TPTP Problem File: SWV778-1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWV778-1 : TPTP v8.2.0. Released v4.1.0.
% Domain : Software Verification
% Problem : Needham-Schroeder shared-key protocol 406_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-406_1 [Nip10]
% Status : Unsatisfiable
% Rating : 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.00 v6.1.0, 0.14 v6.0.0, 0.00 v5.5.0, 0.15 v5.4.0, 0.10 v5.3.0, 0.11 v5.2.0, 0.06 v5.1.0, 0.12 v5.0.0, 0.14 v4.1.0
% Syntax : Number of clauses : 443 ( 193 unt; 60 nHn; 169 RR)
% Number of literals : 841 ( 375 equ; 341 neg)
% Maximal clause size : 7 ( 1 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 22 ( 21 usr; 0 prp; 1-5 aty)
% Number of functors : 82 ( 82 usr; 8 con; 0-5 aty)
% Number of variables : 1489 ( 308 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments :
%------------------------------------------------------------------------------
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_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_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_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_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_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__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_drop__eq__Nil_0,axiom,
( c_List_Odrop(V_n,V_xs,T_a) != c_List_Olist_ONil(T_a)
| c_lessequals(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_n,tc_nat) ) ).
cnf(cls_drop__all_0,axiom,
( c_List_Odrop(V_n,V_xs,T_a) = c_List_Olist_ONil(T_a)
| ~ c_lessequals(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_n,tc_nat) ) ).
cnf(cls_append__eq__append__conv__if_2,axiom,
( c_List_Oappend(V_xs_092_060_094isub_0621,V_xs_092_060_094isub_0622,T_a) != c_List_Oappend(V_ys_092_060_094isub_0621,V_ys_092_060_094isub_0622,T_a)
| c_List_Otake(c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),V_xs_092_060_094isub_0621,T_a) = V_ys_092_060_094isub_0621
| c_lessequals(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),tc_nat) ) ).
cnf(cls_take__append_0,axiom,
c_List_Otake(V_n,c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Otake(V_n,V_xs,T_a),c_List_Otake(c_HOL_Ominus__class_Ominus(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat),V_ys,T_a),T_a) ).
cnf(cls_append__eq__append__conv__if_0,axiom,
( c_List_Oappend(V_xs_092_060_094isub_0621,V_xs_092_060_094isub_0622,T_a) != c_List_Oappend(V_ys_092_060_094isub_0621,V_ys_092_060_094isub_0622,T_a)
| V_xs_092_060_094isub_0621 = c_List_Otake(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),V_ys_092_060_094isub_0621,T_a)
| ~ c_lessequals(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),tc_nat) ) ).
cnf(cls_append__eq__append__conv__if_1,axiom,
( c_List_Oappend(V_xs_092_060_094isub_0621,V_xs_092_060_094isub_0622,T_a) != c_List_Oappend(V_ys_092_060_094isub_0621,V_ys_092_060_094isub_0622,T_a)
| V_xs_092_060_094isub_0622 = c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),V_ys_092_060_094isub_0621,T_a),V_ys_092_060_094isub_0622,T_a)
| ~ c_lessequals(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),tc_nat) ) ).
cnf(cls_append__eq__append__conv__if_3,axiom,
( c_List_Oappend(V_xs_092_060_094isub_0621,V_xs_092_060_094isub_0622,T_a) != c_List_Oappend(V_ys_092_060_094isub_0621,V_ys_092_060_094isub_0622,T_a)
| c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),V_xs_092_060_094isub_0621,T_a),V_xs_092_060_094isub_0622,T_a) = V_ys_092_060_094isub_0622
| c_lessequals(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),tc_nat) ) ).
cnf(cls_drop__append_0,axiom,
c_List_Odrop(V_n,c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Odrop(V_n,V_xs,T_a),c_List_Odrop(c_HOL_Ominus__class_Ominus(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat),V_ys,T_a),T_a) ).
cnf(cls_agent_Osplit_5,axiom,
( hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,t_a)))
| V_x = c_Message_Oagent_OSpy
| ~ hBOOL(hAPP(V_P,hAPP(V_f2,v_sko__Message__Xagent__Xsplit__1(V_P,V_f2,V_x))))
| V_x = c_Message_Oagent_OServer ) ).
cnf(cls_agent_Ocase__cong_2,axiom,
( hAPP(V_f2,c_Message_Osko__Message__Xagent__Xcase__cong__1__1(V_x,V_f2,V_g2,T_a)) != hAPP(V_g2,c_Message_Osko__Message__Xagent__Xcase__cong__1__1(V_x,V_f2,V_g2,T_a))
| V_x = c_Message_Oagent_OServer
| c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,T_a) = c_Message_Oagent_Oagent__case(V_g1,V_g2,V_g3,V_x,T_a)
| V_x = c_Message_Oagent_OSpy ) ).
cnf(cls_agent_Osplit__asm_5,axiom,
( hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,t_a)))
| V_x = c_Message_Oagent_OSpy
| ~ hBOOL(hAPP(V_P,hAPP(V_f2,v_sko__Message__Xagent__Xsplit__asm__1(V_P,V_f2,V_x))))
| V_x = c_Message_Oagent_OServer ) ).
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_agent_Osplit__asm_7,axiom,
( hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,t_a)))
| V_x = c_Message_Oagent_OSpy
| V_x = c_Message_Oagent_OFriend(v_sko__Message__Xagent__Xsplit__asm__1(V_P,V_f2,V_x))
| ~ hBOOL(hAPP(V_P,V_f1)) ) ).
cnf(cls_agent_Ocase__cong_4,axiom,
( c_Message_Oagent_Oagent__case(V_x,V_f2,V_f3,V_xa,T_a) = c_Message_Oagent_Oagent__case(V_x,V_g2,V_g3,V_xa,T_a)
| V_xa = c_Message_Oagent_OSpy
| V_xa = c_Message_Oagent_OFriend(c_Message_Osko__Message__Xagent__Xcase__cong__1__1(V_xa,V_f2,V_g2,T_a)) ) ).
cnf(cls_agent_Osplit_7,axiom,
( hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,t_a)))
| V_x = c_Message_Oagent_OSpy
| V_x = c_Message_Oagent_OFriend(v_sko__Message__Xagent__Xsplit__1(V_P,V_f2,V_x))
| ~ hBOOL(hAPP(V_P,V_f1)) ) ).
cnf(cls_agent_Osplit_4,axiom,
( hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,t_a)))
| ~ hBOOL(hAPP(V_P,V_f3))
| V_x = c_Message_Oagent_OFriend(v_sko__Message__Xagent__Xsplit__1(V_P,V_f2,V_x))
| V_x = c_Message_Oagent_OServer ) ).
cnf(cls_agent_Ocase__cong_1,axiom,
( V_xa = c_Message_Oagent_OFriend(c_Message_Osko__Message__Xagent__Xcase__cong__1__1(V_xa,V_f2,V_g2,T_a))
| V_xa = c_Message_Oagent_OServer
| c_Message_Oagent_Oagent__case(V_f1,V_f2,V_x,V_xa,T_a) = c_Message_Oagent_Oagent__case(V_g1,V_g2,V_x,V_xa,T_a) ) ).
cnf(cls_agent_Osplit__asm_4,axiom,
( hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,t_a)))
| ~ hBOOL(hAPP(V_P,V_f3))
| V_x = c_Message_Oagent_OFriend(v_sko__Message__Xagent__Xsplit__asm__1(V_P,V_f2,V_x))
| V_x = c_Message_Oagent_OServer ) ).
