__XtakeWhile__cong__1__1(V_P,V_Q,V_x,T_a)))
| ~ hBOOL(hAPP(V_P,c_List_Osko__List__XtakeWhile__cong__1__1(V_P,V_Q,V_x,T_a))) ) ).
cnf(cls_takeWhile__cong_1,axiom,
( c_List_OtakeWhile(V_P,V_x,T_a) = c_List_OtakeWhile(V_Q,V_x,T_a)
| hBOOL(hAPP(V_Q,c_List_Osko__List__XtakeWhile__cong__1__1(V_P,V_Q,V_x,T_a)))
| hBOOL(hAPP(V_P,c_List_Osko__List__XtakeWhile__cong__1__1(V_P,V_Q,V_x,T_a))) ) ).
cnf(cls_synth_OCrypt_0,axiom,
( c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg) ) ).
cnf(cls_msg_Osimps_I42_J_0,axiom,
c_Message_Omsg_OKey(V_nat) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) ).
cnf(cls_shrK__injective_0,axiom,
( c_Public_OshrK(V_x) != c_Public_OshrK(V_y)
| V_x = V_y ) ).
cnf(cls_distinct__takeWhile_0,axiom,
( c_List_Odistinct(c_List_OtakeWhile(V_P,V_xs,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a) ) ).
cnf(cls_psubsetD_0,axiom,
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_filter_Osimps_I2_J_1,axiom,
( c_List_Ofilter(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Ofilter(V_P,V_xs,T_a)
| hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_dropWhile_Osimps_I2_J_1,axiom,
( c_List_OdropWhile(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a)
| hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_dropWhile_Osimps_I2_J_0,axiom,
( c_List_OdropWhile(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_OdropWhile(V_P,V_xs,T_a)
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_splice__Cons__Cons_0,axiom,
c_List_Osplice(c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Olist_OCons(V_y,c_List_Osplice(V_xs,V_ys,T_a),T_a),T_a) ).
cnf(cls_remove1_Osimps_I2_J_1,axiom,
( c_List_Oremove1(V_x,c_List_Olist_OCons(V_y,V_xs,T_a),T_a) = c_List_Olist_OCons(V_y,c_List_Oremove1(V_x,V_xs,T_a),T_a)
| V_x = V_y ) ).
cnf(cls_dropWhile__eq__Cons__conv_1,axiom,
( c_List_OdropWhile(V_P,V_xs,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a)
| ~ hBOOL(hAPP(V_P,V_y)) ) ).
cnf(cls_filter__eq__ConsD_2,axiom,
( c_List_Ofilter(V_P,V_ys,T_a) != c_List_Olist_OCons(V_x,V_xs,T_a)
| hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_filter_Osimps_I2_J_0,axiom,
( c_List_Ofilter(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Ofilter(V_P,V_xs,T_a),T_a)
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_Cons__eq__filterD_2,axiom,
( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Ofilter(V_P,V_ys,T_a)
| hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_remove1_Osimps_I2_J_0,axiom,
c_List_Oremove1(V_x,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = V_xs ).
cnf(cls_distinct_Osimps_I2_J_1,axiom,
( c_List_Odistinct(V_xs,T_a)
| ~ c_List_Odistinct(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).
cnf(cls_remdups__eq__nil__right__iff_1,axiom,
c_List_Olist_ONil(T_a) = c_List_Oremdups(c_List_Olist_ONil(T_a),T_a) ).
cnf(cls_remdups__eq__nil__iff_0,axiom,
( c_List_Oremdups(V_x,T_a) != c_List_Olist_ONil(T_a)
| V_x = c_List_Olist_ONil(T_a) ) ).
cnf(cls_splice__Nil2_0,axiom,
c_List_Osplice(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs ).
cnf(cls_splice_Osimps_I1_J_0,axiom,
c_List_Osplice(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys ).
cnf(cls_distinct_Osimps_I1_J_0,axiom,
c_List_Odistinct(c_List_Olist_ONil(T_a),T_a) ).
cnf(cls_remdups__eq__nil__iff_1,axiom,
c_List_Oremdups(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_list__inter_Osimps_I1_J_0,axiom,
c_List_Olist__inter(c_List_Olist_ONil(T_a),V_bs,T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_dropWhile_Osimps_I1_J_0,axiom,
c_List_OdropWhile(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_remdups__eq__nil__right__iff_0,axiom,
( c_List_Olist_ONil(T_a) != c_List_Oremdups(V_x,T_a)
| V_x = c_List_Olist_ONil(T_a) ) ).
cnf(cls_filter_Osimps_I1_J_0,axiom,
c_List_Ofilter(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_list__update__nonempty_1,axiom,
c_List_Olist__update(c_List_Olist_ONil(T_a),V_k,V_x,T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_list__update__code_I1_J_0,axiom,
c_List_Olist__update(c_List_Olist_ONil(T_a),V_i,V_y,T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_list__update_Osimps_I1_J_0,axiom,
c_List_Olist__update(c_List_Olist_ONil(T_a),V_i,V_v,T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_remove1_Osimps_I1_J_0,axiom,
c_List_Oremove1(V_x,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_list__update__nonempty_0,axiom,
( c_List_Olist__update(V_xs,V_k,V_x,T_a) != c_List_Olist_ONil(T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_distinct__append_1,axiom,
( c_List_Odistinct(V_ys,T_a)
| ~ c_List_Odistinct(c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).
cnf(cls_distinct__append_0,axiom,
( c_List_Odistinct(V_xs,T_a)
| ~ c_List_Odistinct(c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).
cnf(cls_filter__append_0,axiom,
c_List_Ofilter(V_P,c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Ofilter(V_P,V_xs,T_a),c_List_Ofilter(V_P,V_ys,T_a),T_a) ).
cnf(cls_ns__sharedp_ONil_0,axiom,
c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)) ).
cnf(cls_Says__imp__parts__knows__Spy_0,axiom,
( c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,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) ) ).
cnf(cls_lemma1_0,axiom,
( c_lessequals(c_Message_Oanalz(c_Set_Oinsert(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)),c_Set_Oinsert(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oanalz(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)),c_Message_Oanalz(V_H),tc_Message_Omsg) ) ).
cnf(cls_lemma2_0,axiom,
( c_lessequals(c_Set_Oinsert(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oanalz(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oanalz(c_Set_Oinsert(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(V_K)),c_Message_Oanalz(V_H),tc_Message_Omsg) ) ).
cnf(cls_synth__subset__iff_1,axiom,
( c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_lessequals(V_G,c_Message_Osynth(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_less__fun__def_1,axiom,
( ~ class_HOL_Oord(T_b)
| ~ c_lessequals(V_g,V_f,tc_fun(T_a,T_b))
| ~ c_HOL_Oord__class_Oless(V_f,V_g,tc_fun(T_a,T_b)) ) ).
cnf(cls_linorder__not__le_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_linorder__not__le_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_linorder__not__less_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_linorder__not__less_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_linorder__antisym__conv1_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| c_lessequals(V_x,V_x,T_a) ) ).
cnf(cls_linorder__antisym__conv2_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(V_x,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
cnf(cls_not__leE_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_remdups__filter_0,axiom,
c_List_Oremdups(c_List_Ofilter(V_P,V_xs,T_a),T_a) = c_List_Ofilter(V_P,c_List_Oremdups(V_xs,T_a),T_a) ).
cnf(cls_xt1_I10_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_psubset__trans_0,axiom,
( c_HOL_Oord__class_Oless(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_HOL_Oord__class_Oless(V_B,V_C,tc_fun(T_a,tc_bool))
| ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_order__less__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_shrK__in__knows_0,axiom,
c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Event_Oknows(V_A,V_evs),tc_Message_Omsg) ).
cnf(cls_Says__imp__used_0,axiom,
( 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) ) ).
cnf(cls_synth__mono_0,axiom,
( c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_lessequals(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)) ) ).
cnf(cls_distinct__dropWhile_0,axiom,
( c_List_Odistinct(c_List_OdropWhile(V_P,V_xs,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a) ) ).
cnf(cls_msg_Osimps_I4_J_0,axiom,
( c_Message_Omsg_OKey(V_nat) != c_Message_Omsg_OKey(V_nat_H)
| V_nat = V_nat_H ) ).
cnf(cls_analz__shrK__Decrypt_0,axiom,
( c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),V_X),c_Message_Oanalz(V_H),tc_Message_Omsg) ) ).