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_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_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_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_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_agent_Ocase__cong_7,axiom,
( hAPP(V_f2,c_Message_Osko__Message__Xagent__Xcase__cong__1__1(V_xb,V_f2,V_g2,T_a)) != hAPP(V_g2,c_Message_Osko__Message__Xagent__Xcase__cong__1__1(V_xb,V_f2,V_g2,T_a))
| c_Message_Oagent_Oagent__case(V_xa,V_f2,V_x,V_xb,T_a) = c_Message_Oagent_Oagent__case(V_xa,V_g2,V_x,V_xb,T_a) ) ).
cnf(cls_agent_Osplit_10,axiom,
( hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,t_a)))
| ~ hBOOL(hAPP(V_P,V_f3))
| ~ hBOOL(hAPP(V_P,hAPP(V_f2,v_sko__Message__Xagent__Xsplit__1(V_P,V_f2,V_x))))
| ~ hBOOL(hAPP(V_P,V_f1)) ) ).
cnf(cls_diff__diff__cancel_0,axiom,
( c_HOL_Ominus__class_Ominus(V_n,c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat) = V_i
| ~ c_lessequals(V_i,V_n,tc_nat) ) ).
cnf(cls_butlast__drop_0,axiom,
c_List_Obutlast(c_List_Odrop(V_n,V_xs,T_a),T_a) = c_List_Odrop(V_n,c_List_Obutlast(V_xs,T_a),T_a) ).
cnf(cls_mod__diff__eq_0,axiom,
( ~ class_Divides_Oring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).
cnf(cls_mod__less__eq__dividend_0,axiom,
c_lessequals(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_m,tc_nat) ).
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_diff__commute_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat) ).
cnf(cls_Nat_Odiff__diff__eq_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| ~ c_lessequals(V_k,V_m,tc_nat) ) ).
cnf(cls_diff__le__self_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) ).
cnf(cls_tl__drop_0,axiom,
c_List_Otl(c_List_Odrop(V_n,V_xs,T_a),T_a) = c_List_Odrop(V_n,c_List_Otl(V_xs,T_a),T_a) ).
cnf(cls_drop__butlast_0,axiom,
c_List_Odrop(V_n,c_List_Obutlast(V_xs,T_a),T_a) = c_List_Obutlast(c_List_Odrop(V_n,V_xs,T_a),T_a) ).
cnf(cls_eq__diff__iff_0,axiom,
( c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat) != c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| ~ c_lessequals(V_k,V_m,tc_nat)
| V_m = V_n ) ).
cnf(cls_eq__eqI_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| V_x_H = V_y_H ) ).
cnf(cls_eq__eqI_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)
| V_xa = V_y ) ).
cnf(cls_le__diff__iff_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| ~ c_lessequals(V_k,V_m,tc_nat) ) ).
cnf(cls_le__diff__iff_1,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| ~ c_lessequals(V_k,V_m,tc_nat) ) ).
cnf(cls_diff__le__mono_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_l,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_l,tc_nat),tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_diff__le__mono2_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ) ).
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_mod__diff__right__eq_0,axiom,
( ~ class_Divides_Oring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).
cnf(cls_mod__diff__left__eq_0,axiom,
( ~ class_Divides_Oring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ).
cnf(cls_inj__on__insert_0,axiom,
( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b) ) ).
cnf(cls_drop__tl_0,axiom,
c_List_Odrop(V_n,c_List_Otl(V_xs,T_a),T_a) = c_List_Otl(c_List_Odrop(V_n,V_xs,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_mod__mod__trivial_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).
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_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_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_le__mod__geq_0,axiom,
( c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat)
| ~ c_lessequals(V_n,V_m,tc_nat) ) ).
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_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_le__antisym_0,axiom,
( V_m = V_n
| ~ c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ) ).
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_mod__diff__cong_0,axiom,
( ~ class_Divides_Oring__div(T_a)
| c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
| c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a_H,V_b_H,T_a),V_c,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_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)) ).
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_le__refl_0,axiom,
c_lessequals(V_n,V_n,tc_nat) ).
cnf(cls_le__trans_0,axiom,
( c_lessequals(V_i,V_k,tc_nat)
| ~ c_lessequals(V_j,V_k,tc_nat)
| ~ c_lessequals(V_i,V_j,tc_nat) ) ).
cnf(cls_eq__imp__le_0,axiom,
c_lessequals(V_x,V_x,tc_nat) ).
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_subset__inj__on_0,axiom,
( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Fun_Oinj__on(V_f,V_B,T_a,T_b) ) ).
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_agent_Osplit__asm_10,axiom,
( hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,t_a)))
| ~ hBOOL(hAPP(V_P,V_f3))
| ~ hBOOL(hAPP(V_P,hAPP(V_f2,v_sko__Message__Xagent__Xsplit__asm__1(V_P,V_f2,V_x))))
| ~ hBOOL(hAPP(V_P,V_f1)) ) ).
cnf(cls_le__eqI_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| c_lessequals(V_y_H,V_x_H,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_le__eqI_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_y_H,V_x_H,T_a) ) ).
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_nat__le__linear_0,axiom,
( c_lessequals(V_n,V_m,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ) ).
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_rotate__rev_0,axiom,
c_List_Orotate(V_n,hAPP(c_List_Orev(T_a),V_xs),T_a) = hAPP(c_List_Orev(T_a),c_List_Orotate(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_Divides_Odiv__class_Omod(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat),tc_nat),V_xs,T_a)) ).
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_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_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_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_impossible__Cons_0,axiom,
~ c_lessequals(c_Nat_Osize__class_Osize(c_List_Olist_OCons(V_x,V_ys,T_a),tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_a)),tc_nat) ).
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_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_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_set__take__subset_0,axiom,
c_lessequals(c_List_Oset(c_List_Otake(V_n,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_take__all_0,axiom,
( c_List_Otake(V_n,V_xs,T_a) = V_xs
| ~ c_lessequals(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_n,tc_nat) ) ).
cnf(cls_length__filter__le_0,axiom,
c_lessequals(c_Nat_Osize__class_Osize(c_List_Ofilter(V_P,V_xs,T_a),tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ).