cnf(cls_filter__replicate_0,axiom,
( c_List_Ofilter(V_P,c_List_Oreplicate(V_n,V_x,T_a),T_a) = c_List_Oreplicate(V_n,V_x,T_a)
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_Key__synth_0,axiom,
( c_in(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Osynth(V_H),tc_Message_Omsg) ) ).
cnf(cls_Key__synth__eq_1,axiom,
( c_in(c_Message_Omsg_OKey(V_K),c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg) ) ).
cnf(cls_pushes_I6_J_0,axiom,
c_Set_Oinsert(c_Message_Omsg_OKey(V_K),c_Set_Oinsert(c_Message_Omsg_OCrypt(V_X,V_K_H),V_A,tc_Message_Omsg),tc_Message_Omsg) = c_Set_Oinsert(c_Message_Omsg_OCrypt(V_X,V_K_H),c_Set_Oinsert(c_Message_Omsg_OKey(V_K),V_A,tc_Message_Omsg),tc_Message_Omsg) ).
cnf(cls_distinct__remove1_0,axiom,
( c_List_Odistinct(c_List_Oremove1(V_x,V_xs,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a) ) ).
cnf(cls_shrK__in__initState_0,axiom,
c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Event_OinitState(V_A),tc_Message_Omsg) ).
cnf(cls_less__le__not__le_2,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_psubset__eq_1,axiom,
~ c_HOL_Oord__class_Oless(V_x,V_x,tc_fun(T_a,tc_bool)) ).
cnf(cls_less__fun__def_2,axiom,
( ~ class_HOL_Oord(T_b)
| c_HOL_Oord__class_Oless(V_f,V_g,tc_fun(T_a,T_b))
| c_lessequals(V_g,V_f,tc_fun(T_a,T_b))
| ~ c_lessequals(V_f,V_g,tc_fun(T_a,T_b)) ) ).
cnf(cls_order__less__le_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
cnf(cls_linorder__neqE__ordered__idom_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y ) ).
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_linorder__neqE_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y ) ).
cnf(cls_linorder__less__linear_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_linorder__antisym__conv3_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_msg_Osimps_I43_J_0,axiom,
c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) != c_Message_Omsg_OKey(V_nat) ).
cnf(cls_psubset__eq_0,axiom,
( c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_less__fun__def_0,axiom,
( ~ class_HOL_Oord(T_b)
| c_lessequals(V_f,V_g,tc_fun(T_a,T_b))
| ~ c_HOL_Oord__class_Oless(V_f,V_g,tc_fun(T_a,T_b)) ) ).
cnf(cls_order__le__less_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_order__less__imp__le_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_Notes__imp__used_0,axiom,
( c_in(V_X,c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_ONotes(V_A,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) ).
cnf(cls_remove1__filter__not_0,axiom,
( c_List_Oremove1(V_x,c_List_Ofilter(V_P,V_xs,T_a),T_a) = c_List_Ofilter(V_P,V_xs,T_a)
| hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_takeWhile__eq__all__conv_2,axiom,
( c_List_OtakeWhile(V_P,V_xs,T_a) = V_xs
| ~ hBOOL(hAPP(V_P,c_List_Osko__List__XtakeWhile__eq__all__conv__1__1(V_P,V_xs,T_a))) ) ).
cnf(cls_distinct__remdups_0,axiom,
c_List_Odistinct(c_List_Oremdups(V_xs,T_a),T_a) ).
cnf(cls_synth__increasing_0,axiom,
c_lessequals(V_H,c_Message_Osynth(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_xt1_I7_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_xt1_I8_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_psubset__subset__trans_0,axiom,
( c_HOL_Oord__class_Oless(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_subset__psubset__trans_0,axiom,
( c_HOL_Oord__class_Oless(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_HOL_Oord__class_Oless(V_B,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_order__le__less__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_order__less__le__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_list__update__swap_0,axiom,
( c_List_Olist__update(c_List_Olist__update(V_xs,V_i,V_x,T_a),V_i_H,V_x_H,T_a) = c_List_Olist__update(c_List_Olist__update(V_xs,V_i_H,V_x_H,T_a),V_i,V_x,T_a)
| V_i = V_i_H ) ).
cnf(cls_sorted__remdups_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(c_List_Oremdups(V_l,T_a),T_a)
| ~ c_List_Olinorder__class_Osorted(V_l,T_a) ) ).
cnf(cls_rev__filter_0,axiom,
c_List_Orev(c_List_Ofilter(V_P,V_xs,T_a),T_a) = c_List_Ofilter(V_P,c_List_Orev(V_xs,T_a),T_a) ).
cnf(cls_xt1_I11_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| V_a = V_b
| ~ c_lessequals(V_b,V_a,T_a) ) ).
cnf(cls_xt1_I12_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| V_a = V_b ) ).
cnf(cls_psubset__eq_2,axiom,
( c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool))
| V_A = V_B
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_order__le__less_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_order__less__le_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_subset__iff__psubset__eq_0,axiom,
( V_A = V_B
| c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_order__le__neq__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| V_a = V_b
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_order__neq__le__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| V_a = V_b ) ).
cnf(cls_linorder__antisym__conv1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_linorder__antisym__conv2_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_sorted__dropWhile_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(c_List_OdropWhile(V_P,V_xs,T_a),T_a)
| ~ c_List_Olinorder__class_Osorted(V_xs,T_a) ) ).
cnf(cls_list__update__overwrite_0,axiom,
c_List_Olist__update(c_List_Olist__update(V_xs,V_i,V_x,T_a),V_i,V_y,T_a) = c_List_Olist__update(V_xs,V_i,V_y,T_a) ).
cnf(cls_set__remdups_0,axiom,
c_List_Oset(c_List_Oremdups(V_xs,T_a),T_a) = c_List_Oset(V_xs,T_a) ).
cnf(cls_sorted__remove1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(c_List_Oremove1(V_a,V_xs,T_a),T_a)
| ~ c_List_Olinorder__class_Osorted(V_xs,T_a) ) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
cnf(cls_not__less__iff__gr__or__eq_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_order__less__asym_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_order__less__asym_H_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_sorted__append_5,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(c_List_Oappend(V_xs,V_ys,T_a),T_a)
| ~ c_lessequals(c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1(V_xs,V_ys,T_a),c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2(V_xs,V_ys,T_a),T_a)
| ~ c_List_Olinorder__class_Osorted(V_ys,T_a)
| ~ c_List_Olinorder__class_Osorted(V_xs,T_a) ) ).
cnf(cls_Says__imp__knows_0,axiom,
( c_in(V_X,c_Event_Oknows(V_A,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) ) ).
cnf(cls_Notes__imp__knows_0,axiom,
( c_in(V_X,c_Event_Oknows(V_A,V_evs),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_ONotes(V_A,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) ).
cnf(cls_psubset__insert__iff_0,axiom,
( c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| ~ c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_psubset__insert__iff_6,axiom,
( c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_filter__id__conv_0,axiom,
( c_List_Ofilter(V_P,V_xs,T_a) != V_xs
| hBOOL(hAPP(V_P,V_x))
| ~ c_in(V_x,c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_notin__set__remove1_0,axiom,
( ~ c_in(V_x,c_List_Oset(c_List_Oremove1(V_y,V_xs,T_a),T_a),T_a)
| c_in(V_x,c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_in__set__remove1_0,axiom,
( c_in(V_a,c_List_Oset(V_xs,T_a),T_a)
| ~ c_in(V_a,c_List_Oset(c_List_Oremove1(V_b,V_xs,T_a),T_a),T_a)
| V_a = V_b ) ).
cnf(cls_in__set__remove1_1,axiom,
( c_in(V_a,c_List_Oset(c_List_Oremove1(V_b,V_xs,T_a),T_a),T_a)
| ~ c_in(V_a,c_List_Oset(V_xs,T_a),T_a)
| V_a = V_b ) ).
cnf(cls_splice_Osimps_I2_J_0,axiom,
c_List_Osplice(c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a) ).
cnf(cls_set__remove1__subset_0,axiom,
c_lessequals(c_List_Oset(c_List_Oremove1(V_x,V_xs,T_a),T_a),c_List_Oset(V_xs,T_a),tc_fun(T_a,tc_bool)) ).
cnf(cls_filter__is__subset_0,axiom,
c_lessequals(c_List_Oset(c_List_Ofilter(V_P,V_xs,T_a),T_a),c_List_Oset(V_xs,T_a),tc_fun(T_a,tc_bool)) ).
cnf(cls_synth__cut_0,axiom,
( c_in(V_Y,c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_in(V_Y,c_Message_Osynth(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),tc_Message_Omsg) ) ).
cnf(cls_synth__analz__insert__eq_0,axiom,
( c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(V_G),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(V_H,V_G,tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) ) ).
cnf(cls_synth__analz__insert__eq_1,axiom,
( c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(V_G),tc_Message_Omsg)
| ~ c_lessequals(V_H,V_G,tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) ) ).
cnf(cls_Says__imp__spies_0,axiom,
( c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,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) ) ).
cnf(cls_synth__trans_0,axiom,
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| ~ c_lessequals(V_G,c_Message_Osynth(V_H),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(V_X,c_Message_Osynth(V_G),tc_Message_Omsg) ) ).
cnf(cls_sorted__distinct__set__unique_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Oset(V_xs,T_a) != c_List_Oset(V_ys,T_a)
| ~ c_List_Odistinct(V_ys,T_a)
| ~ c_List_Olinorder__class_Osorted(V_ys,T_a)
| ~ c_List_Odistinct(V_xs,T_a)
| ~ c_List_Olinorder__class_Osorted(V_xs,T_a)
| V_xs = V_ys ) ).
cnf(cls_filter__replicate_1,axiom,
( c_List_Ofilter(V_P,c_List_Oreplicate(V_n,V_x,T_a),T_a) = c_List_Olist_ONil(T_a)
| hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_takeWhile__dropWhile__id_0,axiom,
c_List_Oappend(c_List_OtakeWhile(V_P,V_xs,T_a),c_List_OdropWhile(V_P,V_xs,T_a),T_a) = V_xs ).
cnf(cls_takeWhile__append2_1,axiom,
( c_List_OtakeWhile(V_P,c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(V_xs,c_List_OtakeWhile(V_P,V_ys,T_a),T_a)
| ~ hBOOL(hAPP(V_P,c_List_Osko__List__XtakeWhile__append2__1__1(V_P,V_xs,T_a))) ) ).
cnf(cls_Gets__imp__knows__agents_0,axiom,
( c_in(V_X,c_Event_Oknows(V_A,V_evs),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_A,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| V_A = c_Message_Oagent_OSpy ) ).
cnf(cls_synth__analz__mono_0,axiom,
( c_lessequals(c_Message_Osynth(c_Message_Oanalz(V_G)),c_Message_Osynth(c_Message_Oanalz(V_H)),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_lessequals(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)) ) ).
cnf(cls_synth__insert_0,axiom,
c_lessequals(c_Set_Oinsert(V_X,c_Message_Osynth(V_H),tc_Message_Omsg),c_Message_Osynth(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_hd__dropWhile_0,axiom,
( ~ hBOOL(hAPP(V_P,c_List_Ohd(c_List_OdropWhile(V_P,V_xs,T_a),T_a)))
| c_List_OdropWhile(V_P,V_xs,T_a) = c_List_Olist_ONil(T_a) ) ).
cnf(cls_used__Gets_0,axiom,
c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OGets(V_A,V_X),V_evs,tc_Event_Oevent)) = c_Event_Oused(V_evs) ).
cnf(cls_event_Osimps_I8_J_0,axiom,
c_Event_Oevent_OGets(V_agent,V_msg) != c_Event_Oevent_ONotes(V_agent_H,V_msg_H) ).
cnf(cls_event_Osimps_I6_J_0,axiom,
c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_ONotes(V_agent_H,V_msg_H) ).
cnf(cls_event_Osimps_I7_J_0,axiom,
c_Event_Oevent_ONotes(V_agent_H,V_msg_H) != c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) ).
cnf(cls_split__list__last__prop__iff_3,axiom,
( c_in(c_List_Osko__List__Xsplit__list__last__prop__iff__1__5(V_P,c_List_Oappend(V_x,c_List_Olist_OCons(V_xa,V_xb,T_a),T_a),T_a),c_List_Oset(c_List_Oappend(V_x,c_List_Olist_OCons(V_xa,V_xb,T_a),T_a),T_a),T_a)
| c_in(c_List_Osko__List__Xsplit__list__last__prop__iff__1__5(V_P,V_xb,T_a),c_List_Oset(V_xb,T_a),T_a)
| ~ hBOOL(hAPP(V_P,V_xa)) ) ).
cnf(cls_split__list__first__prop__iff_5,axiom,
( c_in(c_List_Osko__List__Xsplit__list__first__prop__iff__1__5(V_P,c_List_Oappend(V_x,c_List_Olist_OCons(V_xa,V_xb,T_a),T_a),T_a),c_List_Oset(c_List_Oappend(V_x,c_List_Olist_OCons(V_xa,V_xb,T_a),T_a),T_a),T_a)
| hBOOL(hAPP(V_P,c_List_Osko__List__Xsplit__list__first__prop__iff__1__5(V_P,V_x,T_a)))
| ~ hBOOL(hAPP(V_P,V_xa)) ) ).
cnf(cls_split__list__last__prop__iff_4,axiom,
( hBOOL(hAPP(V_P,c_List_Osko__List__Xsplit__list__last__prop__iff__1__5(V_P,c_List_Oappend(V_x,c_List_Olist_OCons(V_xa,V_xb,T_a),T_a),T_a)))
| c_in(c_List_Osko__List__Xsplit__list__last__prop__iff__1__5(V_P,V_xb,T_a),c_List_Oset(V_xb,T_a),T_a)
| ~ hBOOL(hAPP(V_P,V_xa)) ) ).
cnf(cls_split__list__first__prop__iff_3,axiom,
( c_in(c_List_Osko__List__Xsplit__list__first__prop__iff__1__5(V_P,c_List_Oappend(V_x,c_List_Olist_OCons(V_xa,V_xb,T_a),T_a),T_a),c_List_Oset(c_List_Oappend(V_x,c_List_Olist_OCons(V_xa,V_xb,T_a),T_a),T_a),T_a)
| c_in(c_List_Osko__List__Xsplit__list__first__prop__iff__1__5(V_P,V_x,T_a),c_List_Oset(V_x,T_a),T_a)
| ~ hBOOL(hAPP(V_P,V_xa)) ) ).
cnf(cls_split__list__last__prop__iff_5,axiom,
( c_in(c_List_Osko__List__Xsplit__list__last__prop__iff__1__5(V_P,c_List_Oappend(V_x,c_List_Olist_OCons(V_xa,V_xb,T_a),T_a),T_a),c_List_Oset(c_List_Oappend(V_x,c_List_Olist_OCons(V_xa,V_xb,T_a),T_a),T_a),T_a)
| hBOOL(hAPP(V_P,c_List_Osko__List__Xsplit__list__last__prop__iff__1__5(V_P,V_xb,T_a)))
| ~ hBOOL(hAPP(V_P,V_xa)) ) ).
cnf(cls_split__list__first__prop__iff_4,axiom,
( hBOOL(hAPP(V_P,c_List_Osko__List__Xsplit__list__first__prop__iff__1__5(V_P,c_List_Oappend(V_x,c_List_Olist_OCons(V_xa,V_xb,T_a),T_a),T_a)))
| c_in(c_List_Osko__List__Xsplit__list__first__prop__iff__1__5(V_P,V_x,T_a),c_List_Oset(V_x,T_a),T_a)
| ~ hBOOL(hAPP(V_P,V_xa)) ) ).
cnf(cls_append__butlast__last__id_0,axiom,
( c_List_Oappend(c_List_Obutlast(V_xs,T_a),c_List_Olist_OCons(c_List_Olast(V_xs,T_a),c_List_Olist_ONil(T_a),T_a),T_a) = V_xs
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_knows__Spy__subset__knows__Spy__Gets_0,axiom,
c_lessequals(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OGets(V_A,V_X),V_evs,tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_knows__Spy__subset__knows__Spy__Says_0,axiom,
c_lessequals(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_set__ConsD_0,axiom,
( c_in(V_y,c_List_Oset(V_xs,T_a),T_a)
| V_y = V_x
| ~ c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),T_a) ) ).
cnf(cls_insert__subset_2,axiom,
( c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a) ) ).
cnf(cls_insert__subset_0,axiom,
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_subset__insert__iff_2,axiom,
( c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_A,T_a) ) ).
cnf(cls_subset__insert__iff_1,axiom,
( c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_A,T_a)
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_subset__insert_1,axiom,
( c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_A,T_a) ) ).
cnf(cls_subset__insert_0,axiom,
( c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| c_in(V_x,V_A,T_a) ) ).
cnf(cls_List_Oset_Osimps_I2_J_0,axiom,
c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) ).