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_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_set__drop__subset_0,axiom,
c_lessequals(c_List_Oset(c_List_Odrop(V_n,V_xs,T_a),T_a),c_List_Oset(V_xs,T_a),tc_fun(T_a,tc_bool)) ).
cnf(cls_length__drop_0,axiom,
c_Nat_Osize__class_Osize(c_List_Odrop(V_n,V_xs,T_a),tc_List_Olist(T_a)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_n,tc_nat) ).
cnf(cls_list__update__beyond_0,axiom,
( c_List_Olist__update(V_xs,V_i,V_x,T_a) = V_xs
| ~ c_lessequals(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_i,tc_nat) ) ).
cnf(cls_length__dropWhile__le_0,axiom,
c_lessequals(c_Nat_Osize__class_Osize(c_List_OdropWhile(V_P,V_xs,T_a),tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ).
cnf(cls_drop__take_0,axiom,
c_List_Odrop(V_n,c_List_Otake(V_m,V_xs,T_a),T_a) = c_List_Otake(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_List_Odrop(V_n,V_xs,T_a),T_a) ).
cnf(cls_rotate__conv__mod_0,axiom,
c_List_Orotate(V_n,V_xs,T_a) = c_List_Orotate(c_Divides_Odiv__class_Omod(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat),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_length__remdups__leq_0,axiom,
c_lessequals(c_Nat_Osize__class_Osize(c_List_Oremdups(V_xs,T_a),tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ).
cnf(cls_agent_Osplit__asm_9,axiom,
( hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,t_a)))
| V_x = c_Message_Oagent_OSpy
| ~ hBOOL(hAPP(V_P,hAPP(V_f2,v_sko__Message__Xagent__Xsplit__asm__1(V_P,V_f2,V_x))))
| ~ hBOOL(hAPP(V_P,V_f1)) ) ).
cnf(cls_agent_Ocase__cong_6,axiom,
( hAPP(V_f2,c_Message_Osko__Message__Xagent__Xcase__cong__1__1(V_xa,V_f2,V_g2,T_a)) != hAPP(V_g2,c_Message_Osko__Message__Xagent__Xcase__cong__1__1(V_xa,V_f2,V_g2,T_a))
| c_Message_Oagent_Oagent__case(V_x,V_f2,V_f3,V_xa,T_a) = c_Message_Oagent_Oagent__case(V_x,V_g2,V_g3,V_xa,T_a)
| V_xa = c_Message_Oagent_OSpy ) ).
cnf(cls_agent_Osplit_9,axiom,
( hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,t_a)))
| V_x = c_Message_Oagent_OSpy
| ~ hBOOL(hAPP(V_P,hAPP(V_f2,v_sko__Message__Xagent__Xsplit__1(V_P,V_f2,V_x))))
| ~ hBOOL(hAPP(V_P,V_f1)) ) ).
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_drop__replicate_0,axiom,
c_List_Odrop(V_i,c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(V_k,V_i,tc_nat),V_x,T_a) ).
cnf(cls_set__sublist__subset_0,axiom,
c_lessequals(c_List_Oset(c_List_Osublist(V_xs,V_I,T_a),T_a),c_List_Oset(V_xs,T_a),tc_fun(T_a,tc_bool)) ).
cnf(cls_agent_Osplit_6,axiom,
( hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,t_a)))
| ~ hBOOL(hAPP(V_P,V_f3))
| ~ hBOOL(hAPP(V_P,hAPP(V_f2,v_sko__Message__Xagent__Xsplit__1(V_P,V_f2,V_x))))
| V_x = c_Message_Oagent_OServer ) ).
cnf(cls_agent_Osplit__asm_6,axiom,
( hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,t_a)))
| ~ hBOOL(hAPP(V_P,V_f3))
| ~ hBOOL(hAPP(V_P,hAPP(V_f2,v_sko__Message__Xagent__Xsplit__asm__1(V_P,V_f2,V_x))))
| V_x = c_Message_Oagent_OServer ) ).
cnf(cls_agent_Ocase__cong_3,axiom,
( hAPP(V_f2,c_Message_Osko__Message__Xagent__Xcase__cong__1__1(V_xa,V_f2,V_g2,T_a)) != hAPP(V_g2,c_Message_Osko__Message__Xagent__Xcase__cong__1__1(V_xa,V_f2,V_g2,T_a))
| V_xa = c_Message_Oagent_OServer
| c_Message_Oagent_Oagent__case(V_f1,V_f2,V_x,V_xa,T_a) = c_Message_Oagent_Oagent__case(V_g1,V_g2,V_x,V_xa,T_a) ) ).
cnf(cls_agent_Ocase__cong_5,axiom,
( V_xb = c_Message_Oagent_OFriend(c_Message_Osko__Message__Xagent__Xcase__cong__1__1(V_xb,V_f2,V_g2,T_a))
| c_Message_Oagent_Oagent__case(V_xa,V_f2,V_x,V_xb,T_a) = c_Message_Oagent_Oagent__case(V_xa,V_g2,V_x,V_xb,T_a) ) ).
cnf(cls_agent_Osplit__asm_8,axiom,
( hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,t_a)))
| ~ hBOOL(hAPP(V_P,V_f3))
| V_x = c_Message_Oagent_OFriend(v_sko__Message__Xagent__Xsplit__asm__1(V_P,V_f2,V_x))
| ~ hBOOL(hAPP(V_P,V_f1)) ) ).
cnf(cls_agent_Osplit_8,axiom,
( hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,t_a)))
| ~ hBOOL(hAPP(V_P,V_f3))
| V_x = c_Message_Oagent_OFriend(v_sko__Message__Xagent__Xsplit__1(V_P,V_f2,V_x))
| ~ hBOOL(hAPP(V_P,V_f1)) ) ).
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_list_Oinduct_1,axiom,
( hBOOL(hAPP(V_P,V_list))
| ~ hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__Xlist__Xinduct__1(V_P),v_sko__List__Xlist__Xinduct__2(V_P),t_a)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_list__update_Oinduct_1,axiom,
( hBOOL(hAPP(V_P,V_list))
| ~ hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__Xlist__update__Xinduct__1(V_P),v_sko__List__Xlist__update__Xinduct__2(V_P),t_a)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_removeAll_Oinduct_1,axiom,
( hBOOL(hAPP(V_P,V_list))
| ~ hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__XremoveAll__Xinduct__1(V_P),v_sko__List__XremoveAll__Xinduct__2(V_P),t_a)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_takeWhile_Oinduct_1,axiom,
( hBOOL(hAPP(V_P,V_list))
| ~ hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__XtakeWhile__Xinduct__1(V_P),v_sko__List__XtakeWhile__Xinduct__2(V_P),t_a)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_dropWhile_Oinduct_1,axiom,
( hBOOL(hAPP(V_P,V_list))
| ~ hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__XdropWhile__Xinduct__1(V_P),v_sko__List__XdropWhile__Xinduct__2(V_P),t_a)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_zip_Oinduct_1,axiom,
( hBOOL(hAPP(V_P,V_list))
| ~ hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__Xzip__Xinduct__1(V_P),v_sko__List__Xzip__Xinduct__2(V_P),t_a)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_listset_Oinduct_1,axiom,
( hBOOL(hAPP(V_P,V_list))
| ~ hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__Xlistset__Xinduct__1(V_P),v_sko__List__Xlistset__Xinduct__2(V_P),t_a)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_remove1_Oinduct_1,axiom,
( hBOOL(hAPP(V_P,V_list))
| ~ hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__Xremove1__Xinduct__1(V_P),v_sko__List__Xremove1__Xinduct__2(V_P),t_a)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_distinct_Oinduct_1,axiom,
( hBOOL(hAPP(V_P,V_list))
| ~ hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__Xdistinct__Xinduct__1(V_P),v_sko__List__Xdistinct__Xinduct__2(V_P),t_a)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_listsum_Oinduct_1,axiom,
( hBOOL(hAPP(V_P,V_list))
| ~ hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__Xlistsum__Xinduct__1(V_P),v_sko__List__Xlistsum__Xinduct__2(V_P),t_a)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_last_Oinduct_1,axiom,
( hBOOL(hAPP(V_P,V_list))
| ~ hBOOL(hAPP(V_P,c_List_Olist_OCons(v_sko__List__Xlast__Xinduct__1(V_P),v_sko__List__Xlast__Xinduct__2(V_P),t_a)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_append__eq__append__conv__if_4,axiom,
( c_List_Otake(c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),V_xs_092_060_094isub_0621,T_a) != V_ys_092_060_094isub_0621
| c_lessequals(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),tc_nat)
| c_List_Oappend(V_xs_092_060_094isub_0621,V_xs_092_060_094isub_0622,T_a) = c_List_Oappend(V_ys_092_060_094isub_0621,c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),V_xs_092_060_094isub_0621,T_a),V_xs_092_060_094isub_0622,T_a),T_a) ) ).