cnf(cls_butlast_Osimps_I2_J_1,axiom,
( c_List_Obutlast(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Obutlast(V_xs,T_a),T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_last_Osimps_0,axiom,
c_List_Olast(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = V_x ).
cnf(cls_butlast_Osimps_I2_J_0,axiom,
c_List_Obutlast(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_rev__singleton__conv_0,axiom,
( c_List_Orev(V_xs,T_a) != c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a)
| V_xs = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) ) ).
cnf(cls_takeWhile_Osimps_I2_J_1,axiom,
( c_List_OtakeWhile(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_ONil(T_a)
| hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_singleton__rev__conv_0,axiom,
( c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) != c_List_Orev(V_xs,T_a)
| V_xs = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) ) ).
cnf(cls_rev__singleton__conv_1,axiom,
c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) ).
cnf(cls_last_Osimps_1,axiom,
( c_List_Olast(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olast(V_xs,T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_singleton__rev__conv_1,axiom,
c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) = c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) ).
cnf(cls_splice_Osimps_I2_J_1,axiom,
( c_List_Osplice(c_List_Olist_OCons(V_x,V_xs,T_a),V_ys,T_a) = c_List_Olist_OCons(V_x,c_List_Olist_OCons(c_List_Ohd(V_ys,T_a),c_List_Osplice(V_xs,c_List_Otl(V_ys,T_a),T_a),T_a),T_a)
| V_ys = c_List_Olist_ONil(T_a) ) ).
cnf(cls_takeWhile__append2_0,axiom,
( c_List_OtakeWhile(V_P,c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(V_xs,c_List_OtakeWhile(V_P,V_ys,T_a),T_a)
| c_in(c_List_Osko__List__XtakeWhile__append2__1__1(V_P,V_xs,T_a),c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_sorted__append_4,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(c_List_Oappend(V_xs,V_ys,T_a),T_a)
| c_in(c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2(V_xs,V_ys,T_a),c_List_Oset(V_ys,T_a),T_a)
| ~ c_List_Olinorder__class_Osorted(V_ys,T_a)
| ~ c_List_Olinorder__class_Osorted(V_xs,T_a) ) ).
cnf(cls_sorted__append_3,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(c_List_Oappend(V_xs,V_ys,T_a),T_a)
| c_in(c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1(V_xs,V_ys,T_a),c_List_Oset(V_xs,T_a),T_a)
| ~ c_List_Olinorder__class_Osorted(V_ys,T_a)
| ~ c_List_Olinorder__class_Osorted(V_xs,T_a) ) ).
cnf(cls_sorted__Cons_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_x,V_xs,T_a),T_a)
| c_in(c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1(V_x,V_xs,T_a),c_List_Oset(V_xs,T_a),T_a)
| ~ c_List_Olinorder__class_Osorted(V_xs,T_a) ) ).
cnf(cls_Notes__imp__knows__Spy_0,axiom,
( c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg)
| ~ c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Event_Oevent_ONotes(V_A,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) ).
cnf(cls_Crypt__Spy__analz__bad_0,axiom,
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ).
cnf(cls_ns__sharedp_OFake_0,axiom,
( c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OSpy,V_B,V_X),V_evsf,tc_Event_Oevent))
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evsf))),tc_Message_Omsg)
| ~ c_NS__Shared__Mirabelle_Ons__sharedp(V_evsf) ) ).
cnf(cls_analz__insert__Crypt__subset_0,axiom,
c_lessequals(c_Message_Oanalz(c_Set_Oinsert(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)),c_Set_Oinsert(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Oanalz(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_dropWhile__eq__Cons__conv_2,axiom,
( V_xs != c_List_Oappend(c_List_OtakeWhile(V_P,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_a),T_a)
| c_List_OdropWhile(V_P,V_xs,T_a) = c_List_Olist_OCons(V_y,V_ys,T_a)
| hBOOL(hAPP(V_P,V_y)) ) ).
cnf(cls_dropWhile__eq__Cons__conv_0,axiom,
( c_List_OdropWhile(V_P,V_xs,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a)
| V_xs = c_List_Oappend(c_List_OtakeWhile(V_P,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_a),T_a) ) ).
cnf(cls_analz__insert__eq__I_0,axiom,
( c_Message_Oanalz(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)) = c_Set_Oinsert(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| c_in(c_Message_Osko__Message__Xanalz__insert__eq__I__1__1(V_H,V_X),c_Message_Oanalz(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),tc_Message_Omsg) ) ).
cnf(cls_analz__insert__eq__I_1,axiom,
( c_Message_Oanalz(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)) = c_Set_Oinsert(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Osko__Message__Xanalz__insert__eq__I__1__1(V_H,V_X),c_Set_Oinsert(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg),tc_Message_Omsg) ) ).
cnf(cls_Fake__analz__eq_0,axiom,
( c_Message_Osynth(c_Message_Oanalz(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg))) = c_Message_Osynth(c_Message_Oanalz(V_H))
| ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) ) ).
cnf(cls_takeWhile__eq__all__conv_1,axiom,
( c_List_OtakeWhile(V_P,V_xs,T_a) = V_xs
| c_in(c_List_Osko__List__XtakeWhile__eq__all__conv__1__1(V_P,V_xs,T_a),c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_takeWhile__cong_0,axiom,
( c_List_OtakeWhile(V_P,V_x,T_a) = c_List_OtakeWhile(V_Q,V_x,T_a)
| c_in(c_List_Osko__List__XtakeWhile__cong__1__1(V_P,V_Q,V_x,T_a),c_List_Oset(V_x,T_a),T_a) ) ).
cnf(cls_sorted__Cons_3,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_x,V_xs,T_a),T_a)
| ~ c_lessequals(V_x,c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1(V_x,V_xs,T_a),T_a)
| ~ c_List_Olinorder__class_Osorted(V_xs,T_a) ) ).
cnf(cls_set__update__subset__insert_0,axiom,
c_lessequals(c_List_Oset(c_List_Olist__update(V_xs,V_i,V_x,T_a),T_a),c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a),tc_fun(T_a,tc_bool)) ).
cnf(cls_remove1__append_0,axiom,
( c_List_Oremove1(V_x,c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Oremove1(V_x,V_xs,T_a),V_ys,T_a)
| ~ c_in(V_x,c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_dropWhile__append1_0,axiom,
( c_List_OdropWhile(V_P,c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_OdropWhile(V_P,V_xs,T_a),V_ys,T_a)
| hBOOL(hAPP(V_P,V_x))
| ~ c_in(V_x,c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_remove1__append_1,axiom,
( c_List_Oremove1(V_x,c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(V_xs,c_List_Oremove1(V_x,V_ys,T_a),T_a)
| c_in(V_x,c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_filter__empty__conv_0,axiom,
( c_List_Ofilter(V_P,V_xs,T_a) != c_List_Olist_ONil(T_a)
| ~ hBOOL(hAPP(V_P,V_x))
| ~ c_in(V_x,c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_dropWhile__eq__Nil__conv_0,axiom,
( c_List_OdropWhile(V_P,V_xs,T_a) != c_List_Olist_ONil(T_a)
| hBOOL(hAPP(V_P,V_x))
| ~ c_in(V_x,c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_set__update__subsetI_0,axiom,
( c_lessequals(c_List_Oset(c_List_Olist__update(V_xs,V_i,V_x,T_a),T_a),V_A,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(c_List_Oset(V_xs,T_a),V_A,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_remdups_Osimps_I2_J_0,axiom,
( c_List_Oremdups(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Oremdups(V_xs,T_a)
| ~ c_in(V_x,c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_list__inter_Osimps_I2_J_0,axiom,
( c_List_Olist__inter(c_List_Olist_OCons(V_a,V_as,T_a),V_bs,T_a) = c_List_Olist_OCons(V_a,c_List_Olist__inter(V_as,V_bs,T_a),T_a)
| ~ c_in(V_a,c_List_Oset(V_bs,T_a),T_a) ) ).
cnf(cls_list__inter_Osimps_I2_J_1,axiom,
( c_List_Olist__inter(c_List_Olist_OCons(V_a,V_as,T_a),V_bs,T_a) = c_List_Olist__inter(V_as,V_bs,T_a)
| c_in(V_a,c_List_Oset(V_bs,T_a),T_a) ) ).
cnf(cls_length__unique_Osimps_I2_J_0,axiom,
( c_List_Olength__unique(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olength__unique(V_xs,T_a)
| ~ c_in(V_x,c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_distinct_Osimps_I2_J_0,axiom,
( ~ c_in(V_x,c_List_Oset(V_xs,T_a),T_a)
| ~ c_List_Odistinct(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).
cnf(cls_remdups_Osimps_I2_J_1,axiom,
( c_List_Oremdups(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oremdups(V_xs,T_a),T_a)
| c_in(V_x,c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_distinct_Osimps_I2_J_2,axiom,
( c_List_Odistinct(c_List_Olist_OCons(V_x,V_xs,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a)
| c_in(V_x,c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_psubset__insert__iff_7,axiom,
( c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_A,T_a)
| ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_psubset__insert__iff_3,axiom,
( c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_A,T_a)
| c_in(V_x,V_B,T_a) ) ).
cnf(cls_psubset__insert__iff_2,axiom,
( c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_A,T_a)
| c_in(V_x,V_B,T_a)
| ~ c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Spy__spies__bad__shrK_0,axiom,
( c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg)
| ~ c_in(V_A,c_Event_Obad,tc_Message_Oagent) ) ).
cnf(cls_Says__imp__analz__Spy_0,axiom,
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,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) ) ).
cnf(cls_knows__imp__Says__Gets__Notes__initState_0,axiom,
( c_in(V_X,c_Event_OinitState(V_A),tc_Message_Omsg)
| c_in(c_Event_Oevent_ONotes(V_A,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Event_Oevent_OGets(V_A,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Event_Oevent_OSays(V_A,c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1(V_A,V_X,V_evs),V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| V_A = c_Message_Oagent_OSpy
| ~ c_in(V_X,c_Event_Oknows(V_A,V_evs),tc_Message_Omsg) ) ).
cnf(cls_used__nil__subset_0,axiom,
c_lessequals(c_Event_Oused(c_List_Olist_ONil(tc_Event_Oevent)),c_Event_Oused(V_evs),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_event_Osimps_I9_J_0,axiom,
c_Event_Oevent_ONotes(V_agent_H,V_msg_H) != c_Event_Oevent_OGets(V_agent,V_msg) ).
cnf(cls_knows__subset__knows__Says_0,axiom,
c_lessequals(c_Event_Oknows(V_A,V_evs),c_Event_Oknows(V_A,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A_H,V_B,V_X),V_evs,tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_knows__subset__knows__Gets_0,axiom,
c_lessequals(c_Event_Oknows(V_A,V_evs),c_Event_Oknows(V_A,c_List_Olist_OCons(c_Event_Oevent_OGets(V_A_H,V_X),V_evs,tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_analz__mono__contra_I1_J_0,axiom,
( ~ c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent))),tc_Message_Omsg) ) ).
cnf(cls_analz__mono__contra_I3_J_0,axiom,
( ~ c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OGets(V_A,V_X),V_evs,tc_Event_Oevent))),tc_Message_Omsg) ) ).
cnf(cls_agent_Osimps_I5_J_0,axiom,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer ).
cnf(cls_agent_Osimps_I4_J_0,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy ).
cnf(cls_analz__insert__cong_0,axiom,
( c_Message_Oanalz(V_H) != c_Message_Oanalz(V_H_H)
| c_Message_Oanalz(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)) = c_Message_Oanalz(c_Set_Oinsert(V_X,V_H_H,tc_Message_Omsg)) ) ).
cnf(cls_rev__append_0,axiom,
c_List_Orev(c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Orev(V_xs,T_a),T_a) ).
cnf(cls_append__replicate__commute_0,axiom,
c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oappend(c_List_Oreplicate(V_k,V_x,T_a),c_List_Oreplicate(V_n,V_x,T_a),T_a) ).
cnf(cls_sorted__append_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(V_xs,T_a)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).
cnf(cls_sorted__append_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(V_ys,T_a)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).
cnf(cls_rotate1__hd__tl_0,axiom,
( c_List_Orotate1(V_xs,T_a) = c_List_Oappend(c_List_Otl(V_xs,T_a),c_List_Olist_OCons(c_List_Ohd(V_xs,T_a),c_List_Olist_ONil(T_a),T_a),T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_rev__is__Nil__conv_1,axiom,
c_List_Orev(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_rev__is__Nil__conv_0,axiom,
( c_List_Orev(V_xs,T_a) != c_List_Olist_ONil(T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_sorted_Osimps_I1_J_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(c_List_Olist_ONil(T_a),T_a) ) ).
cnf(cls_rotate__simps_0,axiom,
c_List_Orotate1(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_rotate1__is__Nil__conv_0,axiom,
( c_List_Orotate1(V_xs,T_a) != c_List_Olist_ONil(T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_concat__map_Osimps_I1_J_0,axiom,
c_List_Oconcat__map(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_Nil__is__rev__conv_0,axiom,
( c_List_Olist_ONil(T_a) != c_List_Orev(V_xs,T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_tl_Osimps_I1_J_0,axiom,
c_List_Otl(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_takeWhile_Osimps_I1_J_0,axiom,
c_List_OtakeWhile(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_butlast_Osimps_I1_J_0,axiom,
c_List_Obutlast(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_Nil__is__rev__conv_1,axiom,
c_List_Olist_ONil(T_a) = c_List_Orev(c_List_Olist_ONil(T_a),T_a) ).
cnf(cls_insert__subset_1,axiom,
( c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_subset__insertI2_0,axiom,
( c_lessequals(V_A,c_Set_Oinsert(V_b,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_subset__insertI_0,axiom,
c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) ).
cnf(cls_insert__mono_0,axiom,
( c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_takeWhile_Osimps_I2_J_0,axiom,
( c_List_OtakeWhile(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_OtakeWhile(V_P,V_xs,T_a),T_a)
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_sorted__Cons_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(V_xs,T_a)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).
cnf(cls_sorted_Osimps_I3_J_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_y,V_zs,T_a),T_a)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_x,c_List_Olist_OCons(V_y,V_zs,T_a),T_a),T_a) ) ).
cnf(cls_tl_Osimps_I2_J_0,axiom,
c_List_Otl(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = V_xs ).
cnf(cls_hd_Osimps_0,axiom,
c_List_Ohd(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = V_x ).
cnf(cls_in__set__butlast__appendI_0,axiom,
( c_in(V_x,c_List_Oset(c_List_Obutlast(c_List_Oappend(V_xs,V_ys,T_a),T_a),T_a),T_a)
| ~ c_in(V_x,c_List_Oset(c_List_Obutlast(V_xs,T_a),T_a),T_a) ) ).
cnf(cls_in__set__butlast__appendI_1,axiom,
( c_in(V_x,c_List_Oset(c_List_Obutlast(c_List_Oappend(V_xs,V_ys,T_a),T_a),T_a),T_a)
| ~ c_in(V_x,c_List_Oset(c_List_Obutlast(V_ys,T_a),T_a),T_a) ) ).
cnf(cls_takeWhile__append1_0,axiom,
( c_List_OtakeWhile(V_P,c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_OtakeWhile(V_P,V_xs,T_a)
| hBOOL(hAPP(V_P,V_x))
| ~ c_in(V_x,c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_hd__in__set_0,axiom,
( c_in(c_List_Ohd(V_xs,T_a),c_List_Oset(V_xs,T_a),T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_last__in__set_0,axiom,
( c_in(c_List_Olast(V_as,T_a),c_List_Oset(V_as,T_a),T_a)
| V_as = c_List_Olist_ONil(T_a) ) ).
cnf(cls_set__mp_0,axiom,
( c_in(V_x,V_B,T_a)
| ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_subsetD_0,axiom,
( 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)) ) ).
cnf(cls_set__rev__mp_0,axiom,
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a) ) ).
cnf(cls_subset__iff_0,axiom,
( c_in(V_t,V_B,T_a)
| ~ c_in(V_t,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_le__funD_0,axiom,
( ~ class_HOL_Oord(T_b)
| c_lessequals(hAPP(V_f,V_x),hAPP(V_g,V_x),T_b)
| ~ c_lessequals(V_f,V_g,tc_fun(T_a,T_b)) ) ).
cnf(cls_set__takeWhileD_1,axiom,
( hBOOL(hAPP(V_P,V_x))
| ~ c_in(V_x,c_List_Oset(c_List_OtakeWhile(V_P,V_xs,T_a),T_a),T_a) ) ).
cnf(cls_sorted__Cons_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_xa,T_a)
| ~ c_in(V_xa,c_List_Oset(V_xs,T_a),T_a)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).