cnf(cls_append__eq__append__conv__if_5,axiom,
( V_xs_092_060_094isub_0621 != c_List_Otake(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),V_ys_092_060_094isub_0621,T_a)
| c_List_Oappend(V_xs_092_060_094isub_0621,c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),V_ys_092_060_094isub_0621,T_a),V_ys_092_060_094isub_0622,T_a),T_a) = c_List_Oappend(V_ys_092_060_094isub_0621,V_ys_092_060_094isub_0622,T_a)
| ~ c_lessequals(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),tc_nat) ) ).
cnf(cls_setsum__set__distinct__conv__listsum_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_b)
| c_Finite__Set_Osetsum(V_f,c_List_Oset(V_xs,T_a),T_a,T_b) = c_List_Olistsum(c_List_Omap(V_f,V_xs,T_a,T_b),T_b)
| ~ c_List_Odistinct(V_xs,T_a) ) ).
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_rev__take_0,axiom,
hAPP(c_List_Orev(T_a),c_List_Otake(V_i,V_xs,T_a)) = c_List_Odrop(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_i,tc_nat),hAPP(c_List_Orev(T_a),V_xs),T_a) ).
cnf(cls_rev__drop_0,axiom,
hAPP(c_List_Orev(T_a),c_List_Odrop(V_i,V_xs,T_a)) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_i,tc_nat),hAPP(c_List_Orev(T_a),V_xs),T_a) ).
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__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_agent_Osplit__asm_3,axiom,
( hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,t_a)))
| V_x = c_Message_Oagent_OSpy
| V_x = c_Message_Oagent_OFriend(v_sko__Message__Xagent__Xsplit__asm__1(V_P,V_f2,V_x))
| V_x = c_Message_Oagent_OServer ) ).
cnf(cls_agent_Ocase__cong_0,axiom,
( c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,T_a) = c_Message_Oagent_Oagent__case(V_g1,V_g2,V_g3,V_x,T_a)
| V_x = c_Message_Oagent_OSpy
| V_x = c_Message_Oagent_OFriend(c_Message_Osko__Message__Xagent__Xcase__cong__1__1(V_x,V_f2,V_g2,T_a))
| V_x = c_Message_Oagent_OServer ) ).
cnf(cls_agent_Osplit_3,axiom,
( hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,V_x,t_a)))
| V_x = c_Message_Oagent_OSpy
| V_x = c_Message_Oagent_OFriend(v_sko__Message__Xagent__Xsplit__1(V_P,V_f2,V_x))
| V_x = c_Message_Oagent_OServer ) ).
cnf(cls_rotate__drop__take_0,axiom,
c_List_Orotate(V_n,V_xs,T_a) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat),V_xs,T_a),c_List_Otake(c_Divides_Odiv__class_Omod(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat),V_xs,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_sorted__drop_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(c_List_Odrop(V_n,V_xs,T_a),T_a)
| ~ c_List_Olinorder__class_Osorted(V_xs,T_a) ) ).
cnf(cls_take__map_0,axiom,
c_List_Otake(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Otake(V_n,V_xs,T_b),T_b,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_agent_Osimps_I2_J_0,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OFriend(V_nat_H) ).
cnf(cls_list__all2__takeI_0,axiom,
( c_List_Olist__all2(V_P,c_List_Otake(V_n,V_xs,T_a),c_List_Otake(V_n,V_ys,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b) ) ).
cnf(cls_distinct__map_1,axiom,
( c_Fun_Oinj__on(V_f,c_List_Oset(V_xs,T_b),T_b,T_a)
| ~ c_List_Odistinct(c_List_Omap(V_f,V_xs,T_b,T_a),T_a) ) ).
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_list__all2__eq_1,axiom,
( V_xs = V_ys
| ~ c_List_Olist__all2(c_fequal(T_a),V_xs,V_ys,T_a,T_a) ) ).
cnf(cls_foldl__Cons_0,axiom,
c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b) = c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b) ).
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_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_list__all2__appendI_0,axiom,
( c_List_Olist__all2(V_P,c_List_Oappend(V_a,V_c,T_a),c_List_Oappend(V_b,V_d,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_c,V_d,T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_a,V_b,T_a,T_b) ) ).
cnf(cls_list__all2__append2_5,axiom,
( c_Nat_Osize__class_Osize(V_xa,tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_zs,tc_List_Olist(T_b))
| c_Nat_Osize__class_Osize(V_x,tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
| c_List_Olist__all2(V_P,c_List_Oappend(V_x,V_xa,T_a),c_List_Oappend(V_ys,V_zs,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xa,V_zs,T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_x,V_ys,T_a,T_b) ) ).
cnf(cls_list__all2__append1_5,axiom,
( c_Nat_Osize__class_Osize(V_xa,tc_List_Olist(T_b)) != c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_a))
| c_Nat_Osize__class_Osize(V_x,tc_List_Olist(T_b)) != c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a))
| c_List_Olist__all2(V_P,c_List_Oappend(V_xs,V_ys,T_a),c_List_Oappend(V_x,V_xa,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_ys,V_xa,T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xs,V_x,T_a,T_b) ) ).
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_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_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_append__eq__conv__conj_1,axiom,
V_ys = c_List_Odrop(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_List_Oappend(V_xs,V_ys,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_map__eq__Cons__conv_3,axiom,
c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xa,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xa,T_b,T_a),T_a) ).
cnf(cls_Cons__eq__map__conv_3,axiom,
c_List_Olist_OCons(hAPP(V_f,V_xa),c_List_Omap(V_f,V_xb,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Olist_OCons(V_xa,V_xb,T_b),T_b,T_a) ).
cnf(cls_map_Osimps_I2_J_0,axiom,
c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) ).
cnf(cls_list_Osimps_I5_J_0,axiom,
c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_OCons(V_a,V_list,T_b),T_a,T_b) = hAPP(hAPP(V_f2,V_a),V_list) ).
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_agent_Osimps_I3_J_0,axiom,
c_Message_Oagent_OFriend(V_nat_H) != c_Message_Oagent_OServer ).
cnf(cls_list__all2__Cons_0,axiom,
( hBOOL(hAPP(hAPP(V_P,V_x),V_y))
| ~ c_List_Olist__all2(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_b),T_a,T_b) ) ).
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_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_agent_Osimps_I8_J_0,axiom,
c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,c_Message_Oagent_OServer,T_a) = V_f1 ).
cnf(cls_distinct__map_2,axiom,
( c_List_Odistinct(c_List_Omap(V_f,V_xs,T_b,T_a),T_a)
| ~ c_Fun_Oinj__on(V_f,c_List_Oset(V_xs,T_b),T_b,T_a)
| ~ c_List_Odistinct(V_xs,T_b) ) ).
cnf(cls_append__take__drop__id_0,axiom,
c_List_Oappend(c_List_Otake(V_n,V_xs,T_a),c_List_Odrop(V_n,V_xs,T_a),T_a) = V_xs ).