cnf(cls_set__takeWhileD_0,axiom,
( c_in(V_x,c_List_Oset(V_xs,T_a),T_a)
| ~ c_in(V_x,c_List_Oset(c_List_OtakeWhile(V_P,V_xs,T_a),T_a),T_a) ) ).
cnf(cls_analz__insertI_0,axiom,
( c_in(V_c,c_Message_Oanalz(c_Set_Oinsert(V_a,V_G,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(V_c,c_Message_Oanalz(V_G),tc_Message_Omsg) ) ).
cnf(cls_event_Osimps_I5_J_0,axiom,
c_Event_Oevent_OGets(V_agent_H,V_msg_H) != c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) ).
cnf(cls_sorted__takeWhile_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(c_List_OtakeWhile(V_P,V_xs,T_a),T_a)
| ~ c_List_Olinorder__class_Osorted(V_xs,T_a) ) ).
cnf(cls_analz__insert__eq_0,axiom,
( c_Message_Oanalz(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)) = c_Message_Oanalz(V_H)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) ) ).
cnf(cls_sorted__append_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_xa,T_a)
| ~ c_in(V_xa,c_List_Oset(V_ys,T_a),T_a)
| ~ c_in(V_x,c_List_Oset(V_xs,T_a),T_a)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).
cnf(cls_analz__analzD_0,axiom,
( c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(c_Message_Oanalz(V_H)),tc_Message_Omsg) ) ).
cnf(cls_last__rev_0,axiom,
( c_List_Olast(c_List_Orev(V_xs,T_a),T_a) = c_List_Ohd(V_xs,T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_replicate__eq__replicate_0,axiom,
( c_List_Oreplicate(V_m,V_x,T_a) != c_List_Oreplicate(V_n,V_y,T_a)
| V_m = V_n ) ).
cnf(cls_event_Osimps_I4_J_0,axiom,
c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OGets(V_agent_H,V_msg_H) ).
cnf(cls_analz__cut_0,axiom,
( c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(V_Y,c_Message_Oanalz(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),tc_Message_Omsg) ) ).
cnf(cls_initState__subset__knows_0,axiom,
c_lessequals(c_Event_OinitState(V_A),c_Event_Oknows(V_A,V_evs),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_rev__swap_0,axiom,
V_xs = c_List_Orev(c_List_Orev(V_xs,T_a),T_a) ).
cnf(cls_rev__swap_1,axiom,
c_List_Orev(c_List_Orev(V_ys,T_a),T_a) = V_ys ).
cnf(cls_rev__rev__ident_0,axiom,
c_List_Orev(c_List_Orev(V_xs,T_a),T_a) = V_xs ).
cnf(cls_rev__replicate_0,axiom,
c_List_Orev(c_List_Oreplicate(V_n,V_x,T_a),T_a) = c_List_Oreplicate(V_n,V_x,T_a) ).
cnf(cls_hd__rev_0,axiom,
( c_List_Ohd(c_List_Orev(V_xs,T_a),T_a) = c_List_Olast(V_xs,T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_analz__trans_0,axiom,
( c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_lessequals(V_G,c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(V_X,c_Message_Oanalz(V_G),tc_Message_Omsg) ) ).
cnf(cls_analz__increasing_0,axiom,
c_lessequals(V_H,c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_analz__subset__iff_0,axiom,
( c_lessequals(V_G,c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ) ).
cnf(cls_analz__subset__iff_1,axiom,
( c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_lessequals(V_G,c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool)) ) ).
cnf(cls_event_Osimps_I2_J_1,axiom,
( c_Event_Oevent_OGets(V_agent,V_msg) != c_Event_Oevent_OGets(V_agent_H,V_msg_H)
| V_msg = V_msg_H ) ).
cnf(cls_event_Osimps_I2_J_0,axiom,
( c_Event_Oevent_OGets(V_agent,V_msg) != c_Event_Oevent_OGets(V_agent_H,V_msg_H)
| V_agent = V_agent_H ) ).
cnf(cls_set__rev_0,axiom,
c_List_Oset(c_List_Orev(V_xs,T_a),T_a) = c_List_Oset(V_xs,T_a) ).
cnf(cls_equalityI_0,axiom,
( V_A = V_B
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_set__eq__subset_2,axiom,
( V_A = V_B
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_order__eq__iff_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_order__antisym_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_order__antisym__conv_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_in__set__replicateD_0,axiom,
( V_x = V_y
| ~ c_in(V_x,c_List_Oset(c_List_Oreplicate(V_n,V_y,T_a),T_a),T_a) ) ).
cnf(cls_set__rotate1_0,axiom,
c_List_Oset(c_List_Orotate1(V_xs,T_a),T_a) = c_List_Oset(V_xs,T_a) ).
cnf(cls_sorted_Osimps_I3_J_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_x,c_List_Olist_OCons(V_y,V_zs,T_a),T_a),T_a) ) ).
cnf(cls_rev__is__rev__conv_0,axiom,
( c_List_Orev(V_xs,T_a) != c_List_Orev(V_ys,T_a)
| V_xs = V_ys ) ).
cnf(cls_set__subset__Cons_0,axiom,
c_lessequals(c_List_Oset(V_xs,T_a),c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),tc_fun(T_a,tc_bool)) ).
cnf(cls_gen__analz__insert__eq_0,axiom,
( c_Message_Oanalz(c_Set_Oinsert(V_X,V_G,tc_Message_Omsg)) = c_Message_Oanalz(V_G)
| ~ c_lessequals(V_H,V_G,tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) ) ).
cnf(cls_analz_OInj_0,axiom,
( c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg)
| ~ c_in(V_X,V_H,tc_Message_Omsg) ) ).
cnf(cls_event_Osimps_I1_J_2,axiom,
( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H)
| V_msg = V_msg_H ) ).
cnf(cls_event_Osimps_I1_J_1,axiom,
( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H)
| V_agent2 = V_agent2_H ) ).
cnf(cls_event_Osimps_I1_J_0,axiom,
( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H)
| V_agent1 = V_agent1_H ) ).
cnf(cls_sorted_Osimps_I3_J_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_x,c_List_Olist_OCons(V_y,V_zs,T_a),T_a),T_a)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_y,V_zs,T_a),T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_xt1_I6_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_z,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_order__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_equalityE_0,axiom,
c_lessequals(V_x,V_x,tc_fun(T_a,tc_bool)) ).
cnf(cls_subset__refl_0,axiom,
c_lessequals(V_A,V_A,tc_fun(T_a,tc_bool)) ).
cnf(cls_subset__trans_0,axiom,
( c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_predicate1D_0,axiom,
( hBOOL(hAPP(V_Q,V_x))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ c_lessequals(V_P,V_Q,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_order__eq__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ) ).
cnf(cls_order__eq__refl_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_x,T_a) ) ).
cnf(cls_rev__predicate1D_0,axiom,
( hBOOL(hAPP(V_Q,V_x))
| ~ c_lessequals(V_P,V_Q,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_analz__mono_0,axiom,
( c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_fun(tc_Message_Omsg,tc_bool))
| ~ c_lessequals(V_G,V_H,tc_fun(tc_Message_Omsg,tc_bool)) ) ).
cnf(cls_in__set__butlastD_0,axiom,
( c_in(V_x,c_List_Oset(V_xs,T_a),T_a)
| ~ c_in(V_x,c_List_Oset(c_List_Obutlast(V_xs,T_a),T_a),T_a) ) ).
cnf(cls_takeWhile__eq__all__conv_0,axiom,
( c_List_OtakeWhile(V_P,V_xs,T_a) != V_xs
| hBOOL(hAPP(V_P,V_x))
| ~ c_in(V_x,c_List_Oset(V_xs,T_a),T_a) ) ).
cnf(cls_analz__idem_0,axiom,
c_Message_Oanalz(c_Message_Oanalz(V_H)) = c_Message_Oanalz(V_H) ).
cnf(cls_analz__insert_0,axiom,
c_lessequals(c_Set_Oinsert(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg),c_Message_Oanalz(c_Set_Oinsert(V_X,V_H,tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_linorder__linear_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_sorted_Osimps_I2_J_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) ) ).
cnf(cls_replicate__app__Cons__same_0,axiom,
c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),V_xs,T_a),T_a) ).
cnf(cls_Cons__eq__append__conv_3,axiom,
( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Oappend(V_ys,V_zs,T_a)
| V_xs = c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a)
| c_List_Olist_OCons(V_x,V_xs,T_a) = V_zs ) ).
cnf(cls_append__eq__Cons__conv_2,axiom,
( c_List_Oappend(V_ys,V_zs,T_a) != c_List_Olist_OCons(V_x,V_xs,T_a)
| V_ys = c_List_Olist_OCons(V_x,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a)
| V_zs = c_List_Olist_OCons(V_x,V_xs,T_a) ) ).
cnf(cls_takeWhile__tail_0,axiom,
( c_List_OtakeWhile(V_P,c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,V_l,T_a),T_a),T_a) = c_List_OtakeWhile(V_P,V_xs,T_a)
| hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_split__list__first__prop__iff_6,axiom,
( hBOOL(hAPP(V_P,c_List_Osko__List__Xsplit__list__first__prop__iff__1__5(V_P,c_List_Oappend(V_x,c_List_Olist_OCons(V_xa,V_xb,T_a),T_a),T_a)))
| hBOOL(hAPP(V_P,c_List_Osko__List__Xsplit__list__first__prop__iff__1__5(V_P,V_x,T_a)))
| ~ hBOOL(hAPP(V_P,V_xa)) ) ).
cnf(cls_concat__map_Osimps_I2_J_0,axiom,
c_List_Oconcat__map(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Oappend(hAPP(V_f,V_x),c_List_Oconcat__map(V_f,V_xs,T_b,T_a),T_a) ).
cnf(cls_split__list__last__prop__iff_6,axiom,
( hBOOL(hAPP(V_P,c_List_Osko__List__Xsplit__list__last__prop__iff__1__5(V_P,c_List_Oappend(V_x,c_List_Olist_OCons(V_xa,V_xb,T_a),T_a),T_a)))
| hBOOL(hAPP(V_P,c_List_Osko__List__Xsplit__list__last__prop__iff__1__5(V_P,V_xb,T_a)))
| ~ hBOOL(hAPP(V_P,V_xa)) ) ).
cnf(cls_Cons__eq__append__conv_2,axiom,
( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Oappend(V_ys,V_zs,T_a)
| c_List_Olist_OCons(V_x,c_List_Osko__List__XCons__eq__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a) = V_ys
| c_List_Olist_OCons(V_x,V_xs,T_a) = V_zs ) ).
cnf(cls_append__eq__Cons__conv_3,axiom,
( c_List_Oappend(V_ys,V_zs,T_a) != c_List_Olist_OCons(V_x,V_xs,T_a)
| c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a) = V_xs
| V_zs = c_List_Olist_OCons(V_x,V_xs,T_a) ) ).
cnf(cls_butlast__append_1,axiom,
( c_List_Obutlast(c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(V_xs,c_List_Obutlast(V_ys,T_a),T_a)
| V_ys = c_List_Olist_ONil(T_a) ) ).
cnf(cls_hd__append_0,axiom,
c_List_Ohd(c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a),T_a) = c_List_Ohd(V_ys,T_a) ).
cnf(cls_last__append_0,axiom,
c_List_Olast(c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olast(V_xs,T_a) ).
cnf(cls_last__append_1,axiom,
( c_List_Olast(c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Olast(V_ys,T_a)
| V_ys = c_List_Olist_ONil(T_a) ) ).
cnf(cls_tl__append2_0,axiom,
( c_List_Otl(c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Otl(V_xs,T_a),V_ys,T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_butlast__append_0,axiom,
c_List_Obutlast(c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Obutlast(V_xs,T_a) ).
cnf(cls_hd__append_1,axiom,
( c_List_Ohd(c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Ohd(V_xs,T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_analz__mono__contra_I2_J_0,axiom,
( ~ c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_c,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A,V_X),V_evs,tc_Event_Oevent))),tc_Message_Omsg) ) ).
cnf(cls_knows__subset__knows__Cons_0,axiom,
c_lessequals(c_Event_Oknows(V_A,V_evs),c_Event_Oknows(V_A,c_List_Olist_OCons(V_e,V_evs,tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_Server__not__bad_0,axiom,
~ c_in(c_Message_Oagent_OServer,c_Event_Obad,tc_Message_Oagent) ).
cnf(cls_knows__Nil_0,axiom,
c_Event_Oknows(V_A,c_List_Olist_ONil(tc_Event_Oevent)) = c_Event_OinitState(V_A) ).
cnf(cls_in__set__conv__decomp__first_2,axiom,
( c_in(V_x,c_List_Oset(c_List_Oappend(V_xa,c_List_Olist_OCons(V_x,V_xb,T_a),T_a),T_a),T_a)
| c_in(V_x,c_List_Oset(V_xa,T_a),T_a) ) ).
cnf(cls_in__set__conv__decomp__last_2,axiom,
( c_in(V_x,c_List_Oset(c_List_Oappend(V_xa,c_List_Olist_OCons(V_x,V_xb,T_a),T_a),T_a),T_a)
| c_in(V_x,c_List_Oset(V_xb,T_a),T_a) ) ).
cnf(cls_in__set__conv__decomp_1,axiom,
c_in(V_x,c_List_Oset(c_List_Oappend(V_xa,c_List_Olist_OCons(V_x,V_xb,T_a),T_a),T_a),T_a) ).
cnf(cls_Cons__eq__append__conv_1,axiom,
( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Oappend(V_ys,V_zs,T_a)
| V_xs = c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a)
| V_ys = c_List_Olist_ONil(T_a) ) ).
cnf(cls_append__eq__Cons__conv_0,axiom,
( c_List_Oappend(V_ys,V_zs,T_a) != c_List_Olist_OCons(V_x,V_xs,T_a)
| V_ys = c_List_Olist_OCons(V_x,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a)
| V_ys = c_List_Olist_ONil(T_a) ) ).
cnf(cls_last__snoc_0,axiom,
c_List_Olast(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) = V_x ).
cnf(cls_butlast__snoc_0,axiom,
c_List_Obutlast(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) = V_xs ).
cnf(cls_append__eq__Cons__conv_1,axiom,
( c_List_Oappend(V_ys,V_zs,T_a) != c_List_Olist_OCons(V_x,V_xs,T_a)
| c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a) = V_xs
| V_ys = c_List_Olist_ONil(T_a) ) ).
cnf(cls_Cons__eq__append__conv_0,axiom,
( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Oappend(V_ys,V_zs,T_a)
| c_List_Olist_OCons(V_x,c_List_Osko__List__XCons__eq__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a) = V_ys
| V_ys = c_List_Olist_ONil(T_a) ) ).
cnf(cls_rev_Osimps_I2_J_0,axiom,
c_List_Orev(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Oappend(c_List_Orev(V_xs,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) ).
cnf(cls_rev__eq__Cons__iff_0,axiom,
( c_List_Orev(V_xs,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a)
| V_xs = c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a) ) ).
cnf(cls_rev__eq__Cons__iff_1,axiom,
c_List_Orev(c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),T_a) = c_List_Olist_OCons(V_y,V_ys,T_a) ).
cnf(cls_rotate__simps_1,axiom,
c_List_Orotate1(c_List_Olist_OCons(V_x,V_xs,T_b),T_b) = c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_b),T_b),T_b) ).
cnf(cls_replicate__append__same_0,axiom,
c_List_Oappend(c_List_Oreplicate(V_i,V_x,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oreplicate(V_i,V_x,T_a),T_a) ).
cnf(cls_knows__Says_0,axiom,
c_Event_Oknows(V_A,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(V_A,V_evs),tc_Message_Omsg) ).
cnf(cls_knows__Spy__Gets_0,axiom,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OGets(V_A,V_X),V_evs,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) ).
cnf(cls_knows__subset__knows__Notes_0,axiom,
c_lessequals(c_Event_Oknows(V_A,V_evs),c_Event_Oknows(V_A,c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A_H,V_X),V_evs,tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_knows__Gets_0,axiom,
( c_Event_Oknows(V_A,c_List_Olist_OCons(c_Event_Oevent_OGets(V_A,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(V_A,V_evs),tc_Message_Omsg)
| V_A = c_Message_Oagent_OSpy ) ).
cnf(cls_knows__Spy__Says_0,axiom,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ).
cnf(cls_knows__Spy__subset__knows__Spy__Notes_0,axiom,
c_lessequals(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A,V_X),V_evs,tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool)) ).
cnf(cls_spies__Gets__rev_0,axiom,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(V_evs,c_List_Olist_OCons(c_Event_Oevent_OGets(V_A,V_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) ).
cnf(cls_spies__Says__rev_0,axiom,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(V_evs,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ).
cnf(cls_append__eq__append__conv2_5,axiom,
c_List_Oappend(V_xs,c_List_Oappend(V_x,V_ts,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_x,T_a),V_ts,T_a) ).