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_distinct__drop_0,axiom,
( c_List_Odistinct(c_List_Odrop(V_i,V_xs,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a) ) ).
cnf(cls_list__all_Osimps_I2_J_1,axiom,
( c_List_Olist__all(V_P,V_xs,T_a)
| ~ c_List_Olist__all(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).
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_list__all_Osimps_I2_J_0,axiom,
( hBOOL(hAPP(V_P,V_x))
| ~ c_List_Olist__all(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),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_list__all2__append_2,axiom,
( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
| c_List_Olist__all2(V_P,c_List_Oappend(V_xs,V_us,T_a),c_List_Oappend(V_ys,V_vs,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_us,V_vs,T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b) ) ).
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_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_length__list__update_0,axiom,
c_Nat_Osize__class_Osize(c_List_Olist__update(V_xs,V_i,V_x,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(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_map__update_0,axiom,
c_List_Omap(V_f,c_List_Olist__update(V_xs,V_k,V_y,T_b),T_b,T_a) = c_List_Olist__update(c_List_Omap(V_f,V_xs,T_b,T_a),V_k,hAPP(V_f,V_y),T_a) ).
cnf(cls_agent_Osimps_I9_J_0,axiom,
c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,c_Message_Oagent_OFriend(V_nat),T_a) = hAPP(V_f2,V_nat) ).
cnf(cls_list__all__append_2,axiom,
( c_List_Olist__all(V_P,c_List_Oappend(V_xs,V_ys,T_a),T_a)
| ~ c_List_Olist__all(V_P,V_ys,T_a)
| ~ c_List_Olist__all(V_P,V_xs,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_distinct__take_0,axiom,
( c_List_Odistinct(c_List_Otake(V_i,V_xs,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a) ) ).
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_foldl__append_0,axiom,
c_List_Ofoldl(V_f,V_a,c_List_Oappend(V_xs,V_ys,T_b),T_a,T_b) = c_List_Ofoldl(V_f,c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b),V_ys,T_a,T_b) ).
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_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_agent_Oinject_0,axiom,
( c_Message_Oagent_OFriend(V_nat) != c_Message_Oagent_OFriend(V_nat_H)
| V_nat = V_nat_H ) ).
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_map__is__Nil__conv_0,axiom,
( c_List_Omap(V_f,V_xs,T_b,T_a) != c_List_Olist_ONil(T_a)
| V_xs = c_List_Olist_ONil(T_b) ) ).
cnf(cls_list__all2__Nil_1,axiom,
c_List_Olist__all2(V_P,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_b),T_a,T_b) ).
cnf(cls_empty__null_1,axiom,
( V_xs = c_List_Olist_ONil(T_a)
| ~ c_List_Onull(V_xs,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_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_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_rotate__is__Nil__conv_0,axiom,
( c_List_Orotate(V_n,V_xs,T_a) != c_List_Olist_ONil(T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_list__all2__Nil2_0,axiom,
( V_xs = c_List_Olist_ONil(T_a)
| ~ c_List_Olist__all2(V_P,V_xs,c_List_Olist_ONil(T_b),T_a,T_b) ) ).
cnf(cls_list__all2__Nil_0,axiom,
( V_ys = c_List_Olist_ONil(T_b)
| ~ c_List_Olist__all2(V_P,c_List_Olist_ONil(T_a),V_ys,T_a,T_b) ) ).
cnf(cls_distinct_Osimps_I1_J_0,axiom,
c_List_Odistinct(c_List_Olist_ONil(T_a),T_a) ).
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_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_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_append__in__listsp__conv_0,axiom,
( c_List_Olistsp(V_A,V_xs,T_a)
| ~ c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).
cnf(cls_append__in__listsp__conv_1,axiom,
( c_List_Olistsp(V_A,V_ys,T_a)
| ~ c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),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_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_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_sorted__take_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_List_Olinorder__class_Osorted(c_List_Otake(V_n,V_xs,T_a),T_a)
| ~ c_List_Olinorder__class_Osorted(V_xs,T_a) ) ).
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_list__all2__Cons_1,axiom,
( c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b)
| ~ c_List_Olist__all2(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_b),T_a,T_b) ) ).
cnf(cls_rotate__map_0,axiom,
c_List_Orotate(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Orotate(V_n,V_xs,T_b),T_b,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_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_length__remdups__eq_0,axiom,
( c_Nat_Osize__class_Osize(c_List_Oremdups(V_xs,T_a),tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a))
| c_List_Oremdups(V_xs,T_a) = V_xs ) ).
cnf(cls_length__remdups__eq_1,axiom,
( c_List_Oremdups(V_xs,T_a) != V_xs
| c_Nat_Osize__class_Osize(c_List_Oremdups(V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) ) ).
cnf(cls_append__eq__conv__conj_0,axiom,
V_xs = c_List_Otake(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_List_Oappend(V_xs,V_ys,T_a),T_a) ).
cnf(cls_length__map_0,axiom,
c_Nat_Osize__class_Osize(c_List_Omap(V_f,V_xs,T_b,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_b)) ).
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_map__replicate_0,axiom,
c_List_Omap(V_f,c_List_Oreplicate(V_n,V_x,T_b),T_b,T_a) = c_List_Oreplicate(V_n,hAPP(V_f,V_x),T_a) ).
cnf(cls_foldr__append_0,axiom,
c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a) = c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a) ).
cnf(cls_list__ex_Osimps_I2_J_1,axiom,
( c_List_Olist__ex(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a)
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
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_list__all2__Cons_2,axiom,
( c_List_Olist__all2(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b)
| ~ hBOOL(hAPP(hAPP(V_P,V_x),V_y)) ) ).
cnf(cls_list__all2__Cons1_3,axiom,
( c_List_Olist__all2(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_xa,V_xb,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xs,V_xb,T_a,T_b)
| ~ hBOOL(hAPP(hAPP(V_P,V_x),V_xa)) ) ).
cnf(cls_list__all2__Cons2_3,axiom,
( c_List_Olist__all2(V_P,c_List_Olist_OCons(V_x,V_xa,T_a),c_List_Olist_OCons(V_y,V_ys,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xa,V_ys,T_a,T_b)
| ~ hBOOL(hAPP(hAPP(V_P,V_x),V_y)) ) ).
cnf(cls_list__ex_Osimps_I2_J_2,axiom,
( c_List_Olist__ex(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a)
| ~ c_List_Olist__ex(V_P,V_xs,T_a) ) ).
cnf(cls_list__ex_Osimps_I2_J_0,axiom,
( c_List_Olist__ex(V_P,V_xs,T_a)
| hBOOL(hAPP(V_P,V_x))
| ~ c_List_Olist__ex(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).
cnf(cls_list__all2__def_0,axiom,
( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
| ~ c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b) ) ).
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_listrelp_OCons_0,axiom,
( c_List_Olistrelp(V_r,c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_a),T_a)
| ~ c_List_Olistrelp(V_r,V_xs,V_ys,T_a)
| ~ hBOOL(hAPP(hAPP(V_r,V_x),V_y)) ) ).
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_distinct__sublistI_0,axiom,
( c_List_Odistinct(c_List_Osublist(V_xs,V_I,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a) ) ).
cnf(cls_map__eq__imp__length__eq_0,axiom,
( c_List_Omap(V_f,V_xs,T_b,T_a) != c_List_Omap(V_f,V_ys,T_b,T_a)
| c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_b)) = c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b)) ) ).
cnf(cls_fun__upds__append__drop_0,axiom,
( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
| c_Map_Omap__upds(V_m,c_List_Oappend(V_xs,V_zs,T_a),V_ys,T_a,T_b) = c_Map_Omap__upds(V_m,V_xs,V_ys,T_a,T_b) ) ).
cnf(cls_fun__upds__append2__drop_0,axiom,
( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
| c_Map_Omap__upds(V_m,V_xs,c_List_Oappend(V_ys,V_zs,T_b),T_a,T_b) = c_Map_Omap__upds(V_m,V_xs,V_ys,T_a,T_b) ) ).
cnf(cls_append__eq__conv__conj_2,axiom,
( V_xs != c_List_Otake(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_zs,T_a)
| c_List_Oappend(V_xs,c_List_Odrop(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_zs,T_a),T_a) = V_zs ) ).
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_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_list__all2__append_0,axiom,
( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
| c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b)
| ~ c_List_Olist__all2(V_P,c_List_Oappend(V_xs,V_us,T_a),c_List_Oappend(V_ys,V_vs,T_b),T_a,T_b) ) ).
cnf(cls_list__all2__append_1,axiom,
( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
| c_List_Olist__all2(V_P,V_us,V_vs,T_a,T_b)
| ~ c_List_Olist__all2(V_P,c_List_Oappend(V_xs,V_us,T_a),c_List_Oappend(V_ys,V_vs,T_b),T_a,T_b) ) ).
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_length__rotate_0,axiom,
c_Nat_Osize__class_Osize(c_List_Orotate(V_n,V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) ).
cnf(cls_length__rotate1_0,axiom,
c_Nat_Osize__class_Osize(c_List_Orotate1(V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(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_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_map__append_0,axiom,
c_List_Omap(V_f,c_List_Oappend(V_xs,V_ys,T_b),T_b,T_a) = c_List_Oappend(c_List_Omap(V_f,V_xs,T_b,T_a),c_List_Omap(V_f,V_ys,T_b,T_a),T_a) ).
cnf(cls_agent_Osplit_0,axiom,
( ~ hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,c_Message_Oagent_OServer,t_a)))
| hBOOL(hAPP(V_P,V_f1)) ) ).
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_list__all2__dropI_0,axiom,
( c_List_Olist__all2(V_P,c_List_Odrop(V_n,V_as,T_a),c_List_Odrop(V_n,V_bs,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_as,V_bs,T_a,T_b) ) ).
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_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_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_list_Orecs_I2_J_0,axiom,
c_List_Olist_Olist__rec(V_f1,V_f2,c_List_Olist_OCons(V_a,V_list,T_b),T_a,T_b) = hAPP(hAPP(hAPP(V_f2,V_a),V_list),c_List_Olist_Olist__rec(V_f1,V_f2,V_list,T_a,T_b)) ).
cnf(cls_set__rotate_0,axiom,
c_List_Oset(c_List_Orotate(V_n,V_xs,T_a),T_a) = c_List_Oset(V_xs,T_a) ).
cnf(cls_distinct__map_0,axiom,
( c_List_Odistinct(V_xs,T_b)
| ~ c_List_Odistinct(c_List_Omap(V_f,V_xs,T_b,T_a),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_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_distinct__rotate_0,axiom,
( c_List_Odistinct(V_xs,T_a)
| ~ c_List_Odistinct(c_List_Orotate(V_n,V_xs,T_a),T_a) ) ).
cnf(cls_distinct__rotate_1,axiom,
( c_List_Odistinct(c_List_Orotate(V_n,V_xs,T_a),T_a)
| ~ c_List_Odistinct(V_xs,T_a) ) ).
cnf(cls_append__in__listsp__conv_2,axiom,
( c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a)
| ~ c_List_Olistsp(V_A,V_ys,T_a)
| ~ c_List_Olistsp(V_A,V_xs,T_a) ) ).
cnf(cls_length__replicate_0,axiom,
c_Nat_Osize__class_Osize(c_List_Oreplicate(V_n,V_x,T_a),tc_List_Olist(T_a)) = V_n ).
cnf(cls_agent_Osplit_1,axiom,
( ~ hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,c_Message_Oagent_OFriend(V_nat),t_a)))
| hBOOL(hAPP(V_P,hAPP(V_f2,V_nat))) ) ).
cnf(cls_agent_Osplit__asm_1,axiom,
( ~ hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,c_Message_Oagent_OFriend(V_xa),t_a)))
| hBOOL(hAPP(V_P,hAPP(V_f2,V_xa))) ) ).
cnf(cls_List_Onull_Osimps_I2_J_0,axiom,
~ c_List_Onull(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ).
cnf(cls_foldr_Osimps_I2_J_0,axiom,
c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,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_agent_Orecs_I2_J_0,axiom,
c_Message_Oagent_Oagent__rec(V_f1,V_f2,V_f3,c_Message_Oagent_OFriend(V_nat),T_a) = hAPP(V_f2,V_nat) ).
cnf(cls_list__update__length_0,axiom,
c_List_Olist__update(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,V_ys,T_a),T_a),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_y,T_a) = c_List_Oappend(V_xs,c_List_Olist_OCons(V_y,V_ys,T_a),T_a) ).
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_distinct__remdups_0,axiom,
c_List_Odistinct(c_List_Oremdups(V_xs,T_a),T_a) ).
cnf(cls_append__eq__append__conv__if_6,axiom,
( c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),V_xs_092_060_094isub_0621,T_a),c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),V_ys_092_060_094isub_0621,T_a),V_ys_092_060_094isub_0622,T_a),T_a) != V_ys_092_060_094isub_0622
| c_List_Otake(c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),V_xs_092_060_094isub_0621,T_a) != V_ys_092_060_094isub_0621
| V_xs_092_060_094isub_0621 != c_List_Otake(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),V_ys_092_060_094isub_0621,T_a)
| c_List_Oappend(V_xs_092_060_094isub_0621,c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),V_ys_092_060_094isub_0621,T_a),V_ys_092_060_094isub_0622,T_a),T_a) = c_List_Oappend(V_ys_092_060_094isub_0621,V_ys_092_060_094isub_0622,T_a) ) ).
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_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_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_list__all_Osimps_I2_J_2,axiom,
( c_List_Olist__all(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a)
| ~ c_List_Olist__all(V_P,V_xs,T_a)
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
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_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_drop__map_0,axiom,
c_List_Odrop(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Odrop(V_n,V_xs,T_b),T_b,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_agent_Orecs_I1_J_0,axiom,
c_Message_Oagent_Oagent__rec(V_f1,V_f2,V_f3,c_Message_Oagent_OServer,T_a) = V_f1 ).
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_hd_Osimps_0,axiom,
c_List_Ohd(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = V_x ).
cnf(cls_list__all2__eq_0,axiom,
c_List_Olist__all2(c_fequal(T_a),V_x,V_x,T_a,T_a) ).