cnf(cls_append__eq__append__conv2_4,axiom,
c_List_Oappend(c_List_Oappend(V_zs,V_x,T_a),V_ys,T_a) = c_List_Oappend(V_zs,c_List_Oappend(V_x,V_ys,T_a),T_a) ).
cnf(cls_append__eq__appendI_0,axiom,
c_List_Oappend(V_xs,c_List_Oappend(V_xs1,V_us,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_xs1,T_a),V_us,T_a) ).
cnf(cls_append__assoc_0,axiom,
c_List_Oappend(c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a) = c_List_Oappend(V_xs,c_List_Oappend(V_ys,V_zs,T_a),T_a) ).
cnf(cls_append__is__Nil__conv_2,axiom,
c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_append1__eq__conv_1,axiom,
( c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) != c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a)
| V_x = V_y ) ).
cnf(cls_append1__eq__conv_0,axiom,
( c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) != c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a)
| V_xs = V_ys ) ).
cnf(cls_insert__iff_2,axiom,
( c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a)
| ~ c_in(V_a,V_A,T_a) ) ).
cnf(cls_insertCI_0,axiom,
( c_in(V_a,c_Set_Oinsert(V_b,V_B,T_a),T_a)
| ~ c_in(V_a,V_B,T_a) ) ).
cnf(cls_list_Oinject_1,axiom,
( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
| V_list = V_list_H ) ).
cnf(cls_list_Oinject_0,axiom,
( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
| V_a = V_a_H ) ).
cnf(cls_append__eq__Cons__conv_4,axiom,
c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a) ).
cnf(cls_self__append__conv2_0,axiom,
( V_ys != c_List_Oappend(V_xs,V_ys,T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_append__self__conv2_0,axiom,
( c_List_Oappend(V_xs,V_ys,T_a) != V_ys
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_self__append__conv_0,axiom,
( V_xs != c_List_Oappend(V_xs,V_ys,T_a)
| V_ys = c_List_Olist_ONil(T_a) ) ).
cnf(cls_append__self__conv_0,axiom,
( c_List_Oappend(V_xs,V_ys,T_a) != V_xs
| V_ys = c_List_Olist_ONil(T_a) ) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)) ).
cnf(cls_Spy__in__bad_0,axiom,
c_in(c_Message_Oagent_OSpy,c_Event_Obad,tc_Message_Oagent) ).
cnf(cls_event_Osimps_I3_J_0,axiom,
( c_Event_Oevent_ONotes(V_agent,V_msg) != c_Event_Oevent_ONotes(V_agent_H,V_msg_H)
| V_agent = V_agent_H ) ).
cnf(cls_event_Osimps_I3_J_1,axiom,
( c_Event_Oevent_ONotes(V_agent,V_msg) != c_Event_Oevent_ONotes(V_agent_H,V_msg_H)
| V_msg = V_msg_H ) ).
cnf(cls_list_Osimps_I2_J_0,axiom,
c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) ).
cnf(cls_insertE_0,axiom,
( c_in(V_a,V_A,T_a)
| V_a = V_b
| ~ c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) ) ).
cnf(cls_knows__Notes_0,axiom,
c_Event_Oknows(V_A,c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(V_A,V_evs),tc_Message_Omsg) ).
cnf(cls_append__is__Nil__conv_1,axiom,
( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a)
| V_ys = c_List_Olist_ONil(T_a) ) ).
cnf(cls_append__is__Nil__conv_0,axiom,
( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_Nil__is__append__conv_1,axiom,
( c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs,V_ys,T_a)
| V_ys = c_List_Olist_ONil(T_a) ) ).
cnf(cls_Nil__is__append__conv_0,axiom,
( c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs,V_ys,T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_insert__code_0,axiom,
( hBOOL(hAPP(V_A,V_x))
| V_y = V_x
| ~ hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x)) ) ).
cnf(cls_insert__absorb2_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Set_Oinsert(V_x,V_A,T_a) ).
cnf(cls_self__append__conv2_1,axiom,
V_ys = c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) ).
cnf(cls_append__Nil_0,axiom,
c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys ).
cnf(cls_self__append__conv_1,axiom,
V_xs = c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) ).
cnf(cls_eq__Nil__appendI_0,axiom,
V_x = c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a) ).
cnf(cls_append__Nil2_0,axiom,
c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs ).
cnf(cls_same__append__eq_0,axiom,
( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Oappend(V_xs,V_zs,T_a)
| V_ys = V_zs ) ).
cnf(cls_append__same__eq_0,axiom,
( c_List_Oappend(V_ys,V_xs,T_a) != c_List_Oappend(V_zs,V_xs,T_a)
| V_ys = V_zs ) ).
cnf(cls_insert__iff_1,axiom,
c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) ).
cnf(cls_insertI1_0,axiom,
c_in(V_a,c_Set_Oinsert(V_a,V_B,T_a),T_a) ).
cnf(cls_insertCI_1,axiom,
c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a) ).
cnf(cls_knows__Spy__Notes_0,axiom,
( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg)
| ~ c_in(V_A,c_Event_Obad,tc_Message_Oagent) ) ).
cnf(cls_insert__commute_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_y,V_A,T_a),T_a) = c_Set_Oinsert(V_y,c_Set_Oinsert(V_x,V_A,T_a),T_a) ).
cnf(cls_mem__def_1,axiom,
( c_in(V_x,V_S,T_a)
| ~ hBOOL(hAPP(V_S,V_x)) ) ).
cnf(cls_mem__def_0,axiom,
( hBOOL(hAPP(V_S,V_x))
| ~ c_in(V_x,V_S,T_a) ) ).
cnf(cls_knows__Spy__Notes_1,axiom,
( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(V_A,V_X),V_evs,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent) ) ).
cnf(cls_append__eq__Cons__conv_5,axiom,
c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) ).
cnf(cls_append__Cons_0,axiom,
c_List_Oappend(c_List_Olist_OCons(V_x,V_xs,T_a),V_ys,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xs,V_ys,T_a),T_a) ).
cnf(cls_insert__code_2,axiom,
( hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x))
| ~ hBOOL(hAPP(V_A,V_x)) ) ).
cnf(cls_Cons__eq__append__conv_5,axiom,
c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) ).
cnf(cls_Cons__eq__appendI_0,axiom,
c_List_Olist_OCons(V_x,c_List_Oappend(V_xs1,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xs1,T_a),V_zs,T_a) ).
cnf(cls_insert__ident_0,axiom,
( c_Set_Oinsert(V_x,V_A,T_a) != c_Set_Oinsert(V_x,V_B,T_a)
| c_in(V_x,V_B,T_a)
| c_in(V_x,V_A,T_a)
| V_A = V_B ) ).
cnf(cls_neq__Nil__conv_1,axiom,
c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a) ).
cnf(cls_list_Osimps_I3_J_0,axiom,
c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ).
cnf(cls_insert__absorb_0,axiom,
( c_Set_Oinsert(V_a,V_A,T_a) = V_A
| ~ c_in(V_a,V_A,T_a) ) ).
cnf(cls_not__Cons__self2_0,axiom,
c_List_Olist_OCons(V_x,V_t,T_a) != V_t ).
cnf(cls_not__Cons__self_0,axiom,
V_xs != c_List_Olist_OCons(V_x,V_xs,T_a) ).
cnf(cls_Cons__eq__append__conv_4,axiom,
c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ).
cnf(cls_Nil__is__append__conv_2,axiom,
c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) ).
cnf(cls_conjecture_0,negated_conjecture,
( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) != c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent))
| c_in(v_A,c_Event_Obad,tc_Message_Oagent) ) ).
cnf(cls_conjecture_1,negated_conjecture,
( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) != c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg)
| ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent) ) ).
cnf(cls_conjecture_2,negated_conjecture,
( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) != c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent))
| c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) != c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg) ) ).
cnf(clsarity_fun__Orderings_Opreorder,axiom,
( class_Orderings_Opreorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Opreorder(T_1) ) ).
cnf(clsarity_fun__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Oorder(T_1) ) ).
cnf(clsarity_fun__HOL_Oord,axiom,
( class_HOL_Oord(tc_fun(T_2,T_1))
| ~ class_HOL_Oord(T_1) ) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat) ).
cnf(clsarity_nat__HOL_Oord,axiom,
class_HOL_Oord(tc_nat) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
c_fequal(V_x,V_x,T_a) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( V_X = V_Y
| ~ c_fequal(V_X,V_Y,T_a) ) ).
%------------------------------------------------------------------------------