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_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_list__all__append_0,axiom,
( c_List_Olist__all(V_P,V_xs,T_a)
| ~ c_List_Olist__all(V_P,c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).
cnf(cls_list__all__append_1,axiom,
( c_List_Olist__all(V_P,V_ys,T_a)
| ~ c_List_Olist__all(V_P,c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).
cnf(cls_rotate1__rotate__swap_0,axiom,
c_List_Orotate1(c_List_Orotate(V_n,V_xs,T_a),T_a) = c_List_Orotate(V_n,c_List_Orotate1(V_xs,T_a),T_a) ).
cnf(cls_list_Osplit_1,axiom,
( ~ hBOOL(hAPP(V_P,c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_OCons(V_a,V_list,t_b),t_a,t_b)))
| hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_a),V_list))) ) ).
cnf(cls_list_Osplit__asm_1,axiom,
( ~ hBOOL(hAPP(V_P,c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_OCons(V_xa,V_xb,t_b),t_a,t_b)))
| hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_xa),V_xb))) ) ).
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_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__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__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__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_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_foldl__Nil_0,axiom,
c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ).
cnf(cls_listsum_Oinduct_0,axiom,
( hBOOL(hAPP(V_P,V_list))
| hBOOL(hAPP(V_P,v_sko__List__Xlistsum__Xinduct__2(V_P)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(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_drop__Nil_0,axiom,
c_List_Odrop(V_n,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_Nil__is__map__conv_0,axiom,
( c_List_Olist_ONil(T_a) != c_List_Omap(V_f,V_xs,T_b,T_a)
| V_xs = c_List_Olist_ONil(T_b) ) ).
cnf(cls_removeAll_Oinduct_0,axiom,
( hBOOL(hAPP(V_P,V_list))
| hBOOL(hAPP(V_P,v_sko__List__XremoveAll__Xinduct__2(V_P)))
| ~ hBOOL(hAPP(V_P,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_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_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_last_Oinduct_0,axiom,
( hBOOL(hAPP(V_P,V_list))
| hBOOL(hAPP(V_P,v_sko__List__Xlast__Xinduct__2(V_P)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_take__eq__Nil_2,axiom,
c_List_Otake(V_n,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_takeWhile_Oinduct_0,axiom,
( hBOOL(hAPP(V_P,V_list))
| hBOOL(hAPP(V_P,v_sko__List__XtakeWhile__Xinduct__2(V_P)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_listsp_ONil_0,axiom,
c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ).
cnf(cls_list__update_Oinduct_0,axiom,
( hBOOL(hAPP(V_P,V_list))
| hBOOL(hAPP(V_P,v_sko__List__Xlist__update__Xinduct__2(V_P)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_foldl_Oinduct_0,axiom,
( hBOOL(hAPP(V_P,V_list))
| hBOOL(hAPP(V_P,v_sko__List__Xfoldl__Xinduct__2(V_P)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_list__all_Osimps_I1_J_0,axiom,
c_List_Olist__all(V_P,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_list__ex_Osimps_I1_J_0,axiom,
~ c_List_Olist__ex(V_P,c_List_Olist_ONil(T_a),T_a) ).
cnf(cls_empty__null_0,axiom,
c_List_Onull(c_List_Olist_ONil(T_a),T_a) ).
cnf(cls_list_Osplit_0,axiom,
( ~ hBOOL(hAPP(V_P,c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_ONil(t_b),t_a,t_b)))
| hBOOL(hAPP(V_P,V_f1)) ) ).
cnf(cls_foldr_Osimps_I1_J_0,axiom,
c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a) = V_a ).
cnf(cls_zip_Oinduct_0,axiom,
( hBOOL(hAPP(V_P,V_list))
| hBOOL(hAPP(V_P,v_sko__List__Xzip__Xinduct__2(V_P)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_map__is__Nil__conv_1,axiom,
c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_sublist__nil_0,axiom,
c_List_Osublist(c_List_Olist_ONil(T_a),V_A,T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_listset_Oinduct_0,axiom,
( hBOOL(hAPP(V_P,V_list))
| hBOOL(hAPP(V_P,v_sko__List__Xlistset__Xinduct__2(V_P)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_list_Orecs_I1_J_0,axiom,
c_List_Olist_Olist__rec(V_f1,V_f2,c_List_Olist_ONil(T_b),T_a,T_b) = V_f1 ).
cnf(cls_dropWhile_Oinduct_0,axiom,
( hBOOL(hAPP(V_P,V_list))
| hBOOL(hAPP(V_P,v_sko__List__XdropWhile__Xinduct__2(V_P)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_take_Oinduct_0,axiom,
( hBOOL(hAPP(V_P,V_list))
| hBOOL(hAPP(V_P,v_sko__List__Xtake__Xinduct__2(V_P)))
| ~ hBOOL(hAPP(V_P,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_filtermap_Osimps_I1_J_0,axiom,
c_List_Ofiltermap(V_f,c_List_Olist_ONil(T_b),T_b,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_concat_Oinduct_0,axiom,
( hBOOL(hAPP(V_P,V_list))
| hBOOL(hAPP(V_P,v_sko__List__Xconcat__Xinduct__2(V_P)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
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_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_distinct_Oinduct_0,axiom,
( hBOOL(hAPP(V_P,V_list))
| hBOOL(hAPP(V_P,v_sko__List__Xdistinct__Xinduct__2(V_P)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_map__upds__Nil2_0,axiom,
c_Map_Omap__upds(V_m,V_as,c_List_Olist_ONil(T_b),T_a,T_b) = V_m ).
cnf(cls_map__upds__Nil1_0,axiom,
c_Map_Omap__upds(V_m,c_List_Olist_ONil(T_a),V_bs,T_a,T_b) = V_m ).
cnf(cls_remove1_Oinduct_0,axiom,
( hBOOL(hAPP(V_P,V_list))
| hBOOL(hAPP(V_P,v_sko__List__Xremove1__Xinduct__2(V_P)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_list_Osimps_I4_J_0,axiom,
c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_ONil(T_b),T_a,T_b) = V_f1 ).
cnf(cls_rotate__is__Nil__conv_1,axiom,
c_List_Orotate(V_n,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_list_Oinduct_0,axiom,
( hBOOL(hAPP(V_P,V_list))
| hBOOL(hAPP(V_P,v_sko__List__Xlist__Xinduct__2(V_P)))
| ~ hBOOL(hAPP(V_P,c_List_Olist_ONil(t_a))) ) ).
cnf(cls_Nil__is__map__conv_1,axiom,
c_List_Olist_ONil(T_a) = c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,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_listrelp_ONil_0,axiom,
c_List_Olistrelp(V_r,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) ).
cnf(cls_map_Oinduct_0,axiom,
( hBOOL(hAPP(V_P,V_list))
| hBOOL(hAPP(V_P,v_sko__List__Xmap__Xinduct__2(V_P)))
| ~ hBOOL(hAPP(V_P,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_hd__rev_0,axiom,
( c_List_Ohd(hAPP(c_List_Orev(T_a),V_xs),T_a) = c_List_Olast(V_xs,T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_last__rev_0,axiom,
( c_List_Olast(hAPP(c_List_Orev(T_a),V_xs),T_a) = c_List_Ohd(V_xs,T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_rev_Osimps_I2_J_0,axiom,
hAPP(c_List_Orev(T_a),c_List_Olist_OCons(V_x,V_xs,T_a)) = c_List_Oappend(hAPP(c_List_Orev(T_a),V_xs),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) ).
cnf(cls_rev__eq__Cons__iff_0,axiom,
( hAPP(c_List_Orev(T_a),V_xs) != c_List_Olist_OCons(V_y,V_ys,T_a)
| V_xs = c_List_Oappend(hAPP(c_List_Orev(T_a),V_ys),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a) ) ).
cnf(cls_rev__eq__Cons__iff_1,axiom,
hAPP(c_List_Orev(T_a),c_List_Oappend(hAPP(c_List_Orev(T_a),V_ys),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a)) = c_List_Olist_OCons(V_y,V_ys,T_a) ).
cnf(cls_agent_Osimps_I10_J_0,axiom,
c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,c_Message_Oagent_OSpy,T_a) = V_f3 ).
cnf(cls_agent_Osimps_I6_J_0,axiom,
c_Message_Oagent_OFriend(V_nat) != c_Message_Oagent_OSpy ).
cnf(cls_agent_Orecs_I3_J_0,axiom,
c_Message_Oagent_Oagent__rec(V_f1,V_f2,V_f3,c_Message_Oagent_OSpy,T_a) = V_f3 ).
cnf(cls_agent_Osimps_I4_J_0,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy ).
cnf(cls_agent_Osplit_2,axiom,
( ~ hBOOL(hAPP(V_P,c_Message_Oagent_Oagent__case(V_f1,V_f2,V_f3,c_Message_Oagent_OSpy,t_a)))
| hBOOL(hAPP(V_P,V_f3)) ) ).
cnf(cls_agent_Osimps_I7_J_0,axiom,
c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(V_nat) ).
cnf(cls_agent_Osimps_I5_J_0,axiom,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer ).
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_rev__filter_0,axiom,
hAPP(c_List_Orev(T_a),c_List_Ofilter(V_P,V_xs,T_a)) = c_List_Ofilter(V_P,hAPP(c_List_Orev(T_a),V_xs),T_a) ).
cnf(cls_length__rev_0,axiom,
c_Nat_Osize__class_Osize(hAPP(c_List_Orev(T_a),V_xs),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) ).
cnf(cls_list__all__rev_1,axiom,
( c_List_Olist__all(V_P,hAPP(c_List_Orev(T_a),V_xs),T_a)
| ~ c_List_Olist__all(V_P,V_xs,T_a) ) ).
cnf(cls_list__all__rev_0,axiom,
( c_List_Olist__all(V_P,V_xs,T_a)
| ~ c_List_Olist__all(V_P,hAPP(c_List_Orev(T_a),V_xs),T_a) ) ).
cnf(cls_listsum__rev_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_List_Olistsum(hAPP(c_List_Orev(T_a),V_xs),T_a) = c_List_Olistsum(V_xs,T_a) ) ).
cnf(cls_set__rev_0,axiom,
c_List_Oset(hAPP(c_List_Orev(T_a),V_xs),T_a) = c_List_Oset(V_xs,T_a) ).
cnf(cls_rev__replicate_0,axiom,
hAPP(c_List_Orev(T_a),c_List_Oreplicate(V_n,V_x,T_a)) = c_List_Oreplicate(V_n,V_x,T_a) ).
cnf(cls_list__all2__rev_1,axiom,
( c_List_Olist__all2(V_P,hAPP(c_List_Orev(T_a),V_xs),hAPP(c_List_Orev(T_b),V_ys),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b) ) ).
cnf(cls_list__all2__rev_0,axiom,
( c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b)
| ~ c_List_Olist__all2(V_P,hAPP(c_List_Orev(T_a),V_xs),hAPP(c_List_Orev(T_b),V_ys),T_a,T_b) ) ).
cnf(cls_rev__map_0,axiom,
hAPP(c_List_Orev(T_a),c_List_Omap(V_f,V_xs,T_b,T_a)) = c_List_Omap(V_f,hAPP(c_List_Orev(T_b),V_xs),T_b,T_a) ).
cnf(cls_inj__on__rev_0,axiom,
c_Fun_Oinj__on(c_List_Orev(T_a),V_A,tc_List_Olist(T_a),tc_List_Olist(T_a)) ).
cnf(cls_distinct__rev_1,axiom,
( c_List_Odistinct(hAPP(c_List_Orev(T_a),V_xs),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(hAPP(c_List_Orev(T_a),V_xs),T_a) ) ).
cnf(cls_rev__append_0,axiom,
hAPP(c_List_Orev(T_a),c_List_Oappend(V_xs,V_ys,T_a)) = c_List_Oappend(hAPP(c_List_Orev(T_a),V_ys),hAPP(c_List_Orev(T_a),V_xs),T_a) ).
cnf(cls_list__all2__rev1_1,axiom,
( c_List_Olist__all2(V_P,hAPP(c_List_Orev(T_a),V_xs),V_ys,T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xs,hAPP(c_List_Orev(T_b),V_ys),T_a,T_b) ) ).
cnf(cls_list__all2__rev1_0,axiom,
( c_List_Olist__all2(V_P,V_xs,hAPP(c_List_Orev(T_b),V_ys),T_a,T_b)
| ~ c_List_Olist__all2(V_P,hAPP(c_List_Orev(T_a),V_xs),V_ys,T_a,T_b) ) ).
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_ns__sharedp_ONil_0,axiom,
c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)) ).
cnf(cls_rev__singleton__conv_0,axiom,
( hAPP(c_List_Orev(T_a),V_xs) != 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_singleton__rev__conv_0,axiom,
( c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) != hAPP(c_List_Orev(T_a),V_xs)
| V_xs = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) ) ).
cnf(cls_rev__singleton__conv_1,axiom,
hAPP(c_List_Orev(T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a)) = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) ).
cnf(cls_singleton__rev__conv_1,axiom,
c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) = hAPP(c_List_Orev(T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a)) ).
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_Nil__is__rev__conv_1,axiom,
c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) ).
cnf(cls_Nil__is__rev__conv_0,axiom,
( c_List_Olist_ONil(T_a) != hAPP(c_List_Orev(T_a),V_xs)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_rev__is__rev__conv_0,axiom,
( hAPP(c_List_Orev(T_a),V_xs) != hAPP(c_List_Orev(T_a),V_ys)
| V_xs = V_ys ) ).
cnf(cls_rev__rev__ident_0,axiom,
hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
cnf(cls_rev__swap_1,axiom,
hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_ys)) = V_ys ).
cnf(cls_rev__swap_0,axiom,
V_xs = hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) ).
cnf(cls_rev__is__Nil__conv_0,axiom,
( hAPP(c_List_Orev(T_a),V_xs) != c_List_Olist_ONil(T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_rev__is__Nil__conv_1,axiom,
hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)) != c_Event_Oknows(c_Message_Oagent_OSpy,hAPP(c_List_Orev(tc_Event_Oevent),c_List_Olist_ONil(tc_Event_Oevent))) ).
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__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat) ).
cnf(clsarity_nat__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_nat) ).
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,
hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( V_X = V_Y
| ~ hBOOL(hAPP(hAPP(c_fequal(T_a),V_X),V_Y)) ) ).
%------------------------------------------------------------------------------